BUS 640 Week 4 Discussions 1&2, with Week 4 assignment and week 4 journal

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Pricing Decisions in Practice

Learning Objectives

A�er reading this chapter, you should be able to:

Explain how managers can u�lize es�mates of cost and revenue data, and es�mates of price elas�city, to determine the profit-maximizing price. Explain how markup pricing can be the profit-maximizing means of price se�ng when search cost for data is significant. Reconcile markup pricing with marginal pricing, and understand that markup pricing can remain profit- maximizing despite shi�s of the demand and cost curves. Iden�fy ways that price discrimina�on can increase the profitability of the firm. Recognize when bundle pricing can increase the firm's profitability.

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Search costs are the costs associated with finding informa�on. Profit-maximizing firms only incur these costs if doing so improves the profit of the decision.

Introduction

In this chapter, we u�lize the theore�cal concepts introduced in prior chapters to help the manager make profit- maximizing decisions in the real world where cost and demand data is not available without incurring significant informa�on search costs. Informa�on search costs, defined previously as the costs of obtaining reasonably accurate data or knowledge pertaining to the issue at hand, are discre�onary costs that may be avoided. In all cases, the profit-maximizing firm should incur search costs only if doing so would increase profit by enough to cover the cost of obtaining the data necessary to make the decision. In some cases, search costs will be rela�vely low, such as is possible by u�lizing data that is internal to the firm and that has been rou�nely collected in past produc�on periods. In other cases search costs to obtain data from customers or suppliers might be so large that the manager's educated guess will be profit-maximizing as long as it misses the mark by less than the search costs that were avoided.

Accordingly, this chapter is organized on the basis of the "search versus don't search" dichotomy. In the next sec�on, we start with marginalist pricing—se�ng price using the marginal cost equals marginal revenue rule using es�mated cost, revenue, and price elas�city data that can be obtained from informa�on search ac�vity by firms from prior produc�on and market experience. We then turn to the use of simple (search-cost avoiding) pricing rules that allow a sufficiently accurate price and output decision such that the firm might maximize profits by avoiding expenditures on search costs and choosing a price that is "near enough" to that which would maximize profits with full informa�on. We introduce markup pricing—whereby price is determined as a percentage markup over the firm's average costs—and examine the condi�ons under which it is likely to be, and to remain, profit maximizing despite shi�s in the cost and demand condi�ons facing the firm. Finally, we examine two specific pricing topics, namely price discrimina�on and bundle pricing, which can allow the firm to make larger profit from the same number of customers.

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8.1 Marginalist Pricing Using Estimated Revenue and Cost Data

First, a quick review of what we learned in Chapter 4 about es�ma�ng the demand func�on. We saw that a manager can es�mate the firm's demand func�on by collec�ng data on both the firm's sales volume and the main variables that influence sales, and then using mul�ple regression analysis to es�mate the coefficients in the demand func�on for each of those determinants of the firm's demand. The equa�on we used for the demand func�on in Chapter 4 was

Qx = α + β1Px + β2Py + β3Ax + β4Ay + β5GNI (8-1)

where Qx represents quan�ty demanded of product X (in physical units); α (alpha) represents the influence of variables not included in the regression

analysis; and the βs (betas) are the coefficients to the independent variables used in the regression equa�on, with each one showing the marginal impact on Qx of a change in each of the independent variables, for example β1 = δQx/δPx. The independent variables included in this regression equa�on were the

prices of product X and product Y; the adver�sing expenditures of product X and product Y; and the level of gross na�onal income (GNI), the la�er being a proxy variable represen�ng the income of customers for product X. In Chapter 4 we found the constant term and the coefficients to the independent variables as follows:

Qx = 5,030 − 3,806.2Px + 1,458.5Py + 256.6Ax − 32.3Ay + 0.18GNI (8-2)

The es�mated demand func�on must be evaluated for its predic�ve reliability by considering the regression sta�s�cs that are provided by the regression analysis so�ware. First, the level of significance of each of the independent variables is checked by observing whether its P-value is 0.05 or smaller for each variable—the P-values indicate the probability that the dependent variable (Qx) really does not depend on each independent variable (e.g., Ay). For example,

a P-value of 0.05 indicates that we can be confident at the 95% level of significance that the independent variable is indeed a significant determinant of demand.

Second, we consider the coefficient of determina�on (R2), which indicates the propor�on of the variance in the dependent variable that is explained by

varia�ons in the independent variables that were included in the regression equa�on. For example R2 = 0.65 indicates that 65% of the varia�on in demand is explained by the independent variables on the right-hand side of the regression equa�on (and thus 35% of the variance in Qx demanded must be

explained by missing variables). The es�mated demand func�on is the best measure of central tendency within the data, but predic�ons of sales (for any

price level, for example) will be surrounded by a range of possible outcomes above and below the predicted value of sales, and as R2 becomes smaller, this

range of outcomes becomes larger. Note that the value of R2 might range from a minimum of zero, indica�ng no correla�on at all, to a maximum of 1.0, indica�ng perfect correla�on.

