economics for economic tutor

2 C H A P T E R

Fundamental Economic Concepts CHAPTER PREVIEW A few fundamental microeconomic concepts provide cornerstones for all of the analysis in managerial economics. Four of the most important are demand and supply, marginal analysis, net present value, and the meaning and measurement of risk. We will first review how the determinants of demand and supply establish a market equilibrium price for gasoline, crude oil, and hybrid electric cars. Marginal analysis tools are central when a decision maker is seeking to optimize some objective, such as maximizing cost savings from changing a lightbulb (e.g., from normal incandescent to compact fluorescent [CFL]). The net present value concept makes directly comparable alternative cash flows occurring at different points in time. In so doing, it provides the linkage between the timing and risk of a firm’s projected profits and the shareholder wealth-maximization objective. Risk-return analysis is important to an understanding of the many trade-offs that managers must consider as they introduce new products, expand capacity, or outsource overseas in order to increase expected profits at the risk of greater variation in profits.

Two appendices elaborate these topics for those who want to know more analytical details and seek exposure to additional application tools. Appendix C develops the relationship between marginal analysis and differential calculus. Web Appendix F shows how managers incorporate explicit probability information about the risk of various outcomes into individual choice models, decision trees, risk-adjusted discount rates, simulation analysis, and scenario planning.

MANAGERIAL CHALLENGE Why Charge $25 per Bag on Airline Flights?

In May 2008, American Airlines (AA) announced that it would immediately begin charging $25 per bag on all AA flights, not for extra luggage but for the first bag! Crude oil had doubled from $70 to $130 per barrel in the previ- ous 12 months, and jet fuel prices had accelerated even faster. AA’s new baggage policy applied to all ticketed passengers except first class and business class. On top of incremental airline charges for sandwiches and snacks

introduced the previous year, this new announcement stunned the travel public. Previously, only a few deep- discount U.S. carriers with very limited route structures such as People Express had charged separately for both food and baggage service. Since American Airlines and many other major carriers had belittled that policy as part of their overall marketing campaign against deep discounters, AA executives faced a dilemma.

26

Cont.

DEMAND AND SUPPLY: A REVIEW Demand and supply simultaneously determine equilibrium market price (Peq). Peq equates the desired rate of purchase Qd/t with the planned rate of sale Qs/t. Both con- cepts address intentions—that is, purchase intentions and supply intentions. Demand is therefore a potential concept often distinguished from the transactional event of “units sold.” In that sense, demand is more like the potential sales concept of customer traffic than it is the accounting receivables concept of revenue from completing an actual sale. Analogously, supply is more like scenario planning for operations than it is like actual

Jet fuel surcharges had recovered the year-over-year average variable cost increase for jet fuel expenses, but incremental variable costs (the marginal cost) re- mained uncovered. A quick back-of-the-envelope calcu- lation outlines the problem. If total variable costs for a 500-mile flight on a 180-seat 737-800 rise from $22,000 in 2007 Q2 to $36,000 in 2008 Q2 because of $14,000 of additional fuel costs, then competitively priced carriers would seek to recover $14,000/180 = $78 per seat in jet fuel surcharges. The average variable cost rise of $78 would be added to the price for each fare class. For example, the $188 Super Saver airfare restricted to 14-day advance purchase and Saturday night stay overs would go up to $266. Class M airfares requiring 7-day advance purchase but no Saturday stay overs would rise from $289 to $367. Full coach economy airfares without purchase restrictions would rise from $419 to $497, and so on.

The problem was that by 2008 Q2, the marginal cost for jet fuel had risen to approximately $1 for each pound transported 500 miles. Carrying an additional 170-pound passenger in 2007 had resulted in $45 of additional fuel costs. By May 2008, the marginal fuel cost was $170 – $45 = $125 higher! So although the $78 fuel surcharge was offsetting the accounting expense increase when one averaged in cheaper earlier fuel pur- chases, additional current purchases were much more expensive. It was this much higher $170 marginal cost that managers realized they should focus upon in decid- ing upon incremental seat sales and deeply discounted prices.

And similarly, this marginal $1 per pound for 500 miles became the focus of attention in analyzing bag- gage cost. A first suitcase was traveling free under the prior baggage policy as long as it weighed less than 42 pounds. But that maximum allowed suitcase imposed $42 of marginal cost in May 2008. Therefore, in

mid-2008, American Airlines (and now other major car- riers) announced a $25 baggage fee for the first bag in order to cover the marginal cost of the representative suitcase on AA, which weighs 25.4 pounds.

Discussion Questions

� How should the airline respond when presented with an overweight bag (more than 42 pounds)?

� Explain whether or not each of the following should be considered a variable cost that in- creases with each additional airline seat sale: baggage costs, crew costs, commissions on ticket sales, airport parking costs, food costs, and additional fuel costs from passenger weight.

� If jet fuel prices reverse their upward trend and begin to decline, fuel surcharges based on av- erage variable cost will catch up with and sur- pass marginal costs. How should the airlines respond then?

MANAGERIAL CHALLENGE Continued

© A P Im ag es /J ef f Ro be rs on

Chapter 2: Fundamental Economic Concepts 27

production, distribution, and delivery. In addition, supply and demand are explicitly rates per unit time period (e.g., autos per week at a Chevy dealership and the aggregate purchase intentions of the households in the surrounding target market). Hence, Peq is a market-clearing equilibrium concept, a price that equates the flow rates of intended pur- chase and planned sale.

When the order flow to buy at a given price (Qd/t) in Figure 2.1 just balances against the order flow to sell at that price (Qs/t), Peq has emerged, but what ultimately deter- mines this metric of “value” in a marketplace? Among the earliest answers can be found in the Aristotelian concept of intrinsic use value. Because diamonds secure marriage covenants and peace pacts between nations, they provide enormous use value and should therefore exhibit high market value. The problem with this theory of value taken alone arises when one considers cubic zirconium diamonds. No one other than a jewel mer- chant can distinguish the artificial cubic zirconium from the real thing, and therefore the intrinsic uses of both types are identical. Yet, cubic zirconium diamonds sell for many times less than natural stones of like grade and color. Why? One clue arose at the end of the Middle Ages, when Catholic monasteries produced beautiful hand- copied Bibles and sold them for huge sums (i.e., $22,000 in 2010 dollars) to other mon- asteries and the nobility. In 1455, Johannes Guttenberg offered a “mass produced” printed facsimile that could be put to exactly the same intrinsic use, and yet, the market value fell almost one-hundred-fold to $250 in 2010 dollars. Why?

Equilibrium market price results from the interaction of demanders and suppliers in- volved in an exchange. In addition to the use value demanders anticipate from a product, a supplier’s variable cost will also influence the market price observed. Ultimately, there- fore, what minimum asking price suppliers require to cover their variable costs is just as pivotal in determining value in exchange as what maximum offer price buyers are willing to pay. Guttenberg Bibles and cubic zirconium diamonds exchange in a marketplace at lower “value” not because they are intrinsically less useful than prior copies of the Bible

FIGURE 2.1 Demand and Supply Determine the Equilibrium Market Price

0

Equilibrium price ($/unit)

Peq

St

Dt

Planned rate of sale

Desired rate of purchase

Qdt = Q s t

Quantity (units/time)

28 Part 1: Introduction

or natural stones but simply because the bargain struck between buyers and sellers of these products will likely be negotiated down to a level that just covers their lower vari- able cost plus a small profit. Otherwise, preexisting competitors are likely to win the business by asking less.

Even when the cost of production is nearly identical and intrinsic use value is nearly identical, equilibrium market prices can still differ markedly. One additional determinant of value helps to explain why. Market value depends upon the relative scarcity of re- sources. Hardwoods are scarce in Japan but plentiful in Sweden. Even though the cost of timber cutting and sawmill planing is the same in both locations, hardwood trees have scarcity value as raw material in Japan that they do not have in Sweden where they are plentiful. To take another example, whale oil for use in lamps throughout the nineteenth and early twentieth centuries stayed at a nearly constant price until whale species began to be harvested at rates beyond their sustainable yield. As whale resources became scarcer, the whalers who expended no additional cost on better equipment or longer voyages came home with less oil from reduced catches. With less raw material on the market, the input price of whale oil rose quickly. Consequently, despite un- changed other costs of production, the scarcer input led to a higher final product price. Similar results occur in the commodity market for coffee beans or orange juice when climate changes or insect infestations in the tropics cause crop projections to decline and scarcity value to rise.

Example Discovery of Jojoba Bean Causes a Collapse of Whale Oil Lubricant Prices

1

Until the last decade of the twentieth century, the best-known lubricant for high- friction machinery with repeated temperature extremes like fan blades in aircraft jet engines, contact surfaces in metal cutting tools, and gearboxes in auto transmis- sions was a naturally occurring substance—sperm whale oil. In the early 1970s, the United States placed sperm whales on the endangered species list and banned their harvest. With the increasing scarcity of whales, the world market price of whale oil lubricant approached $200 per quart. Research and development for synthetic oil substitutes tried again and again but failed to find a replacement. Finally, a Califor- nia scientist suggested the extract of the jojoba bean as a natural, environmentally friendly lubricant. The jojoba bean grows like a weed throughout the desert of the southwestern United States on wild trees that can be domesticated and cultivated to yield beans for up to 150 years.

After production ramped up from 150 tons in 1986 to 700 tons in 1995, solvent-extracted jojoba sold for $10 per quart. When tested in the laboratory, jojoba bean extract exhibits some lubrication properties that exceed those of whale oil (e.g., thermal stability over 400°F). Although 85 to 90 percent of jojoba bean output is used in the production of cosmetics, the confirmation of this plentiful substitute for high-friction lubricants caused a collapse in whale lubricant prices. Sperm whale lubricant has the same cost of production and the same use value as before the discovery of jojoba beans, but the scarcity value of the raw material in- put has declined tenfold. Consequently, a quart of sperm whale lubricant now sells for under $20 per quart.

1Based on “Jojoba Producers Form a Marketing Coop,” Chemical Marketing Reporter (January 8, 1995), p. 10.