The standard error of es�mate (Se) sta�s�c provides a measure of the range of possible outcomes around the predicted value of sales. We can be confident

at the 95% confidence level that the actual value of demand will lie within plus or minus 2Se of the es�mated value (for any level of price, for example). The

standard error of the coefficient, Sβ, (for each independent variable) provides a range of values around the es�mated value of each β coefficient in the

regression equa�on within which the true value might fall.1 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.1#ch08txt1) Again, we can be confident at the 95% level of confidence that the true value of the coefficient lies within a range that is plus or minus 2Sβ from the es�mated value of the β. Thus, managers

can use these regression sta�s�cs to conduct sensi�vity analysis on their predic�ons of sales for any level of price (or other independent variable) selected.

On the cost side, in Chapter 6, we considered several methods for the es�ma�on of cost func�ons u�lizing known data points. We demonstrated that we could es�mate the loca�on and shape of a par�cular cost curve (e.g., TVC) by interpola�ng between the known data points using gradient analysis, and then calculate the value of related cost measures (e.g., AVC and MC). With a greater number of known data points, we can achieve a more accurate es�ma�on of the TVC func�on by fi�ng a "line of best fit" to the data using regression analysis and, subsequently, calculate the AVC and MC values for any output level. The line of best fit may be a linear, quadra�c, or cubic func�on of output, the choice being made on the basis of which func�onal form best fits the data.

This will be the form that exhibits the highest coefficient of determina�on (R2) while maintaining 95% confidence levels of significance (P-values less than 0.05) for the independent variables included in the equa�on.

If your understanding of the terms and concepts in the above two paragraphs is a li�le rusty, you should go back and quickly review the relevant parts of Chapters 4 and 6 to refresh your memory.

Using Estimated Lines of Best Fit

Given the es�ma�on of the demand and cost func�ons, we can find the profit-maximizing output level either by solving for Q using a pair of simultaneous equa�ons, or by deriving and plo�ng the relevant curves (i.e., MC and MR) on a graph and observing the intersec�on point of these curves. The first method starts with deriving equa�ons for the MR and MC curves. Considering first the MR curve, we know it has the same slope and twice the slope of the demand curve, so we need to first derive the demand curve from the demand func�on, as we did in Chapter 4. To do this we need to collapse equa�on 8-2 into the reduced form equa�on Qx = AOV + βPx (where AOV represents the influence of all other variables except the price of X). In Chapter 4, using the

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values Py = $6; Ax = 168 (in thousands of dollars); Ay = 182 (in thousands of dollars); and GNI = 12,875 (in billions of dollars), we evaluated AOV to find the

reduced form of the demand func�on shown as follows:

Qx = 53,328.7 − 3,806.2Px (8-3)

Next we inverted the demand func�on equa�on to find an expression for the firm's demand curve:

Px = 14.011 − 0.00026273Qx (8-4)

As we noted in Chapter 4, this very small coefficient to the variable Qx is hard to comprehend, so we define Qx in thousands of units and mul�ply the

coefficient to Qx by 1000, to express the demand curve equivalently as:

Px = 14.011 − 0.26273Qx (8-5)

Because the marginal revenue (MR) curve has the same intercept and twice the slope of the demand curve, it must be represented by:

MR = 14.011 − 0.52546Qx (8-6)

Now on the cost side, suppose (as we found in Chapter 6) that our most reliable es�mate of the TVC func�on is a straight line of best fit in the form TVC = α + βQ, namely:

TVC = 2.2873 + 5.9639Qx (8-7)

where TVC is in thousands of dollars and Qx is in thousands of units. We know from Chapter 6 that MC is the first deriva�ve of TVC, so:

MC = 5.9639 (8-8)

In this case, TVC was es�mated as a linear func�on of output over the range of output levels represented by the sample data. Note that the first term (2.2873) on the right-hand side of equa�on 8-7 is the residual, or the amount of TVC that is not explained by the varia�on in Qx. The first term serves as

the ver�cal intercept value of the es�mated TVC line and operates to raise the TVC line to the appropriate height to best represent the rela�onship between TVC and Qx in the relevant range of the data observa�ons. We illustrate this in Figure 8.1 where the do�ed line indicates the unobserved TVC curve for all

values of Qx, and the straight line with intercept 2.2873 and slope 5.9639 for each thousand units of Qx represents the es�mated TVC that best fits the data

in the range of data observa�ons actually observed.2 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.1#ch08txt2)