Chapter 2: Fundamental Economic Concepts 29

The Diamond-Water Paradox and the Marginal Revolution So equilibrium price in a marketplace is related to (1) intrinsic use value, (2) production cost, and (3) input scarcity. In addition, however, most products and services have more than one use and more than one method of production. And often these differences re- late to how much or how often the product has already been consumed or produced. For example, the initial access to e-mail servers or the Internet for several hours per day is often essential to maintaining good communication with colleagues and business associ- ates. Additional access makes it possible to employ search engines such as Google for information related to a work assignment. Still more access affords an opportunity to meet friends in a chat room. Finally, some households might purchase even more hours of access on the chance that a desire to surf the Web would arise unexpectedly. Each of these uses has its own distinct value along a continuum starting with necessities and end- ing with frivolous non-essentials. Accordingly, what a customer will pay for another hour of Internet access depends on the incremental hour in question. The greater the utilization already, the lower the use value remaining.

This concept of a marginal use value that declines as the rate of consumption increases leads to a powerful insight about consumer behavior. The question was posed: “Why should something as essential to human life as water sell for low market prices while something as frivolous as cosmetic diamonds sell for high market prices?” The initial an- swer was that water is inexpensive to produce in most parts of the world while diamonds require difficult search and discovery, expensive mining, and extensive transportation and security expenses. In other words, diamonds cost more than water, so minimum asking prices of suppliers dictate the higher market value observed for diamonds. However, recall that supply is only one of what Alfred Marshall famously called “two blades of the scis- sors” representing demand and supply. You can stab with one blade but you can’t cut paper, and using supply alone, you can’t fully explain equilibrium market price.

The diamond-water paradox was therefore restated more narrowly: “Why should con- sumers bid low offer prices for something as essential as water while bidding high offer prices for something as frivolous as diamonds?” The resolution of this narrower paradox hinges on distinguishing marginal use value (marginal utility) from total use value (total utility). Clearly, in some circumstances and locales, the use value of water is enormous. At an oasis in the desert, water does prevent you from thirsting to death. And even in the typical city, the first couple of ounces of some liquid serve this same function, but that’s the first couple of ounces. The next couple of dozen gallons per day remain at high use value for drinking, flushing indoor plumbing, cooking, body washing, and so forth. Thereafter, water is used for clothes washing, landscape watering, car washing, and sundry lesser purposes. Indeed, if one asks the typical American household (which consumes 80–100 gallons per person per day) to identify its least valuable use of water each day, the answer may come back truly frivolous—perhaps something like the water that runs down the sink drain while brushing teeth. In other words, the marginal use value of water in most developed countries is the water that saves the consumer the in- convenience of turning the water taps (on and off) twice rather than just once. And it is this marginal use value at the relevant margin, not the total utility across all uses, that determines a typical water consumer’s meager willingness to pay.

Marginal Utility and Incremental Cost Simultaneously

Determine Equilibrium Market Price Alfred Marshall had it right: demand and supply do simultaneously determine market equilibrium price. On the one hand, marginal utility determines the maximum offer

marginal use value The additional value of the consumption of one more unit; the greater the utilization already, the lower the use value remaining.

marginal utility The use value obtained from the last unit consumed.

30 Part 1: Introduction

price consumers are willing to pay for each additional unit of consumption on the de- mand side of the market. On the other hand, variable cost at the margin (an incremental cost concept sometimes referred to as “marginal cost”) determines the minimum asking price producers are willing to accept for each additional unit supplied. Water is both cheaper to produce and more frivolous than diamonds at the relevant margin, and hence water’s market equilibrium price is lower than that of diamonds. Figure 2.2 illustrates this concept of marginal use value for water varying from the absolutely essential first few ounces to the frivolous water left running while brushing one’s teeth.

At the same time, the marginal cost of producing water remains low throughout the 90- gallon range of a typical household’s consumption. In contrast, diamonds exhibit steeply rising marginal cost even at relatively small volume, and customers continue to employ cos- metic diamonds for highly valuable uses even out to the relevant margin (one to three car- ats) where typical households find their purchases occurring. Therefore, diamonds should trade for equilibrium market prices that exceed the equilibrium market price of water.

Individual and Market Demand Curves We have seen that the market-clearing equilibrium price (Peq) that sets the desired rate of purchase (Qd/t) equal to the planned rate of sale (Qs/t) is simultaneously both the maximum offer price demanders are willing to pay (the “offer”) and the minimum ask- ing price sellers are willing to accept (the “ask”). But what determines the desired rate of purchase Qd/t and planned rate of sales Qs/t? The demand schedule (sometimes called the “demand curve”) is the simplest form of the demand relationship. It is merely a list of prices and corresponding quantities of a commodity that would be demanded by some individual or group of individuals at uniform prices. Table 2.1 shows the demand schedule for regular-size pizzas at a Pizza Hut restaurant. This demand schedule

FIGURE 2.2 The Diamond-Water Paradox Resolved

Equilibrium price ($/unit)

Offer pricew = f(M.U.w)

P d eq

Pw eq

Sdiamonds

Swater

Dwater

Ddiamonds

Quantity (gallons/day)

(carats/lifetime)

2 carats 90 gallons

Asking priced = g(M.C.d)

Chapter 2: Fundamental Economic Concepts 31

indicates that if the price were $9.00, customers would purchase 60 per night. Note that the lower the price, the greater the quantity that will be demanded. This is the strongest form of the law of demand—if a product or service is income superior, a household will always purchase more as the relative price declines.

The Demand Function The demand schedule (or curve) specifies the relationship between prices and quantity demanded, holding constant the influence of all other factors. A demand function speci- fies all these other factors that management will often consider, including the design and packaging of products, the amount and distribution of the firm’s advertising budget, the size of the sales force, promotional expenditures, the time period of adjustment for any price changes, and taxes or subsidies. As detailed in Table 2.2, the demand function for hybrid-electric or all-electric autos can be represented as

QD = f ðP, PS, PC, Y, A, AC, N, CP, PE, TA, T=S …Þ [2.1] where QD = quantity demanded of (e.g., Toyota Prius or Chevy Volt)

P = price of the good or service (the auto)

PS = price of substitute goods or services (e.g., the popular gasoline-powered Honda Accord or Chevy Malibu)

PC = price of complementary goods or services (replacement batteries)

Y = income of consumers

A = advertising and promotion expenditures by Toyota, Honda, and General Motors (GM)

AC = competitors’ advertising and promotion expenditures

N = size of the potential target market (demographic factors)

CP = consumer tastes and preferences for a “greener” form of transportation

PE = expected future price appreciation or depreciation of hybrid autos

TA = purchase adjustment time period

T/S = taxes or subsidies on hybrid autos

The demand schedule or demand curve merely deals with the price-quantity relation- ship itself. Changes in the price (P) of the good or service will result only in movement along the demand curve, whereas changes in any of the other demand determinants in the demand function (PS, PC, Y, A, AC, N, CP, PE, and so on) shift the demand curve. This is illustrated graphically in Figure 2.3. The initial demand relationship is line DD 0. If the

TABLE 2.1 SIMPLIFIED DEMAND SCHEDULE: PIZZA HUT RESTAURANT

PRICE OF PIZZA ($/UNIT)

QUANTITY OF PIZZAS SOLD (UNITS PER TIME PERIOD)

10 50

9 60

8 70

7 80

6 90

5 100

demand function A relationship between quantity demanded and all the determinants of demand.

substitute goods Alternative products whose demand increases when the price of the focal product rises.

complementary goods Complements in consumption whose demand decreases when the price of the focal product rises.

32 Part 1: Introduction

FIGURE 2.3 Shifts in Demand

Price ($/unit)

Quantity (units)

Q1 Q2 Q3 Q40

P1

P2

D

D�

D1

D2

D�2

D�1

TABLE 2.2 PARTIAL LIST OF FACTORS AFFECTING DEMAND

DEMAND FACTOR EXPECTED EFFECT

Increase (decrease) in price of substitute goodsa (PS) Increase (decrease) in demand (QD)

Increase (decrease) in price of complementary goodsb (PC) Decrease (increase) in QD

Increase (decrease) in consumer income levelsc (Y) Increase (decrease) in QD

Increase (decrease) in the amount of advertising and marketing expenditures (A)

Increase (decrease) in QD

Increase (decrease) in level of advertising and marketing by competitors (AC)

Decrease (increase) in QD

Increase (decrease) in population (N) Increase (decrease) in QD

Increase (decrease) in consumer preferences for the good or service (CP)

Increase (decrease) in QD

Expected future price increases (decreases) for the good (PE) Increase (decrease) in QD

Time period of adjustment increases (decreases) (TA) Increase (decrease) in QD

Taxes (subsidies) on the good increase (decrease) (T/S) Decrease (increase) in QD

aTwo goods are substitutes if an increase (decrease) in the price of Good 1 results in an increase (decrease) in the quantity demanded of Good 2, holding other factors constant, such as the price of Good 2, other prices, income, and so on, or vice versa. For example, margarine may be viewed as a rather good substitute for butter. As the price of butter increases, more people will decrease their con- sumption of butter and increase their consumption of margarine. bGoods that are used in conjunction with each other, either in production or consumption, are called complementary goods. For example, DVDs are used in conjunction with DVD players. An increase in the price of DVD players would have the effect of decreasing the demand for DVDs, ceteris paribus. In other words, two goods are complementary if a decrease in the price of Good 1 results in an in- crease in the quantity demanded of Good 2, ceteris paribus. Similarly, two goods are complements if an increase in the price of Good 1 results in a decrease in the quantity demanded of Good 2. cThe case of inferior goods—that is, those goods that are purchased in smaller total quantities as income levels rise—will be discussed in Chapter 3.

Chapter 2: Fundamental Economic Concepts 33

original price were P1, quantity Q1 would be demanded. If the price declined to P2, the quantity demanded would increase to Q2. If, however, changes occurred in the other deter- minants of demand, we would expect to have a shift in the entire demand curve. If, for ex- ample, a subsidy to hybrids were enacted, the new demand curve might become D1D

0 1. At

any price, P1, along D1D 0 1, a greater quantity, Q3, will be demanded than at the same price

before the subsidy on the original curve DD0. Similarly, if the prices of substitute products such as the Honda Accord or Chevy Malibu were to decline sharply, the demand curve would shift downward and to the left. At any price, P1, along the new curve D2

0D2, a smal- ler quantity, Q4, would be demanded than at the same price on either DD

0 or D1D01. In summary, movement along a demand curve is often referred to as a change in the

quantity demanded, while holding constant the effects of factors other than price that de- termine demand. In contrast, a shift of the entire demand curve is often referred to as a change in demand and is always caused by some demand determinant other than price.

Import-Export Traded Goods In addition to the previous determinants of demand, the demand for goods traded in for- eign markets is also influenced by external factors such as exchange rate fluctuations. When Microsoft sells computer software overseas, it prefers to be paid in U.S. dollars. This is because a company like Microsoft incurs few offshore expenses beyond advertising and therefore cannot simply match payables and receivables in a foreign currency. To ac- cept euros, Japanese yen, or Australian dollars in payment for software purchase orders would introduce an exchange rate risk exposure for which Microsoft would want to be compensated in the form of higher prices on its software. Consequently, the foreign ex- ports of Microsoft are typically transacted in U.S. dollars and are therefore tied inextricably to the price of the dollar against other currencies. As the value of the dollar rises, offshore buyers must pay a larger amount of their own currency to obtain the U.S. dollars required to complete a purchase order for Microsoft’s software, and this decreases the export demand. Even in a large domestic market like the United States, companies often find that these export demand considerations are key determinants of their overall demand.

Example Exchange Rate Impacts on Demand: Cummins Engine Company Cummins Engine Company of Columbus, Indiana, is the largest independent man- ufacturer of new and replacement diesel engines for heavy trucks and for construc- tion, mining, and agricultural machinery. Volvo and Daimler-Benz are their major competitors, and 53 percent of sales occur offshore. The Cummins and Daimler- Benz large diesel truck engines sell for approximately $40,000 and €35,000, respec- tively. In the 2002 recession, Cummins suffered substantial declines in cash flow. One reason was obvious: diesel replacement engines are not needed when fewer goods are being delivered, and therefore fewer diesels are wearing out.

In addition, however, between 1999 and 2002, the value of the U.S. dollar (€ per $) increased by 30 percent from €.85/$ to €1.12/$. This meant that a $40,000 Cummins diesel engine that had sold for €34,000 in Munich in 1999 became €44,800, whereas the €35,000 Mercedes diesel alternative that had been selling for $41,176 in Detroit declined to $31,250 because of the stronger U.S. dollar. Cummins faced two unattrac- tive options, either of which would reduce its cash flow. It could either cut its profit margins and maintain unit sales, or maintain margins but have both offshore and

(Continued)

34 Part 1: Introduction

Individual and Market Supply Curves What determines the planned rate of sale Qs/t? Like the demand schedule, the supply schedule is a list of prices and corresponding quantities that an individual or group of sellers desires to sell at uniform prices, holding constant the influence of all other factors. A number of these other determinants of supply that management will often need to consider are detailed in Table 2.3. The supply function can be represented as

QS = f ðP, PI, PUI, T, EE, F, RC, PE, T=S … Þ [2.2]

where Qs = quantity supplied (e.g., of domestic autos)

P = price of the autos

PI = price of inputs (e.g., sheet metal)

PUI = price of unused substitute inputs (e.g., fiberglass)

T = technological improvements (e.g., robotic welding)

EE = entry or exit of other auto sellers

F = accidental supply interruptions from fires, floods, etc.

RC = costs of regulatory compliance

PE = expected (future) changes in price

TA = adjustment time period

T/S = taxes or subsidies

TABLE 2.3 PARTIAL LIST OF FACTORS AFFECTING SUPPLY

SUPPLY FACTOR EXPECTED EFFECT AT EVERY PRICE

Increase (decrease) in the price of inputs (PI) Decrease (increase) in supply

Increase (decrease) in the price of unused substitute inputs (PUI) Decrease (increase) in supply

Technological improvements (T) Increase in supply

Entry (Exit) of other sellers (EE) Increase (decrease) in supply

Supply disruptions (F) Decrease in supply

Increase (decrease) in regulatory costs (RC) Decrease (increase) in supply

Expected future price increases (decreases) (PE) Decrease (increase) in supply

Time period of adjustment lengthens (shortens) (TA) Increase (decrease) in supply

Taxes (subsidies) (T/S) Decrease (increase) in supply

domestic sales collapse. The company chose to cut margins and maintain sales. By 2005, the dollar’s value had eroded, returning to €.85/$, and Cummins’ sales perfor- mance markedly improved. In the interim, demand for Cummins engines was adversely affected by the temporary appreciation of the U.S. dollar.

In 2009, with the U.S. dollar at a still lower value of €.64/$, the Cummins Engine Co. could barely keep up with export demand since diesels to Europe were priced at €25,600 versus Mercedes’ €32,000. Similarly, in Cleveland, St. Louis, and Atlanta, Cummins $40,000 diesels were up against $54,688 Mercedes substitutes. What a great time to be an American company competing against European manufacturers.

supply function A relationship between quantity supplied and all the determinants of supply.

Chapter 2: Fundamental Economic Concepts 35

Again, changes in the price (P) of the good or service will result only in movement along the given supply curve, whereas changes in any of the other independent variables (PS, PC, Y, A, AC, N, CP, PE, and so on) in the function shift the supply curve. As with demand, a movement along a supply curve is referred to as a change in the quantity sup- plied, while holding constant other determinants of supply. A shift of the entire supply curve is often referred to as a change in supply and is always caused by some supply determinant other than price.

Equilibrium Market Price of Gasoline In April–July 2008, Americans woke up to a new reality about gasoline that markedly affected their driving habits as well as U.S. public policy. The price of a gallon of regular octane gasoline skyrocketed from $3.00 per gallon to $4.10 (see Figure 2.4). The previous summer, when gas prices had hovered around $3 per gallon, Americans had cut back only slightly on non-essential driving.

In the summer of 2008, with regular gasoline at $4.10 per gallon, not only summer driving vacations but urban commuting itself changed in extraordinary ways. Overall, customer de- mand by the typical two-person urban household shrank from 16 gallons per week to 11.5 gallons. As a result, for the first time in U.S. history, gasoline expenditure by U.S. households declined despite a rising price at the pump—that is, 16 gallons/week at $3 in 2007 (Q3) = $48 > 11.5 gallons per week at $4.10 in 2008 (Q3) = $47.15.

Several determinants of demand and supply were identified as possible explanations for the spike in gasoline’s equilibrium market price. First, much was written about the fact that no new refinery had been built in the United States in more than 30 years, sug- gesting that refinery capacity shortages or pipeline bottlenecks might be responsible. De- clining capacity does shift the supply curve in Figure 2.2 to the left, which would imply a higher equilibrium price. But no refinery closings or pipeline disruptions could be iden- tified that summer. And the U.S. Department of Energy found refineries command only $0.36 per gallon of the final product price of gasoline for cost recovery plus profit and

Example NAFTA and the Reduced Labor Costs of Ford Assembly Plants in Detroit The North American Free Trade Agreement (NAFTA) made it possible to buy subassemblies like axles and engine blocks from Mexican suppliers like Cifunsa, SA, without paying any import tariff when the parts arrived in the United States. Since United Auto Worker (UAW) labor in Detroit auto assembly plants also makes axle subassemblies, the Mexican labor input can be thought about as an unused substitute input from the point of view of Ford Motor Company. NAFTA in effect lowered the input cost of substitute inputs for Ford. This means fewer employers would pursue labor contracts with UAW labor in Detroit and instead shift some of their production south across the Mexican border. Less demand implies lower equilibrium wages would be offered and accepted by UAW assembly line labor. Hence, the indirect effect of NAFTA was a reduction in the input costs for UAW labor that the Ford Motor Co. did utilize. As usual, lower input cost implies a shift of the supply curve down and to the right, an increase in supply.

supply curve A relationship between price and quantity supplied, holding other determinants of supply constant.

36 Part 1: Introduction

could not therefore be responsible for the $1.10 increase in the equilibrium price between July 2007 and July 2008.

Second, retail gas station owners were accused of gouging the driving public. Higher markups at retail also would shift the supply curve for gasoline back to the left, raising the equilibrium market price. But again, retail markup and indeed all gasoline marketing were found to add only $0.28 per gallon to the $4.10 price, much less than could be re- sponsible for the $1.10 run-up in gasoline’s equilibrium market price. Third, excise taxes on gasoline (earmarked for road building and maintenance) are levied by both the federal and state governments. Gasoline taxes constitute $0.41 per gallon on average across the United States. Any new excise taxes would have shifted the supply curve leftward, result- ing in a higher equilibrium market price for gasoline. President George Bush’s Council of Economic Advisors in 2007 did explore levying an additional $1 per gallon tax on gaso- line to reduce the dependence of the United States on foreign oil, but no tax increase was ever initiated. So what was responsible for the upward spike in gasoline prices?

As we have seen, the variables in the demand and supply functions in Equations 2.1 and 2.2 determining equilibrium market price may be grouped into three broad sets of factors affecting use value, cost of production, and resource scarcity.2 Since crude oil inputs account for $2.96 of the $4.10 final product price of gasoline, resource scar- city was a likely candidate to explain the increase in gasoline prices from $3 to $4.10. Higher crude oil input prices shift the supply curve leftward, leading to higher final product prices for gasoline. Figure 2.5 shows that the previous three times crude oil input prices shot up, supply disruptions in the crude oil input market were involved (i.e., during the first Gulf War in Kuwait in 1991, during an especially effective era for the OPEC cartel 1999–2001, and during the Iraq War in 2004).

In contrast, the crude oil input price rise from $40 to $80 per barrel in 2006–2007 reflected demand-side increased usage especially by India and China. India and China are only 9 percent of the 85 million barrels per day (mbd) worldwide crude oil market but these two countries have been growing very quickly. A 2 to 3 percent additional

FIGURE 2.4 Average Gas Prices in the United States

2005

0.50

1.00

1.50

2.00

2.50

3.00

3.50

$4.00

$2.90 $2.80 $3.00

$4.10

2006 2007 2008

Source: AAA Carolinas.

2Two additional factors are speculation and government intervention in the form of taxes, subsidies, and regulations.

Chapter 2: Fundamental Economic Concepts 37

demand can significantly raise equilibrium prices for crude oil resources because at any point in time there is a very thin inventory (8–10 days supply) working its way through the distribution network from wells to pumps to terminals to tankers to refineries. By late 2007, crude oil input prices were rising beyond $80 per barrel. As gasoline headed toward $4.10 per gallon in the United States, $9.16 per gallon in Germany, and $8.80 per gallon in Great Britain, Western drivers substantially cut back consumption. Brazil approached $6.40 per gallon and pursued a successful energy independence campaign focused on sugar cane-based ethanol plants.