Figure 8.1: Es�mated TVC func�on that best fits the data in the observed range

Now, se�ng the expression for MR, which is equa�on (8-5), equal to the expression for MC, which is equa�on (8-7), we have:

14.011 − 0.52546Qx = 5.9639 (8-9)

This is a single equa�on with one unknown variable, so we can solve3 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.1#ch08txt3) for the value of Qx by

subtrac�ng 14.011 from both sides, and then dividing both sides by –0.52546, to find Qx = 15.314. This is the profit-maximizing output (in thousands of

units), so inser�ng this value of Qx into the demand curve, equa�on 8-5, and solving for Px we find the profit-maximizing price level to be $9.99. 4

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.1#ch08txt4) Total revenue (TR, in thousands of dollars) is calculated as PxQx = 152.9869 and total variable

cost (TVC, in thousands of dollars) can be calculated (from equa�on 8-6) as TVC = 2.2873 + 5.9639(15.314) = 93.6185. The contribu�on to total fixed cost and profit is equal to TR − TVC = 152.9869 − 93.61185 = 59.3684, or $59,368.40. Thus, if total fixed cost is less than $59,368.40 then the firm would be making a profit.Processing math: 0%

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Now let's find the same result using graphical analysis. In Figure 8.2, we show the demand curve having an intercept value at 14.011, as per equa�on 8-5. To plot the demand curve we need to find a second point on the (straight line) demand curve. We do this by solving equa�on 8-5 to find a value for Px at

any par�cular value of Qx, for example 15. When Qx = 15, we solve for Px = 10.07 from equa�on 8-5, which provides the coordinates for a second point on

the demand curve. A straight line drawn from the intercept point (where Px = 14.011 and Qx = 0) that also passes through the point where Px = 10.07 and

Qx = 15, thus represents the demand curve. To plot the MR curve we know the MR curve has the same intercept and twice the slope of the demand curve,

so we know that the MR curve must also intercept the ver�cal axis at 14.011 and then slope down toward the horizontal axis at twice the rate that the demand curve does. Since we found that Px = 10.07 when Qx was 15, we can conclude that when MR = 10.7, the Qx coordinate of the MR curve must be

7.5 (i.e., half of 15), so we can sketch in the MR curve as shown in Figure 8.2.5 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.1#ch08txt5)

Figure 8.2: Graphical representa�on of the price and output decision

For the marginal cost curve, we know from the regression equa�on that TVC = 2.2873 + 5.9639Qx and that MC = 5.9639, because marginal cost is the first

deriva�ve of the TVC func�on. Thus, MC is constant at $5.96 per thousand units regardless of output level, in this par�cular case. Plo�ng MC as the horizontal line at $5.96 we see that the MR curve crosses the MC curve at approximately Qx = 15.314 units of output, and following that up ver�cally to the

demand curve we find the profit-maximizing price level is $9.99. These graphical results confirm the accuracy of our earlier algebraic results, or vice versa!

Using Estimates of Price Elasticity

Now, let's suppose that a manager knows the current price is $7 and the output level is 25,000 units and has es�mated the price elas�city of demand (ε) to be –2.5. As we saw in Chapter 4, price elas�city can be expressed as the percentage change in quan�ty demanded over the percentage change in the price level. For example, if ε = –2.5 this implies that the quan�ty demanded would increase by 2.5% if price was reduced by 1%. Since a 1% price change might not be no�ced by consumers we would usually expect a more substan�al price adjustment; for example, the manager would expect that a 10% price reduc�on would cause a 25% increase in quan�ty demanded (or conversely a 25% reduc�on in demand for a 10% price increase). Price elas�city of demand, as we saw in Chapter 4, can also be expressed as:

ε = ΔQ/ΔP • P/Q (8-10)

We can subs�tute the known or es�mated values of ε, P, and Q from above into this equa�on to say –2.5 = ΔQ/ΔP • 7/25 and solve this equa�on to find ΔQ/ΔP = –8.9286 (where Q is in thousands). Note that ΔQ/ΔP is the reciprocal of the slope of the demand curve, so 1/–8.9286 = –0.112 must be the slope of the demand curve. To find the intercept of the demand curve, we know that P = a − 0.112Q, where a is the intercept term, and since we know P = 7 when Q = 25, we can subs�tute these values into the equa�on to solve for the intercept term a = 9.8. Thus, the es�mated expression for the demand curve is P = 9.8 − 0.112Q, and the marginal revenue curve must be MR = 9.8 − 0.224Q (having the same intercept and twice the slope).

Now, supposing that the manager does regression analysis of TVC data and finds that the line of best fit is TVC = 2Q + 0.2Q2, and (taking the first deriva�ve) finds that MC = 2 + 0.4Q. Having an expression for both MC and MR we can now solve for the profit-maximizing output and price, either mathema�cally or graphically. The former will be faster, so let's set MC = MR and solve for Q as follows:

2 + 0.4Q = 9.8 − 0.224Q (8-11)

By adding 0.224Q to both sides and subtrac�ng 2 from both sides we find 0.264Q = 7.8. From this we find Q = 7.8/0.264 = 29.545 (thousands). Subs�tu�ng this profit-maximizing output level into the demand curve expression we find P = 9.8 − 0.112(29.545) = 6.49. Thus, the profit-maximizing price is $6.49, so the manager should reduce price from the current level of $7 in order to maximize profit. Doing so would soon verify or disprove the ini�al es�mate of price elas�city that formed the basis of the es�ma�on of the demand curve, as quan�ty demanded should increase to about 29,545 units and profit should increase from the ini�al level. If profit does not increase as expected, then the resultant Q observa�on at the new price level ($6.49) provides a second known point on the demand curve, which allows the slope and intercept to be calculated (assuming no changes in the other determinants of demand) and, thus, the manager can proceed to find the profit-maximizing price and output level.

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1. The "true" value is the value we would find if the en�re popula�on of observa�ons is used in the regression analysis. Typically, we select a sample that we expect to be representa�ve of the popula�on and thereby keep informa�on search costs to a tolerable level. The standard errors of the coefficients indicate the extent to which sampling error might have occurred. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.1#return1) ]

2. As in Chapter 6, we choose the func�onal form of the line of best fit on the basis of which form (e.g., linear, quadra�c, or cubic) that best fits the observed data points, and we judge

"best fit" by the highest R2 value when all of the independent variables that are included in the regression equa�on (e.g., Q, Q2, and Q3) are significant at the 95% confidence level. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.1#return2) ]

3. To do this step by step, we start with 14.011 − 0.52546Qx = 5.9639. By subtrac�ng 14.011 from both sides we have –8.0471 = –0.52546Qx. Then, by dividing both sides of this equa�on

by –0.52546 we find Qx = 15.314. Subs�tu�ng 15.314 for Qx in the demand curve expression Px = 14.011 − 0.26273Qx we have Px = 14.011 − 0.26273(15.314) which evaluates to be Px = $9.99. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.1#return3) ]

4. When the profit-maximizing price turns out to be an odd number, such as $9.52, it may require a cosme�c adjustment to let's say $9.49, to be more suitable for marke�ng purposes. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.1#return3) ]

5. Alterna�vely, we could find the horizontal-axis intercept of the demand curve by se�ng Px = 0 and solving for Qx in the demand curve, and then halve this Qx value to find where the

MR curve must cut the horizontal axis. We found earlier (see Figure 4.1 in Chapter 4) that this demand curve intercepts the horizontal axis at Qx = 53.328, so the MR curve must

intercept that axis at 26.664 (thousand units). [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.1#return5) ]

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When implemen�ng markup pricing, firms must take into account the price elas�city of demand, since higher markups translate to higher prices which reduce demand by an amount that depends on the price elas�city of demand.

8.2 Markup (or Cost-Plus) Pricing

In prac�ce, many firms use markup pricing, whereby average variable costs, AVC (also known as direct costs per unit), are marked up by a percentage of AVC to arrive at the price level. Thus:

P = AVC + X(AVC) (8-12)

where X is the markup percentage and X(AVC) is the contribu�on margin, which as we saw previously is equal to P − AVC and represents the contribu�on that the price makes to the overhead costs and profit of the firm. Markup pricing is o�en called "cost-based pricing," but it is clear that the markup percentage must also take into account the price elas�city of demand, since higher markups mean higher prices and these will cause demand to be reduced by an amount that depends on the price elas�city of demand. In fact, markup pricing can be reconciled with the marginalist pricing rule (i.e., MC = MR) in the case where AVC is constant (and therefore AVC = MC), which we shall do in the next sec�on.

Reconciliation With Marginalist Pricing

In Figure 8.3, we show two graphs—on the le�-hand side, we show the $7.50 price as determined by a 50% markup over direct costs of $5 per unit, and, subsequently, the firm's customers demand Q units, thus revealing one known point on the demand curve (depicted by the star). On the right-hand side of Figure 8.3, we show the complete demand and MR curves that are unknown to the firm. In this carefully drawn case, it is clear that the 50% markup is indeed profit-maximizing, since MC = MR at that price and output level.

Figure 8.3: Markup pricing and marginalist pricing reconciled

By observing the graph on the right-hand side, you can see that if the markup had been set instead at, say, 60% (for an $8 price with a $3 contribu�on margin), the consequent level of quan�ty demanded would be less than Q units and MC would be less than MR at that higher price and lower output combina�on, and thus that price and output combina�on would not be profit maximizing. Similarly, if the markup rate had been only 40% the price would be $7, quan�ty demanded would be more than Q, and, again, profit would not maximized because MC > MR at that price and quan�ty combina�on.