Was the $80 price in late 2007 the highest price ever in the crude oil input market prior to that time? The answer is “no.” In 1981, the equilibrium crude oil price reached $36 per barrel. Using the U.S. consumer price index (CPI), since crude oil transactions worldwide are denominated in U.S. dollars, cumulative price increases between 1981 and 2007 total 228.8 percent, so $36 × a 2.288 inflation-adjustment multiplier equals $82 in 2007, and $80/2.288 equals $35 in 1981. Consequently, the $80 crude oil price in late 2007 was in fact lower than the inflation-adjusted $36 crude price in 1981 at the height of the influence of the OPEC II oil cartel. However, in early 2008, the equilibrium price of crude continued to spike upward.

When the crude price climbed above $100, large numbers of speculators acquired long positions in the crude oil futures market betting on a further price rise. Speculative

FIGURE 2.5 Supply Disruptions and Developing Country Demand Fuel Crude Oil Price Spikes

1990

Gulf War OPEC III

Iraq War

Indian, Chinese demand

1992 1994 1996 1998 2000 2002 2004 2006 2008 2010

50

60

70

80

90

100

110

120

130

40

30

20

10

0

O il

p ri

ce ,

in c

o n

st an

t 2

0 0

0 U

.S .$

1990–2010 Real price per barrel, mean (standard deviation)

Mean +/– 2 Standard deviations

Source: Federal Reserve Bank, St. Louis, National Economics Trends, September 2000; FedDallas, Regional Economic Data, 2006.

38 Part 1: Introduction

demand (supply) is always motivated by the anticipation of equilibrium market prices being higher (lower) tomorrow. Those who “go long” and buy futures contracts to take delivery at prices agreed on today are betting the price will go up, and those who “sell short” and write futures contracts promising to deliver in the future at prices agreed on today are betting the other way. The net long direction of speculative trading in the first half of 2008 added to the growing market demand from India and China and drove the crude oil equilibrium price still higher, eventually reaching $146 per barrel in July 2008.

Faced with $4.10 per gallon gasoline, as ExxonMobil and Shell sought to recover their extraordinary input costs for crude, American consumers decided to vacate their SUVs, join carpools, and ride the buses and trains to work. Urban mass transit system ridership shot up 20 percent in a matter of months. Other Americans purchased fuel-efficient hy- brids like the Toyota Prius. Still others mobilized behind T. Boone Pickens’s plan to con- vert the federal trucking fleet to natural gas. Fearing an onslaught of feasible substitutes like hybrid electric cars and natural gas-powered trucks, the Saudis ramped up crude oil production from their average 8.5 mbd 1990–2006 all the way to 10.5 and 10.9 mbd in 2007 and 2008 (see Figure 2.6).

FIGURE 2.6 Saudi Arabia Crude Oil Production

1970

M il li o n s

o f

b ar

re l/

d ay

10.9

8.5

1975 1980 1985 1990 1995 2000 2005 2010

Source: U.S. Energy Information Administration.

Chapter 2: Fundamental Economic Concepts 39

With U.S. demand for gasoline declining and capacity to extract and refine expand- ing, the equilibrium price of crude finally turned and began to decline. The late 2008 crude oil price reversal was caused by a combination of increasing supply fundamentals (shifting the supply curve to the right), slowing demand growth, and a speculative expec- tation that in the near term crude prices would be lower (not higher). Consequently, the supply of crude oil (and especially of highly leveraged crude oil futures contracts) mush- roomed. Angola doubled production capacity to 2.1 mbd, and Saudi capacity grew to 12.5 mbd. Saudi Arabia and Kuwait also broke ground on two giant new refining facilities.

Example Speculation Sends Crude Oil Input Price on a Roller-Coaster Ride at ExxonMobil and Shell With reversed expectations of lower crude prices in the near term, the speculative bubble in crude oil quickly burst. Despite 5 percent higher market demand over the last four months of 2008 (again primarily from China and India), the equilibrium price of crude oil plummeted more than $100 a barrel from $146 in September 2008 to a low of $40 by January 2009 (see Figure 2.7). By 2009 (Q3), the crude price stood again at $75 per barrel, and gasoline was selling for $2.74 per gallon. Although North American import demand for crude oil has been flat in recent years, OPEC members clearly believe that the spectacular 22 percent demand growth from Asian developing countries in 2000–2008 will continue. Over a two- year period, rising Asian demand, massive capacity expansions, a worldwide finan- cial boom, then collapse, and speculative buying followed by speculative selling had taken oil companies and gasoline buyers on quite a roller-coaster ride.

FIGURE 2.7 Crude Oil Price, West Texas Intermediate

1999 2001 2003 2005 2007 2009 0

25

$ p

er b

ar re

l

50

75

100

125

150

Source: Thomson Datasteam.

40 Part 1: Introduction

MARGINAL ANALYSIS Marginal analysis is one of the most useful concepts in microeconomics. Resource- allocation decisions typically are expressed in terms of the marginal equilibrium conditions that must be satisfied to attain an optimal solution. The familiar profit- maximization rule for the firm of setting output at the point where “marginal cost equals marginal revenue” is one such example. Long-term investment decisions (capital expen- ditures) also are made using marginal analysis decision rules. Only if the expected return from an investment project (that is, the marginal return to the firm) exceeds the cost of funds that must be acquired to finance the project (the marginal cost of capital), should the project be undertaken. Following this important marginal decision rule leads to the maximization of shareholder wealth.

More generally, a change in the level of an economic activity is desirable if the mar- ginal benefits exceed the marginal (that is, the incremental) costs. If we define net mar- ginal return as the difference between marginal benefits and marginal costs, then an equivalent optimality condition is that the level of the activity should be increased to the point where the net marginal return is zero.

In summary, marginal analysis instructs decision makers to determine the additional (marginal) costs and additional (marginal) benefits associated with a proposed action. Only if the marginal benefits exceed the marginal costs (that is, if net marginal benefits are positive) should the action be taken.

Total, Marginal, and Average Relationships Revenue, cost, profit, and many other economic relationships can be presented using tab- ular, graphic, and algebraic frameworks. Let us first use a tabular presentation. Suppose

Example Tenneco Shipyard Marginal Analysis Resource-allocation decisions should be made by comparing the marginal (or incremental) benefits of a change in the level of an activity with the incremental costs of the change. For example, the marginal revenue benefit derived from producing and selling one more supertanker is equal to the difference between total revenue, assuming the additional unit is not sold, and total revenue includ- ing the additional sale. Similarly, marginal cost is defined as the change in total costs that occurs from undertaking some economic activity, such as the produc- tion of an additional ship design including the opportunity costs, and therefore may not necessarily always be equal to the cash outlays alone. Perhaps the Ten- neco design team has an opportunity for higher net profit as subcontractors on Boeing projects. If so, Tenneco’s routine ship-design work should be contracted out to other shipbuilding design firms who can become a trusted subcontractor to Tenneco.

marginal analysis A basis for making various economic decisions that analyzes the additional (marginal) benefits derived from a particular decision and compares them with the additional (marginal) costs incurred.

Chapter 2: Fundamental Economic Concepts 41

Example Marginal Analysis and Capital Budgeting Decisions: Sara Lee Corporation The capital budgeting decision problem facing a typical firm, such as Sara Lee Cor- poration, can be used to illustrate the application of marginal analysis decision rules. Sara Lee has the following schedule of potential investment projects (all assumed to be of equal risk) available to it:

PROJECT

INVESTMENT REQUIRED ($ MILLION)

EXPECTED RATE OF RETURN

CUMULATIVE INVESTMENT ($ MILLION)

A $25.0 27.0% $ 25.0

B 15.0 24.0 40.0

C 40.0 21.0 80.0

D 35.0 18.0 115.0

E 12.0 15.0 127.0

F 20.0 14.0 147.0

G 18.0 13.0 165.0

H 13.0 11.0 178.0

I 7.0 8.0 185.0

Sara Lee has estimated the cost of acquiring the funds needed to finance these investment projects as follows:

BLOCK OF FUNDS ($ MILLION)

COST OF CAPITAL

CUMULATIVE FUNDS RAISED ($ MILLION)

First $50.0 10.0% $ 50.0

Next 25.0 10.5 75.0

Next 40.0 11.0 115.0

Next 50.0 12.2 165.0

Next 20.0 14.5 185.0

The expected rate of return on the projects listed above can be thought of as the marginal (or incremental) return available to Sara Lee as it undertakes each addi- tional investment project. Similarly, the cost-of-capital schedule may be thought of as the incremental cost of acquiring the needed funds. Following the marginal analysis rules means that Sara Lee should invest in additional projects as long as the expected rate of return on the project exceeds the marginal cost of capital funds needed to finance the project.

Project A, which offers an expected return of 27 percent and requires an out- lay of $25 million, is acceptable because the marginal return exceeds the mar- ginal cost of capital (10.0 percent for the first $50 million of funds raised by Sara Lee). In fact, an examination of the tables indicates that projects A through G all meet the marginal analysis test because the marginal return from each of these projects exceeds the marginal cost of capital funds needed to finance these projects. In contrast, projects H and I should not be undertaken because they offer returns of 11 percent and 8 percent, respectively, compared with a marginal cost of capital of 14.5 percent for the $20 million in funds needed to finance those projects.

42 Part 1: Introduction

that the total profit πT of a firm is a function of the number of units of output produced Q, as shown in columns 1 and 2 of Table 2.4.

Marginal profit, which represents the change in total profit resulting from a one-unit increase in output, is shown in column 3 of the table. (A Δ is used to represent a “change” in some variable.) The marginal profit Δπ(Q) of any level of output Q is calcu- lated by taking the difference between the total profit at this level πT(Q) and at one unit below this level πT(Q − 1).

3 In comparing the marginal and total profit functions, we

Example Marginal Analysis of Driving a Mini Cooper versus a Chevy Volt Urban sprawl and flight to the suburbs have now resulted in the mean commuter trip in the United States rising to 33 miles one way. With the housing density in most American cities well below what would be required to support extensive light rail and subway lines, the typical household must find economical ways to get at least one worker from a suburban home to the central business district and back each day. A fuel-efficient, small commuter car like the Mini Cooper is one alterna- tive. Others have recently been proposed—the Chevy Volt and Nissan Leaf, both all-electric vehicles that are recharged at the end of each 40-mile commuting trip. Technically, the Leaf and the Volt are e-REVs, extended-range electric vehicles. Each contains a small gasoline-driven internal combustion engine that runs an electric generator, but unlike hybrids such as the Ford Fusion and Toyota Prius, these e-REVs have no mechanical connection between the gasoline engine and the drivetrain. Instead, the Chevy Volt goes 40 miles on the charge contained in 220 lithium ion (L-ion) batteries which are plugged in for a recharging cycle of 8 hours at 220 volts (or 3 hours at 110 volts) at work and at home. When the battery pack falls to a 30 percent state of charge (SOC), the gasoline engine comes on to turn the generator and maintain battery power above 25 percent SOC.

Automotive engineers calculate that each mile traveled in the Chevy Volt’s all- electric mode “burns” 0.26 kilowatt hours of electricity. So, the mean commuter trip of 33 miles requires 8.58 kWh of electricity. The price of electricity in the United States varies from a peak period in the afternoon and evening to a much cheaper off- peak period late at night, and from a low of $0.07 per kWh in Washington state to $0.12 in Rhode Island. On average, a representative nighttime rate is $0.10, and a representative daytime rate is $0.13. This means that each nighttime charge will run the household $0.86, and the comparable daytime charge downtown at work will be $1.12 for a total operating cost per day of just under $2. For 300 days of work, that’s $600 per year. In contrast, the gasoline-powered Mini Cooper gets 32 mpg, so at $3.00 per gallon, the Mini’s operating cost is approximately $6 per day or $1,800 per year. The typical commuter use of e-Rev vehicles will save $4 per day or $1,200 per year relative to popular fuel-efficient gasoline-powered cars.

At an EPA-measured 41 mpg throughout a range of driving conditions, the hybrid-electric Ford Fusion qualifies for a federal tax credit of $3,400. In contrast, at an EPA-measured 238 mpg, the Chevy Volt qualifies for a $7,500 tax credit to offset the $12,000 additional cost of the L-ion battery pack over the cost of a con- ventional battery. Because the Chevy Volt’s battery pack is expected to last 10 years, the $1,200 annual capital cost for the battery pack is equal to the $1,200 energy cost savings even without the federal tax credit.

3Web Appendix A expands upon the idea that the total profit function can be maximized by identifying the level of activity at which the marginal profit function goes to zero.

Chapter 2: Fundamental Economic Concepts 43

note that for increasing output levels, the marginal profit values remain positive as long as the total profit function is increasing. Only when the total profit function begins de- creasing—that is, at Q = 10 units—does the marginal profit become negative. The average profit function values πA(Q), shown in column 4 of Table 2.4, are obtained by dividing the total profit figure πT(Q) by the output level Q. In comparing the marginal and the average profit function values, we see that the average profit function πA(Q) is increasing as long as the marginal profit is greater than the average profit—that is, up to Q = 7 units. Beyond an output level of Q = 7 units, the marginal profit is less than the average profit and the average profit function values are decreasing.

By examining the total profit function πT(Q) in Table 2.4, we see that profit is maxi- mized at an output level of Q = 9 units. Given that the objective is to maximize total profit, then the optimal output decision would be to produce and sell 9 units. If the mar- ginal analysis decision rule discussed earlier in this section is used, the same (optimal) decision is obtained. Applying the rule to this problem, the firm would expand produc- tion as long as the net marginal return—that is, marginal revenue minus marginal cost (marginal profit)—is positive. From column 3 of Table 2.4, we can see that the marginal profit is positive for output levels up to Q = 9. Therefore, the marginal profit decision rule would indicate that 9 units should be produced—the same decision that was ob- tained from the total profit function.

The relationships among the total, marginal, and average profit functions and the optimal output decision also can be represented graphically. A set of continuous profit functions, analogous to those presented in Table 2.4 for discrete integer values of out- put (Q), is shown in Figure 2.8. At the break-even output level Q1, both total profits and average profits are zero. The marginal profit function, which equals the slope of the total profit function, takes on its maximum value at an output of Q2 units. This point corresponds to the inflection point. Below the inflection point, total profits are increasing at an increasing rate, and hence marginal profits are increasing. Above the inflection point, up to an output level Q4, total profits are increasing at a decreasing rate, and consequently marginal profits are decreasing. The average profit function, which represents the slope of a straight line drawn from the origin 0 to each point on

TABLE 2.4 TOTAL, MARGINAL, AND AVERAGE PROFIT RELATIONSHIPS

(1) (2) (3) (4)

NUMBER OF UNITS OF OUTPUT PER UNIT OF

TIME Q TOTAL PROFIT

πT(Q) ($)

MARGINAL PROFIT Δπ(Q) = πT(Q) − πT(Q − 1)

($/UNIT)

AVERAGE PROFIT πA(Q) = πT(Q)/Q

($/UNIT)

0 −200 0 —

1 −150 50 −150.00

2 −25 125 −12.50

3 200 225 66.67

4 475 275 118.75

5 775 300 155.00

6 1,075 300 179.17

7 1,325 250 189.29

8 1,475 150 184.38

9 1,500 25 166.67

10 1,350 −150 135.00

44 Part 1: Introduction

the total profit function, takes on its maximum value at an output of Q3 units. The average profit necessarily equals the marginal profit at this point. This follows because the slope of the 0A line, which defines the average profit, is also equal to the slope of the total profit function at point A, which defines the marginal profit. Finally, total profit is maximized at an output of Q4 units where marginal profit equals 0. Beyond Q4 the total profit function is decreasing, and consequently the marginal profit function takes on negative values.

THE NET PRESENT VALUE CONCEPT When costs and benefits occur at approximately the same time, the marginal decision rule (proceed with the action if marginal benefit exceeds marginal cost) applies. But, many economic decisions require that costs be incurred immediately to capture a stream of benefits over several future time periods. In these cases, the net present value (NPV) rule replaces the marginal decision rule and provides appropriate guidance for longer-term decision makers. The NPV of an investment represents the contribution of that investment to the value of the firm and, accordingly, to shareholder wealth maximization.

FIGURE 2.8 Total, Average, and Marginal Profit Functions

Total profit ($) (πT(Q))

Inflection point

A

Maximum total profit

Total profit πT(Q)

Break-even point

0

Average profit (πA(Q)) Marginal profit (Δπ(Q)) ($/unit)

Units of output (Q)

Units of output (Q)Q1 Q2 Q3 Q4

Marginal profit Δπ(Q)

Average profit πA(Q)

Maximum average profit point

0

Maximum marginal profit point

Chapter 2: Fundamental Economic Concepts 45

Determining the Net Present Value of an Investment To understand the NPV rule, consider the following situation. You are responsible for investing $1 million to support the retirement of several family members. Your financial advisor has suggested that you use these funds to purchase a piece of land near a proposed new highway interchange. A trustworthy state road commissioner is certain that the interchange will be built and that in one year the value of this land will increase to $1.2 million. Hence, you believe initially that this is a riskless investment. At the end of one year you plan to sell the land. You are being asked to invest $1 million today in the anticipation of receiving $1.2 million a year from today, or a profit of $200,000. You wonder whether this profit represents a sufficient return on your investment.

You feel it is important to recognize that a return of $1.2 million received one year from today must be worth less than $1.2 million today because you could invest your $1 million today to earn interest over the coming year. Therefore, to compare a dollar received in the future with a dollar in hand today, it is necessary to multiply the future dollar by a discount factor that reflects the alternative investment opportunities that are available.

Instead of investing $1 million in the land venture, you are aware that you could also invest in a one-year U.S. government bond that currently offers a return of 3 percent. The 3 percent return represents the return (the opportunity cost) forgone by investing in the land project. The 3 percent rate also can be thought of as the compensation to an investor who agrees to postpone receiving a cash return for one year. The discount factor, also called a present value interest factor (PVIF), is equal to

PVIF = 1

1 + i

where i is the compensation for postponing receipt of a cash return for one year. The present value (PV0) of an amount received one year in the future (FV1) is equal to that amount times the discount factor, or

PV0 = FV1 × ðPVIFÞ [2.3]

In the case of the land project, the present value of the promised $1.2 million expected to be received in one year is equal to

PV0 = $1:2 million 1

1 + 0:03

� � = $1,165,049

If you invested $1,165,049 today to earn 3 percent for the coming year, you would have $1.2 million at the end of the year. You are clearly better off with the proposed land investment (assuming that it really is riskless like the U.S. government bond invest- ment). How much better off are you?

The answer to this question is at the heart of NPV calculations. The land investment project is worth $1,165,049 today to an investor who demands a 3 percent return on this type of investment. You, however, have been able to acquire this investment for only $1,000,000. Thus, your wealth has increased by undertaking this investment by $165,049 ($1,165,049 present value of the projected investment opportunity payoffs minus the required initial investment of $1,000,000). The NPV of this investment is $165,049. In general, the NPV of an investment is equal to

NPV = Present value of future returns − Initial outlay [2.4]

This example was simplified by assuming that the returns from the investment were received exactly one year from the date of the initial outlay. If the payoff from the land

present value The value today of a future amount of money or a series of future payments evaluated at the appropriate discount rate.

46 Part 1: Introduction

investment had been not one but two years away, the PVIF would have been 1/(1.03)2 = 0.942596, and the NPV would have been 1.2 million (.942596) – 1.0 million = $131,115. The NPV rule can be generalized to cover returns received over any number of future time periods with projected growth or decay and terminal values as salvage or disposal costs. In Appendix A at the end of the book, the present value concept is developed in more detail so that it can be applied in these more complex investment settings.

Example Changing a Lightbulb Saves $40 and May Save the Planet

4

Incandescent lightbulbs replaced oil lamps for interior lighting more than 100 years ago. Thomas Edison himself improved on some basic designs running electric cur- rent through a carbonized filament in an oxygen-free vacuum tube, producing less combustion and more light. General Electric had its origins selling long-lasting tungsten filament incandescent bulbs. Today, the new compact fluorescent light (CFL) bulb uses 75 percent less electricity to heat an argon vapor that emits ultra- violet light. The UV light excites a fluorescent phosphor coating on the inside of the tube, which then emits visible light. The U.S. Department of Energy estimates that if all 105 million U.S. households replaced just one heavily used incandescent bulb with a CFL bulb yielding comparable light, the electricity saved could light 3 million homes. In addition, the energy saved would remove from the environ- ment an amount of greenhouse gases from coal-burning power plants equal to the CO2 emitted by 800,000 cars. The U.K. Department of Business, Enterprise, and Reg- ulatory Reform estimates that replacing the three most frequently used lightbulbs in U.K. households would save the electricity used by all the street lamps in Britain.