So, to be profit-maximizing the markup rate must reflect the height and slope of the demand curve, rela�ve to the MC curve. As we have seen, the price elas�city of demand is related to the height and slope of the demand curve, and, indeed, there is a special rela�onship between price elas�city and the profit-maximizing markup rate over AVC, which is evident in the following expression:

(8-13)

This expression shows that the profit-maximizing markup rate (the term in brackets in equa�on 8-13) is inversely related to the price elas�city of demand

and is derived to include the requirement that MC = MR.6 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.2#ch08txt6) Note that this formula is only correct for the case where direct costs (AVC) are constant and, thus, AVC = MC in the relevant output range.

In Table 8.1 we show the profit-maximizing markup rates for a selec�on of price-elas�city values. It is evident that the higher (in absolute terms) is the price elas�city the lower the markup rate must be if the price is to be profit-maximizing. From Chapter 4, we know that price elas�city has an extremely high nega�ve value near the ver�cal intercept with the price axis, with these values increasing as we move towards the midpoint of the demand curve, where ε = −1. We also know that MR falls to zero at the midpoint of the demand curve, and, therefore, any price below the midpoint cannot be profit-maximizing

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because we want MR = MC (and MC cannot be nega�ve). Closer to the midpoint of the demand curve, where MR is quite low, MC must also be quite low if MR is to be equal to MC, and, hence, the higher will be the markup rate. Conversely, at points higher on the demand curve the MR is also higher, so for MR to be equal to MC, the MC must also be rela�vely high and, thus, the markup rate must be rela�vely low.

Table 8.1: Profit-maximizing markup rate (X) given price elas�city of demand (ε) ε –9 –8 –7 –6 –5 –4 –3 –2 –1.5

X 12.5% 14.3% 16.7% 20% 25% 33.3% 50% 100% 200%

This is illustrated by the examples in Figure 8.4 (where the same demand situa�on is depicted with two different cost situa�ons), and in Figure 8.5 (where the cost situa�ons are the same but the demand situa�ons differ). Fundamentally, the markup percentages are different because the price elas�city of demand is different at the profit-maximizing-price levels, and these differ because of the differences in the cost levels (see Figure 8.4) or because of the differences in the demand situa�on (see Figure 8.5). Thus it is clearly important for managers to have in their minds an es�mate of price elas�city before se�ng prices via markups over direct costs in situa�ons where they do not know much about the height and slope of the demand curve.

Figure 8.4: Low markup rates versus high markup rates with different cost condi�ons

Figure 8.5: Low markup rates versus high markup rates with different demand condi�ons

As discussed in Chapter 4, managers should understand that price elas�city depends on two main drivers—namely, the subs�tu�on effect and the income

effect.7 (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.2#ch08txt7) The subs�tu�on effect is greater if the number and closeness of subs�tutes is greater; thus a 10% price increase, for example, might be expected to cause the loss of, say, 40% of sales when there are many close subs�tutes (as in monopolis�c compe��on). Conversely, a 10% price increase would expect to cause the loss of only, say, 15% of sales if there are not many close subs�tutes (as in a highly-differen�ated-products oligopoly) for example. The income effect is about affordability—if the price is rela�vely high compared to the customer's income, a price increase is more likely to cause the customer to stop purchasing that product, compared to a product where the price is small rela�ve to customers' incomes. These are things that managers should know about their product and their customers, and so managers should be able to make a rough es�mate of the value of price elas�city for that product.

How would managers use this informa�on? They might either calculate (from equa�on 8-13) the profit-maximizing markup rate based on their best es�mate of price elas�city, or conversely work from their preferred markup rate to find the implied price elas�city if that markup is to be profit-maximizing. Having arrived at an implied markup rate, managers must then ask themselves the ques�on: Does that seem right? Is it congruent with what I know about the number and closeness of subs�tutes for my product and the general affordability of my product? For example, if a manager wants to maximize profit and intends to apply a 25% markup on direct costs to determine its price, this implies that the price elas�city of demand is –5, which infers that quan�ty demanded would drop by 50% if price were to be raised by 10%. The manager must ask the ques�on "Does it seem reasonable that fully half the firm's demand would disappear if the firm raised price by 10%?" This implies either that the product has very close subs�tutes or that it is rela�vely expensive in rela�on to customers' incomes. If the implied price elas�city seems too high this means the chosen markup rate is probably too low and should be increased to increase profit. Oppositely, if the implied price elas�city seems too low, given the availability of subs�tutes and the ra�o of price to customer

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Managers must strategically set a markup rate. If the implied price elas�city seems too high, the markup rate is probably too high and should be reduced to increase profit.

incomes, the markup rate is probably too high and profits will increase if a lower markup (and price) is used. A simple test is possible, of course—the manager could go ahead and reduce the price slightly and see what happens to volume and profit, and then make a subsequent adjustment one way or the other.