The magnitude of these energy savings is certainly staggering, but at what cost? Bought for $1.19 per bulb, 1,000-hour incandescent 75-watt bulbs cost much less to install than CFL bulbs that create the same 1,250 lumens of light, last 8,000 hours, burn only 18 to 22 watts of electricity, but cost $14. So, the lifetime cost comparison hinges on whether the extra $12.81 acquisition cost of the CFL bulb is worth the extended lifetime of energy savings. Net present value techniques are designed to answer just such questions of the time value of money (savings) that are delayed.

Table 2.5 shows the initial net investments of $14 and $1.19 per bulb, the 55 kilowatt hours (kWh) of power saved on average by the CFL bulb each year, the $0.10 per kWh representative cost of the electricity,5 and the additional $1.19 in- candescent bulb replacement every 1,000 hours (the typical U.S. household’s an- nual usage). Assuming a 6 percent discount rate, the net present value of the $5.50 annual energy savings plus the $1.19 replacement cost for incandescent bulbs avoided each year for seven years yields a net present value cost savings of $40.79, which exceeds the differential $12.81 acquisition cost for the CFL bulb by $27.98. The European Union has found this $28 net present value of the cost savings from switching to CFL bulbs (plus their CO2 abatement) so compelling that incandes- cent bulbs are no longer approved for manufacture or import into the EU. More gradual U.S. phaseout of incandescent bulbs will begin in 2012.

4Based on “DOE Launches Change a Light, Change the World Campaign” (October 3, 2007), www.energy.gov and www.energystar.gov. 5Electric rates for incremental power vary by region from $.06 per kWh in the state of Washington to $.08 in the Carolinas, to $.12 in California, New York, and across New England.

Chapter 2: Fundamental Economic Concepts 47

Sources of Positive Net Present Value Projects What causes some projects to have a positive NPV and others to have a negative NPV? When product and factor markets are other than perfectly competitive, it is possible for a firm to earn above-normal profits (economic rents) that result in positive net present value projects. The reasons why these above-normal profits may be available arise from condi- tions that define each type of product and factor market and distinguish it from a perfectly competitive market. These reasons include the following barriers to entry and other factors:

1. Buyer preferences for established brand names 2. Ownership or control of favored distribution systems (such as exclusive auto dealer-

ships or airline hubs) 3. Patent control of superior product designs or production techniques 4. Exclusive ownership of superior natural resource deposits 5. Inability of new firms to acquire necessary factors of production (management,

labor, equipment) 6. Superior access to financial resources at lower costs (economies of scale in attracting

capital) 7. Economies of large-scale production and distribution arising from

a. Capital-intensive production processes b. High initial start-up costs

These factors can permit a firm to identify positive net present value projects for internal investment. If the barriers to entry are sufficiently high (such as a patent on key technology) so as to prevent any new competition, or if the start-up period for competitive ventures is sufficiently long, then it is possible that a project may have a positive net present value. However, in assessing the viability of such a project, the manager or analyst must consider the likely period of time when above-normal returns can be earned before new competitors emerge and force cash flows back to a more normal level. It is generally unrealistic to expect to be able to earn above-normal returns over the entire life of an investment project.

Risk and the NPV Rule The previous land investment example assumed that the investment was riskless. There- fore, the rate of return used to compute the discount factor and the net present value was the riskless rate of return available on a U.S. government bond having a one-year maturity. What if you do not believe that the construction of the new interchange is a cer- tainty, or you are not confident about of the value of the land in one year? To compensate

TABLE 2.5 LIFETIME COST SAVINGS OF COMPACT FLUORESCENT LIGHT (CFL) BULBS

t=0 t=1 t=2 t=3 t=4 t=5 t=6 t=7 t=8

(END OF PERIOD VALUES)

Incandescent −$1.19 −$1.19 −$1.19 −$1.19 −$1.19 −$1.19 −$1.19 −$1.19 0

CFL −$14.00 55 kWh × $.10 = $5.50 $5.50 $5.50 $5.50 $5.50 $5.50 $5.50 $5.50

Cost difference −$12.81 NPV (8 years of $5.50 energy savings at d=6%) = $34.15

NPV (7 years of $1.19 incandescent replacement cost at d=6%) = $6.64

NPV (Lifetime cost savings) − Cost difference

($34.15 + $6.64) $40.79 $12.81

= $27.98

48 Part 1: Introduction

for the perceived risk of this investment, you decide that you require a 15 percent rate of return on your investment. Using a 15 percent required rate of return in calculating the discount factor, the present value of the expected $1.2 million sales price of the land is $1,043,478 ($1.2 million times [1/1.15]). Thus, the NPV of this investment declines to $43,478. The increase in the perceived risk of the investment results in a dramatic $121,571 decline from $165,049 in the NPV on a $1 million investment.

A primary problem facing managers is the difficulty of evaluating the risk associated with investments and then translating that risk into a discount rate that reflects an ade- quate level of risk compensation. In the next section of this chapter, we discuss the risk concept and the factors that affect investment risk and influence the required rate of return on an investment.

MEANING AND MEASUREMENT OF RISK Risk implies a chance for some unfavorable outcome to occur—for example, the possibility that actual cash flows will be less than the expected outcome. When a range of potential outcomes is associated with a decision and the decision maker is able to assign probabilities to each of these possible outcomes, risk is said to exist. A decision is said to be risk free if the cash flow outcomes are known with certainty. A good example of a risk-free investment is U.S. Treasury securities. There is virtually no chance that the Treasury will fail to redeem these securities at maturity or that the Treasury will default on any interest payments owed. In contrast, US Airways bonds constitute a risky investment because it is possible that US Airways will default on one or more interest payments and will lack sufficient funds at ma- turity to redeem the bonds at face value. In summary, risk refers to the potential variability of outcomes from a decision. The more variable these outcomes are, the greater the risk.

Probability Distributions The probability that a particular outcome will occur is defined as the relative frequency or percentage chance of its occurrence. Probabilities may be either objectively or subjec- tively determined. An objective determination is based on past outcomes of similar events, whereas a subjective determination is merely an opinion made by an individual about the likelihood that a given event will occur. In the case of decisions that are fre- quently repeated, such as the drilling of developmental oil wells in an established oil field, reasonably good objective estimates can be made about the success of a new well. In contrast, for totally new decisions or one-of-a-kind investments, subjective estimates about the likelihood of various outcomes are necessary. The fact that many probability estimates in business are at least partially subjective does not diminish their usefulness.

Using either objective or subjective methods, the decision maker can develop a probability distribution for the possible outcomes. Table 2.6 shows the probability distribution of net cash flows for two sample investments. The lowest estimated annual

TABLE 2.6 PROBABILITY DISTRIBUTIONS OF THE ANNUAL NET CASH

FLOWS (NCF) FROM TWO INVESTMENTS

INVESTMENT I INVESTMENT II

POSSIBLE NCF PROBABILITY POSSIBLE NCF PROBABILITY

$200 0.2 $100 0.2

300 0.6 300 0.6

400 0.2 500 0.2

1.0 1.0

risk A decision-making situation in which there is variability in the possible outcomes, and the probabilities of these outcomes can be specified by the decision maker.

probability The percentage chance that a particular outcome will occur.

Chapter 2: Fundamental Economic Concepts 49

net cash flow (NCF) for each investment—$200 for Investment I and $100 for Investment II—represents pessimistic forecasts about the investments’ performance; the middle values— $300 and $300—could be considered normal performance levels; and the highest values— $400 and $500—are optimistic estimates.

Expected Values From this information, the expected value of each decision alternative can be calculated. The expected value is defined as the weighted average of the possible outcomes. It is the value that is expected to occur on average if the decision (such as an investment) were repeated a large number of times.

Algebraically, the expected value may be defined as

r = ∑ n

j = 1 rjpj [2.5]

where r is the expected value; rj is the outcome for the jth case, where there are n possible outcomes; and pj is the probability that the jth outcome will occur. The expected cash flows for Investments I and II are calculated in Table 2.8 using Equation 2.5. In this exam- ple, both investments have expected values of annual net cash flows equaling $300.

Example Probability Distributions and Risk: US Airways Bonds 6

Consider an investor who is contemplating the purchase of US Airways bonds. That investor might assign the probabilities associated with the three possible outcomes from this investment, as shown in Table 2.7. These probabilities are interpreted to mean that a 30 percent chance exists that the bonds will not be in default over their life and will be redeemed at maturity, a 65 percent chance of interest default during the life of the bonds, and a 5 percent chance that the bonds will not be redeemed at maturity. In this example, no other outcomes are deemed possible.

6The annual report for the US Airways Corporation can be found at http://investor.usairways.com

TABLE 2.7 POSSIBLE OUTCOMES FROM INVESTING IN US

AIRWAYS BONDS

OUTCOME PROBABILITY

No default, bonds redeemed at maturity 0.30

Default on interest for one or more periods 0.65

No interest default, but bonds not redeemed at maturity 0.05

1.00

TABLE 2.8 COMPUTATION OF THE EXPECTED RETURNS FROM TWO

INVESTMENTS

INVESTMENT I INVESTMENT II

rj pj rj × pj rj pj rj × pj

$200 0.2 $ 40 $100 0.2 $ 20

300 0.6 180 300 0.6 180

400 0.2 80 500 0.2 100

Expected value: rI = $300 rII = $300

expected value The weighted average of the possible outcomes where the weights are the probabilities of the respective outcomes.

50 Part 1: Introduction

Standard Deviation: An Absolute Measure of Risk The standard deviation is a statistical measure of the dispersion of a variable about its mean. It is defined as the square root of the weighted average squared deviations of in- dividual outcomes from the mean:

σ =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ∑ n

j = 1 ðrj − rjÞ2pj

s [2.6]

where σ is the standard deviation. The standard deviation can be used to measure the variability of a decision alter-

native. As such, it gives an indication of the risk involved in the alternative. The larger the standard deviation, the more variable the possible outcomes and the riskier the decision alternative. A standard deviation of zero indicates no variability and thus no risk.

Table 2.9 shows the calculation of the standard deviations for Investments I and II. These calculations show that Investment II appears to be riskier than Investment I because the expected cash flows from Investment II are more variable.

Normal Probability Distribution The possible outcomes from most investment decisions are much more numerous than in Table 2.6 but their effects can be estimated by assuming a continuous proba- bility distribution. Assuming a normal probability distribution is often correct or nearly correct, and it greatly simplifies the analysis. The normal probability distribu- tion is characterized by a symmetrical, bell-like curve. A table of the standard normal probability function (Table 1 in Appendix B at the end of this book) can be used to compute the probability of occurrence of any particular outcome. From this table, for example, it is apparent that the actual outcome should be between plus and minus 1

TABLE 2.9 COMPUTATION OF THE STANDARD DEVIATIONS FOR TWO INVESTMENTS

j rj r rj − r ðrj − rÞ2 pj ðrj − rÞ2pj Investment I 1 $200 $300 −$100 $10,000 0.2 $2,000

2 300 300 0 0 0.6 0

3 400 300 100 10,000 0.2 2,000

∑ 3

j = 1 ðrj − rÞ2pj = $4,000

σ = ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ∑ n

j = 1 ðrj − rÞ2pj

r =

ffiffiffiffiffiffiffiffiffiffiffi 4,000

p = $63:25

Investment II 1 $100 $300 −$200 $40,000 0.2 $8,000

2 300 300 0 0 0.6 0

3 500 300 200 40,000 0.2 8,000

∑ 3

j = 1 ðrj − rÞ2pj = $16,000

σ = ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ∑ n

j = 1 ðrj − rÞ2pj

r =

ffiffiffiffiffiffiffiffiffiffiffiffiffi 16,000

p = $126:49

standard deviation A statistical measure of the dispersion or variability of possible outcomes.

Chapter 2: Fundamental Economic Concepts 51

standard deviation from the expected value 68.26 percent of the time,7 between plus and minus 2 standard deviations 95.44 percent of the time, and between plus and minus 3 standard deviations 99.74 percent of the time (see Figure 2.9). So a “3 sigma event” occurs less than 1 percent of the time with a relative frequency 0.0026 (i.e., 1.0 − 0.9974), and a “9 sigma event” occurs almost never, with a relative frequency less than 0.0001. Nevertheless, such extraordinary events can and do happen (see following box on LTCM).

The number of standard deviations z that a particular value of r is from the mean r can be computed as

z = r − r σ

[2.7]

Table 1 in Appendix B and Equation 2.5 can be used to compute the probability of an annual net cash flow for Investment I being less than some value r—for example, $205. First, the number of standard deviations that $205 is from the mean must be cal- culated. Substituting the mean and the standard deviation from Tables 2.8 and 2.9 into Equation 2.7 yields

z = $205 − $300

$63:25

= −1:50

In other words, the annual cash flow value of $205 is 1.5 standard deviations below the mean. Reading from the 1.5 row in Table 1 gives a value of 0.0668, or 6.68 percent.

FIGURE 2.9 A Sample Illustration of Areas under the Normal Probability Distribution Curve

0

Standard deviations

–1σ–2σ–3σ +1σ +2σ +3σ

95.44% 99.74%

68.26%

P ro

b ab

il it

y o

f o

cc u

rr en

ce

15.87%

7For example, Table 1 indicates a probability of 0.1587 of a value occurring that is greater than +1σ from the mean and a probability of 0.1587 of a value occurring that is less than −1σ from the mean. Hence the proba- bility of a value between +1σ and −1σ is 68.26 percent—that is, 1.00 − (2 × 0.1587).

52 Part 1: Introduction

Thus, a 6.68 percent probability exists that Investment I will have annual net cash flows less than $205. Conversely, there is a 93.32 percent probability (1 − 0.0668) that the in- vestment will have a cash flow greater than $205.

Coefficient of Variation: A Relative Measure of Risk The standard deviation is an appropriate measure of risk when the decision alternatives being compared are approximately equal in size (that is, have similar expected values of the outcomes) and the outcomes are estimated to have symmetrical probability distributions. Because the standard deviation is an absolute measure of variability,

WHAT WENT RIGHT • WHAT WENT WRONG

Long-Term Capital Management (LTCM) 8

LTCM operated from June 1993–September 1998 as a hedge fund that invested highly leveraged private capital in arbitrage trading strategies on the financial derivative markets. LTCM’s principal activity was examining interest rate derivative contracts throughout the world for evidence of very minor mispricing and then betting enormous sums on the subsequent convergence of those contracts to pre- dictable equilibrium prices. Since the mispricing might be only several cents per thousand dollars invested, LTCM often needed to risk millions or even billions on each bet to secure a nontrivial absolute dollar return. With some- times as many as 100 independent bets spread across doz- ens of different government bond markets, LTCM appeared globally diversified.

In a typical month, 60 such convergence strategies with positions in several thousand counterparty contracts would make money and another 40 strategies with a similar num- ber of counterparties would lose money. Steadily, the prof- its mounted. From approximately $1 billion net asset value (equity) in February 1994, LTCM reached $7 billion of net asset value in January 1998. LTCM then paid out $2.4 bil- lion in a one-time distribution to non-partners, which equaled a 40 percent annual compound return on their investment (ROI). Shortly thereafter, in August 1998, the remaining $4.6 billion equity shrank by 45 percent, and then one month later shrank by another 82 percent to less than $600 million. In September 1998, the hedge fund was taken over by 14 Wall Street banks who, in ex- change for inserting $3.6 billion to cover the firm’s debts, acquired 90 percent of the equity ownership. What went wrong?

One potential explanation is that such events are fully expected in an enterprise so risky that it returns a 40 percent ROI. Anticipated risk and expected return are highly positively correlated across different types of investments. However, LTCM’s annual return had a standard deviation from June 1993 to June 1998 of only

11.5 percent per year as compared to 10 percent as the average for all S&P 500 stocks. In this respect, LTCM’s return volatility was quite ordinary. Another potential ex- planation is that LTCM’s $129 billion on the June 1998 balance sheet was overwhelmed by excessive off-balance sheet assets and liabilities. Although the absolute size of the numbers is staggering (e.g., $1.2 trillion in interest rate swaps, $28 billion in foreign exchange derivatives, and $36 billion in equity derivatives), LTCM’s 9 percent ratio of on-balance sheet to off-balance sheet assets was similar to that of a typical securities firm (about 12 per- cent). Even LTCM’s high financial leverage ($129 billion assets to $4.7 billion equity = 26 to 1) was customary practice for hedge funds.

What appears to have gone wrong for LTCM was that a default of the Russian government on debt obligations in August 1998 set in motion a truly extraordinary “flight to quality.” General turmoil in the bond markets caused in- terest rate volatility to rise to a standard deviation of 36 percent when 3 percent would have been typical. LTCM was caught on the wrong side of many interest rate derivative positions for which no trade was available at any price. Although LTCM had “stress tested” their trading positions against so-called “3 sigma events” (a one-day loss of $35 million), this August–September 1998 volatility proved to be a 9 sigma event (i.e., a one- day loss of $553 million).

With massive investments highly leveraged and ex- posed to a 9 sigma event, LTCM hemorrhaged $2 billion in one month. Because liquidity risk exposure of an other- wise fully diversified portfolio was to blame, many invest- ment houses have concluded that leverage should be substantially reduced as a result of the events at LTCM.

8R. Lowenstein, When Genius Failed (New York: Random House, 2000); remarks by Dave Modest, NBER Conference, May 1999; and “Case Study: LTCM,” eRisk, (2000).

Chapter 2: Fundamental Economic Concepts 53

however, it is generally not suitable for comparing alternatives of differing size. In these cases the coefficient of variation provides a better measure of risk.

The coefficient of variation (v) considers relative variation and thus is well suited for use when a comparison is being made between two unequally sized decision alternatives. It is defined as the ratio of the standard deviation σ to the expected value r, or

ν = σ

r [2.8]

RISK AND REQUIRED RETURN The relationship between risk and required return on an investment can be defined as

Required return = Risk-free return + Risk premium [2.9]

The risk-free rate of return refers to the return available on an investment with no risk of default. For debt securities, no default risk means that promised interest and prin- cipal payments are guaranteed to be made. The best example of risk-free debt securities are short-term government securities, such as U.S. Treasury bills. The buyer of a U.S. government debt security always is assured of receiving the promised principal and inter- est payments because the U.S. government always can print more money. The risk-free return on T-bills equals the real rate of interest plus the expected rate of inflation. The second term in Equation 2.9 is a potential “reward” that an investor can expect to receive

Example Relative Risk Measurement: Arrow Tool Company Arrow Tool Company is considering two investments, T and S. Investment T has ex- pected annual net cash flows of $100,000 and a standard deviation of $20,000, whereas Investment S has expected annual net cash flows of $4,000 and a $2,000 standard de- viation. Intuition tells us that Investment T is less risky because its relative variation is smaller. As the coefficient of variation increases, so does the relative risk of the deci- sion alternative. The coefficients of variation for Investments T and S are computed as

Investment T:

ν = σ

r

= $20,000 $100,000

= 0:20

Investment S:

ν = σ

r

= $2,000 $4,000

= 0:5

Cash flows of Investment S have a larger coefficient of variation (0.50) than do cash flows of Investment T (0.20); therefore, even though the standard deviation is smaller, Investment S is the more risky of the two alternatives.

coefficient of variation The ratio of the standard deviation to the expected value. A relative measure of risk.

54 Part 1: Introduction

from providing capital for a risky investment. This risk premium may arise for any number of reasons. The borrower firm may default on its contractual repayment obligations (a default risk premium). The investor may have little seniority in presenting claims against a bankrupt borrower (a seniority risk premium). The investor may be un- able to sell his security interest (a liquidity risk premium as we saw in the case of LTCM), or debt repayment may occur early (a maturity risk premium). Finally, the re- turn the investor receives may simply be highly volatile, exceeding expectations during one period and plummeting below expectations during the next period. Investors gener- ally are considered to be risk averse; that is, they expect, on average, to be compensated for any and all of these risks they assume when making an investment.

Example Risk-Return Trade-Offs in Stocks, Bonds, Farmland, and Diamonds Investors require higher rates of return on debt securities based primarily on their default risk. Bond-rating agencies, such as Moody’s, Standard and Poor’s, and Fitch, provide evaluations of the default risk of many corporate bonds. Moody’s, for example, rates bonds on a 9-point scale from Aaa through C, where Aaa- rated bonds have the lowest expected default risk. As can be seen in Table 2.10, the yields on bonds increase as the risk of default increases, again reflecting the positive relationship between risk and required returns.