Search Costs and the Range of Acceptable Markup Rates

Search costs, as you know, are the costs associated with finding informa�on. The search costs of es�ma�ng price elas�city and/or the demand and TVC func�ons can be avoided by using simple pricing rules like markup pricing. If search costs are avoided the markup rate can be "wrong" (i.e., not profit-maximizing) to some extent yet s�ll allow the firm to make greater profit as compared to first undertaking informa�on search ac�vity and later se�ng the profit-maximizing price (but having higher overhead costs due to the expenditures on search ac�vity). We show the extent to which the markup can be wrong in Figure 8.6 for a presumed case where search ac�vity, if

undertaken, would increase the firm's total fixed costs (TFC) by a substan�al amount.8

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.2#ch08txt8) We exaggerate the size of the search costs in Figure 8.5 to allow a clear explana�on of the effect.

In Figure 8.5, the curve labeled TC shows the total costs including the search costs, while the curve labeled TCʹ represents total costs when search costs are avoided. You will note that these total cost curves emanate from the

ver�cal axis at the level of total fixed costs and rise at a constant rate (equal to MC) reflec�ng a linear TVC curve. The ver�cal difference between the total revenue curve, TR, and the TC curve is mapped as the profit curve Π (the Greek le�er pi) while the ver�cal difference between the TR and the TCʹ curve is mapped as the profit curve Πʹ. No�ce that the "no-search-costs" profit curve Πʹ lies above the "search-cost-included" profit curve Π for a considerable range of outputs, this range being shown as Q1 to Q2 in the lower graph.

Figure 8.6: The range of acceptable markup rates for the firm avoiding search costs

The profit-maximizing price and output levels, with or without search costs, are shown as P* and Q* where MR = MC. But note that price could be anywhere between P1 and P2 if search costs are avoided and yet allow profit (on Πʹ) to exceed the profit available a�er incurring search costs (on Π). In

terms of markup rates, while the profit-maximizing markup rate in this example looks to be about 50% (at P*), the markup rate could range anywhere between about 80% at P1 to about 20% at P2 and s�ll earn more profit (if search costs are avoided) compared to first spending the search costs and then

se�ng price at the profit-maximizing level P*. So you can see there is a lot of room for error in choosing the markup rate! But, be cau�oned that this example shows extraordinarily high search costs as a propor�on of total costs; in most cases the range for error in the markup rate will be somewhatProcessing math: 0%

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Infla�on is caused by an excess of aggregate demand over aggregate supply of all goods and services resul�ng in

smaller than in this "teaching example." Note also that the range of acceptable markup rates will be smaller if price elas�city in the relevant range of outputs is higher (causing the demand curve to be less steeply sloping). If the demand curve is not as steep (as in Figure 8.6), the range of "wrong" markup rates that nonetheless allow greater profit, will be smaller, other things being equal. So, managers must first ask themselves the ques�on: "What is the likely magnitude of search costs that would need to be spent to gain suitably reliable es�mates of the cost and revenue curves?" Then, they must couple this es�mate with their best es�mate of the price elas�city of demand to complete an analysis of whether their chosen markup rate is likely to be profit- maximizing if they avoid search costs.

Markup Pricing and Demand Shifts

When the demand curve shi�s (due to a change in one of the "shi� variables" such as customer incomes or adver�sing) the profit-maximizing price (and hence the profit-maximizing markup rate) would generally need to change because the price elas�city of demand will be different at the new price level associated with each quan�ty level. But in the case of iso-elas�c demand shi�s, where the price elas�city stays the same at each output level when the demand curve shi�s, the same markup rate remains profit-maximizing despite the shi� of the demand curve. In Figure 8.7, we show an iso-elas�c demand shi� from D to Dʹ that involves a rota�on of the demand curve while maintaining the same price axis intercept value, shown as P. Since the demand curve rotates from the same intercept point, the marginal revenue curve must also rotate to maintain its "same intercept, twice the slope" rela�onship with the demand curve. But, as you can see in Figure 8.7, the shi�ing demand curve does not require a change in the profit-maximizing price, because MR = MC at the same price level (P*) as before. Quan�ty demanded increases from Q to Qʹ units per period due to the shi� in demand but the same price (P*) and

markup rate (100%) remain appropriate because the price elas�city remains the same (ε = –2) at both price-quan�ty combina�ons.9

(h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.2#ch08txt9)

Figure 8.7: Constant markup rate despite an iso-elas�c shi� of the demand curve

It is probably unlikely that a demand shi� would be precisely iso-elas�c, but we have seen in the preceding sec�on that it does not need to be so for a con�nua�on of the same markup rate to remain the profit-maximizing policy if significant search costs must be expended to find the exact intercept and slope of the demand curve. What we have demonstrated here is that iso-elas�c demand shi�s mean that the firm does not have to change its price level. Thus, the demand shi�s that are somewhere close to being iso-elas�c will make it likely that the exis�ng markup rate remains profit-maximizing. This reduces the financial incen�ve to incur search costs to iden�fy the precise loca�on of the demand and costs func�ons.