Table 2.10 also shows investment in diamonds has returned 3 percent whereas farmland has returned 6.5 percent, U.S. stocks have returned 10 percent, biotech stocks have returned 12.6 percent, and emerging market stocks have returned 16 percent compounded annually from 1970 to 2010. These compound annual returns mirror the return variance of diamonds (lowest), farmland, U.S. stocks, biotech stocks, and emerging market stocks (highest).

TABLE 2.10 RELATIONSHIP BETWEEN RISK AND REQUIRED RETURNS

DEBT SECURITY YIELD

U.S. Treasury bill 3.8%

U.S. Treasury bonds (25 year +) 5.06

Aaa-rated corporate bonds 6.49

Aa-rated bonds 6.93

A-rated bonds 7.18

Baa-rated corporate bonds 7.80

Other investments

Diamonds 3.0

Farmland 6.5

Stocks

All U.S. stocks 10.1

Biotech stocks 12.6

Emerging market stocks 16.0

Source: Board of Governors of the Federal Reserve System, Federal Reserve Bulletin.

Chapter 2: Fundamental Economic Concepts 55

SUMMARY

� Demand and supply simultaneously determine equilibrium market price. The determinants of de- mand (supply) other than price shift the demand (supply) curve. A change in price alone leads to a change in quantity demanded (supplied) without any shift in demand (supply).

� The offer price demanders are willing to pay is determined by the marginal use value of the pur- chase being considered. The asking price suppliers are willing to accept is determined by the variable cost of the product or service being supplied.

� The equilibrium price of gasoline fluctuates pri- marily because of spikes and collapses in crude oil input prices caused at various times by supply disruptions and gluts, increasing demand in devel- oping countries, and speculation.

� Changes in price result in movement along the de- mand curve, whereas changes in any of the other variables in the demand function result in shifts of the entire demand curve. Thus “changes in quan- tity demanded along” a particular demand curve result from price changes. In contrast, when one speaks of “changes in demand,” one is referring to shifts in the entire demand curve.

� Some of the factors that cause a shift in the entire demand curve are changes in the income level of consumers, the price of substitute and complemen- tary goods, the level of advertising, competitors’

advertising expenditures, population, consumer preferences, time period of adjustment, taxes or subsidies, and price expectations.

� The marginal analysis concept requires that a deci- sion maker determine the additional (marginal) costs and additional (marginal) benefits associated with a proposed action. If the marginal benefits exceed the marginal costs (that is, if the net mar- ginal benefits are positive), the action should be taken.

� The net present value of an investment is equal to the present value of expected future returns (cash flows) minus the initial outlay.

� The net present value of an investment equals the contribution of that investment to the value of the firm and, accordingly, to the wealth of share- holders. The net present value of an investment depends on the return required by investors (the firm), which, in turn, is a function of the perceived risk of the investment.

� Risk refers to the potential variability of outcomes from a decision alternative. It can be measured ei- ther by the standard deviation (an absolute mea- sure of risk) or coefficient of variation (a relative measure of risk).

� A positive relationship exists between risk and re- quired rates of return. Investments involving greater risks must offer higher expected returns.

Exercises 1. For each of the determinants of demand in Equation 2.1, identify an example

illustrating the effect on the demand for hybrid gasoline-electric vehicles such as the Toyota Prius. Then do the same for each of the determinants of supply in Equation 2.2. In each instance, would equilibrium market price increase or de- crease? Consider substitutes such as plug-in hybrids, the Nissan Leaf and Chevy Volt, and complements such as gasoline and lithium ion laptop computer batteries.

2. Gasoline prices above $3 per gallon have affected what Enterprise Rental Car Co. can charge for various models of rental cars. SUVs are $37 with one-day return and subcompacts are $41 with one-day return. Why would the equilibrium price of SUVs be lower than the equilibrium price of subcompacts?

Answers to the exercises in blue can be found in Appendix D at the back

of the book.

56 Part 1: Introduction

3. The Ajax Corporation has the following set of projects available to it:

PROJECT* INVESTMENT REQUIRED

($ MILLION) EXPECTED RATE

OF RETURN

A 500 23.0%

B 75 18.0

C 50 21.0

D 125 16.0

E 300 14.0

F 150 13.0

G 250 19.0

*Note: All projects have equal risk.

Ajax can raise funds with the following marginal costs:

First $250 million 14.0%

Next 250 million 15.5

Next 100 million 16.0

Next 250 million 16.5

Next 200 million 18.0

Next 200 million 21.0

Use the marginal cost and marginal revenue concepts developed in this chapter to derive an optimal capital budget for Ajax.

4. The demand for MICHTEC’s products is related to the state of the economy. If the economy is expanding next year (an above-normal growth in GNP), the com- pany expects sales to be $90 million. If there is a recession next year (a decline in GNP), sales are expected to be $75 million. If next year is normal (a moderate growth in GNP), sales are expected to be $85 million. MICHTEC’s economists have estimated the chances that the economy will be either expanding, normal, or in a recession next year at 0.2, 0.5, and 0.3, respectively. a. Compute expected annual sales. b. Compute the standard deviation of annual sales. c. Compute the coefficient of variation of annual sales.

5. Two investments have the following expected returns (net present values) and standard deviation of returns:

PROJECT EXPECTED RETURNS STANDARD DEVIATION

A $ 50,000 $ 40,000

B $250,000 $125,000

Which one is riskier? Why? 6. The manager of the aerospace division of General Aeronautics has estimated the

price it can charge for providing satellite launch services to commercial firms. Her most optimistic estimate (a price not expected to be exceeded more than 10 per- cent of the time) is $2 million. Her most pessimistic estimate (a lower price than this one is not expected more than 10 percent of the time) is $1 million. The expected value estimate is $1.5 million. The price distribution is believed to be approximately normal.

Chapter 2: Fundamental Economic Concepts 57

a. What is the expected price? b. What is the standard deviation of the launch price? c. What is the probability of receiving a price less than $1.2 million?

Case Exercise REVENUE MANAGEMENT AT AMERICAN

AIRLINES 9

Airlines face highly cyclical demand; American reported profitability in the strong ex- pansion of 2006–2007 but massive losses in the severe recession of 2008–2009. De- mand also fluctuates day to day. One of the ways American copes with random demand is through marginal analysis using revenue management techniques. Revenue or “yield” management (RM) is an integrated demand-management, order-booking, and capacity-planning process.

To win orders in a service industry without slashing prices requires that companies create perceived value for segmented classes of customers. Business travelers on air- lines, for example, will pay substantial premiums for last-minute responsiveness to their flight change requests. Other business travelers demand exceptional delivery re- liability and on-time performance. In contrast, most vacation excursion travelers want commodity-like service at rock-bottom prices. Although only 15–20 percent of most airlines’ seats are in the business segment, 65–75 percent of the profit contribution on a typical flight comes from this group.

The management problem is that airline capacity must be planned and allocated well in advance of customer arrivals, often before demand is fully known, yet unsold inventory perishes at the moment of departure. This same issue faces hospitals, con- sulting firms, TV stations, and printing businesses, all of whom must acquire and schedule capacity before the demands for elective surgeries, a crisis management team, TV ads, or the next week’s press run are fully known.

One approach to minimizing unsold inventory and yet capturing all last-minute high-profit business is to auction off capacity to the highest bidder. The auction for free-wheeling electricity works just that way: power companies bid at quarter ’til the hour for excess supplies that other utilities agree to deliver on the hour. However, in airlines, prices cannot be adjusted quickly as the moment of departure approaches. Instead, revenue managers employ large historical databases to predict segmented cus- tomer demand in light of current arrivals on the reservation system. They then ana- lyze the expected marginal profit from holding in reserve another seat in business class in anticipation of additional “last-minute” demand and compare that seat by seat to the alternative expected marginal profit from accepting one more advance res- ervation request from a discount traveler.

Suppose on the 9:00 A.M. Dallas to Chicago flight next Monday, 63 of American’s 170 seats have been “protected” for first class, business class, and full coach fares but only 50 have been sold; the remaining 107 seats have been authorized for sale at a discount. Three days before departure, another advance reservation request arrives in the discount class, which is presently full. Should American reallocate capacity and

9Based on Robert Cross, Revenue Management (New York: Broadway Books, 1995); and Frederick Harris and Peter Peacock, “Hold My Place Please: Yield Management Improves Capacity Allocation Guesswork,” Marketing Management (Fall 1995), pp. 34–46.

58 Part 1: Introduction

take on the new discount passenger? The answer depends on the marginal profit from each class and the predicted probability of excess demand (beyond 63 seats) next Monday in the business classes.

If the $721 full coach fare has a $500 marginal profit and the $155 discount fare has a $100 marginal profit, the seat in question should not be reallocated from busi- ness to discount customers unless the probability of “stocking out” in business is less than 0.20 (accounting for the likely incidence of cancellations and no-shows). There- fore, if the probability of stocking out is 0.25, the expected marginal profit from hold- ing an empty seat for another potential business customer is $125, whereas the marginal profit from selling that seat to the discount customer is only $100 with cer- tainty. Even a pay-in-advance no-refund seat request from the discount class should be refused. Every company has some viable orders that should be refused because ad- ditional capacity held in reserve for the anticipated arrival of higher profit customers is not “idle capacity” but rather a predictable revenue opportunity waiting to happen.

In this chapter, we developed the marginal analysis approach used in solving American’s seat allocation decision problem. The Appendix to Chapter 14 discusses further the application of revenue management to baseball, theatre ticketing, and hotels.

Questions 1. Make a list of some of the issues that will need to be resolved if American Air-

lines decides to routinely charge different prices to customers in the same class of service.

2. Would you expect these revenue management techniques of charging differential prices based on the target customers’ willingness to pay for change order respon- siveness, delivery reliability, schedule frequency, and so forth to be more effective in the trucking industry, the outpatient health care industry, or the hotel indus- try? Why or why not?

3. Sometimes when reservation requests by deep discount travelers are refused, de- manders take their business elsewhere; they “balk.” At other times, such deman- ders negotiate and can be “sold up” to higher fare service like United’s Economy Plus. If United experiences fewer customers balking when reservation requests for the cheapest seats are refused, should they allocate preexisting capacity to protect fewer seats (or more) for late-arriving full-fare passengers?

Chapter 2: Fundamental Economic Concepts 59