Markup Pricing and Cost Shifts due to Inflation

Infla�on is the con�nuing increase in cost and price levels due to the decrease in the value of the na�onal monetary unit (i.e., the dollar). At the firm level, management may find that their AVC has risen, for example, by 10% over the past year and that this has reduced their profit. They may wonder whether they should simply raise their price level by 10% to restore their profit margin and overall profit level, or whether they should increase prices by more or less. The answer depends on how much more their customers can afford to pay. If customers' incomes have also risen by 10%, this product will require the same propor�on of their incomes as it did before the period of infla�on. In Figure 8.8, we show a situa�on where each point on the ini�al demand curve (D) has shi�ed ver�cally by a constant propor�on—10% in this case—to the new demand curve Dʹ. This reflects each customer's ability to pay 10% more for each unit of quan�ty demanded. Similarly, the AVC = MC curve has shi�ed ver�cally by 10% due to infla�onary increases in the cost of direct materials, direct labor, and variable overheads. Note that the new marginal cost and revenue curves (MCʹ and MRʹ) cross at the same output level (Q*) as the pre-infla�on MC and MR curves. Also note that the profit-maximizing markup remains the same, at 40% in this case. Thus, in the case where customers' incomes and the firm's AVC rise by the same percentage due to infla�on (or, indeed for reasons that apply only to this firm and its customers) it is profit-maximizing to con�nue to use the same markup rate as before.

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increased costs and a decrease in the value of the na�onal monetary unit.

Figure 8.8: Constant markup rate with infla�onary shi�s of both demand and costs

Note that Figure 8.8 is drawn in nominal-dollar terms, that is, using the nominal values for costs and prices. In real terms—constant purchasing power terms —neither the demand curve nor the costs curves would have shi�ed at all. But, people generally think (and make purchases) in nominal dollar terms. Managers must be aware of their customers' percep�ons of the firm's price increases and ensure that they are not perceived to be passing on more than is jus�fied by their cost increases. In this case, AVC increased by 60 cents and, yet, the price was increased by 84 cents, which, although not an increase in real terms, might be perceived as such by customers. In most cases, of course, the customer is not privy to the magnitude of cost increase suffered by the firm. But in some cases the magnitude of cost increase is known to the public; for example, when the Federal Reserve Bank raises the rate at which it lends money to the commercial banks, by, say, 50 basis points (e.g., from 3.5% to 4%), home-mortgage holders typically complain loudly if the commercial banks subsequently raise their mortgage rates by more than 50 basis points—from 5% to more than 5.5%. Yet as we have seen above, the profit-maximizing home mortgage rate may well be higher than 5.5% if the commercial banks' other direct costs and variable overheads have also increased. Managers in this case must argue to their customers that their other costs have gone up, while, at the same �me, assuring their shareholders that they are trying to maximize shareholder return on investment.

We should note in this context that fixed costs, comprising deprecia�on charges against revenue for capital costs incurred in preceding periods plus unavoidable present period costs such as managers' salaries, lease costs, and so on, may not have increased at the rate of infla�on in the current produc�on period (due to lags in salary increases, longer term agreements on lease costs, and so on). Thus, the increase in the firm's contribu�on to overheads and costs due to the applica�on of a constant markup rate during infla�onary �mes might actually increase profit, rather than simply restoring the profit rate to the prior level. Thus, those customers (and the business press) who cri�cize the commercial banks who "pass on more than their cost increase" may have a valid point. On the other hand, their managers would argue that salaries and lease costs must be adjusted upwards in subsequent periods (to retain the use of resources and to maintain produc�on efficiency) and that the "leads and lags" roughly offset each other in the longer term.

Markup Pricing as a Coordinating Device

Finally, in jus�fica�on of markup pricing, we note that it provides a simple and effec�ve means for firms who compete in oligopolis�c markets, where mutual dependence must be recognized, to coordinate their price increases in infla�onary �mes or in response to other cost increases that apply specifically to firms in that industry. By all firms independently using a markup pricing rule, the firms each raise their prices in "conscious parallelism" (see Chapter 7), and, thus, avoid raising their price independently and suffering a highly-elas�c demand reac�on along the upper half of the kinked demand curve. Coordina�on of price increases by oligopolists allows their market shares to remain the same, other things remaining equal. Retaining market share is important to firms because it avoids fluctua�ons in output levels and the consequent need for fluctua�ons in the purchases of variable inputs and the hiring of direct labor.

6. To express X in terms of the MC = MR rule, we start by finding an alterna�ve expression for MR. Since MR = dTR/dQ, and TR = P • Q, and since P also depends on Q, we use the chain rule of deriva�on to express marginal revenue as MR = P + Q(dP/dQ). Now mul�ply and divide the last term in equa�on 8-11 by P to find MR = P + QP/P • dP/dQ. Factoring out P we obtain MR = P {1 Q/P • dP/dQ}. Now note that the term in the brackets is equivalent to one plus the reciprocal of the price elas�city of demand (since ε = dQ/dP • P/Q). Hence, MR = P (1 + 1/ε). Se�ng MC = MR and invoking the special case where MC = AVC we have AVC = P (1 + 1/ε), which can be rewri�en as P = AVC + [–1/(ε + 1)] AVC. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.2#return6) ]

7. Recall that the subs�tu�on effect is the change in quan�ty demanded due to a change in the price of a product rela�ve to the unchanged prices of its subs�tute (rival) products, with a no�onal compensa�on for the change in real income (the purchasing power of money income) caused by the price change. The income effect is the change in the quan�ty demanded due to the change in real income due to the changed price of the focal product, holding rela�ve prices constant. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.2#return7) ]

8. Search costs are a fixed (or overhead) cost because they are unrelated to output levels (and thus are not a variable cost). Search costs would be expended and then become a sunk cost that the firm hopes will be paid for later by the contribu�on margins of units sold. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.2#return8) ]

9. Note that although price elas�city stays the same for any given price level despite shi�s in the demand curve, the price elas�city changes as we move along each demand curve. A different concept is the iso-elas�c demand curve, where price elas�city is the same at all points along a given demand curve—such curves must be rectangular hyperbolas where the rectangular areas under all points on the curve, where the area is defined by each price (height) �mes its associated quan�ty (width), are the same. Looking back at the price elas�city formula you will appreciate that for elas�city to remain at the same level at different prices, the changes in the slope of the curvilinear demand curve (ΔP/ΔQ) must be exactly offset by the change in the ra�o of P/Q as we "move down" the demand curve. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.2#return9) ]Processing math: 0%

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Auc�ons are o�en used to establish the price of highly differen�ated items. Auc�ons can occur in person or through websites such as eBay, which allow poten�al buyers to bid on a wide variety of items online.

Market Price

8.3 Pricing Topics

In this final sec�on, we examine some varia�ons on the theme of profit-maximizing prices. We shall consider price discrimina�on, in which different customers are charged different prices, and bundle pricing, where the prices of products that are complementary in consump�on are adjusted to increase the firm's overall profits.

Price Discrimination

Price discrimina�on, for our purposes here, is defined as the prac�ce of charging different prices to different buyers (or groups of buyers) for essen�ally the same product, where customer differences mean they are more or less willing to pay higher prices. Note that under the United States' Robinson-Patman Act, price discrimina�on is defined as systema�cally charging different prices to different people for iden�cal products sold under the same circumstances and is illegal. However, here we are considering products sold under different circumstances where those circumstances effec�vely produce different a�ributes of the product, such as the convenience of immediate versus delayed delivery. We shall consider three types of price discrimina�on. You will likely recognize that it is happening all around us in the business world and that customers willingly pay higher prices in some circumstances.

Auc�ons

Auc�ons are examples of first-degree price discrimina�on, defined as the seller forcing the buyer to pay the maximum or close to the maximum that the buyer is willing to pay. An auc�on discriminates against customers who are willing to pay more by requiring them to pay higher prices, and ul�mately allows only the person who was willing to pay the most to actually purchase the product. There are two styles of auc�on. In a so-called English auc�on, prices are bid upwards sequen�ally by compe�ng buyers un�l the last bid made is the highest price that anyone is prepared to bid, and thus, the sale is made to the last bidder. English auc�ons are rou�nely used to establish the price of highly differen�ated or unique items such as racehorses, pain�ngs, the bric-a-brac of celebri�es, and private homes or apartments. The winning bidder is charged a rela�vely high price, and that price is determined by the maximum price that the second-highest bidder was prepared to pay plus the small increment included in the last bid by the winning bidder. Note that the winning bidder may have been prepared to pay even more, but only had to offer slightly more than the second-most-keen buyer. English auc�ons are now prevalent online—you can buy (or sell) a wide variety of items in an auc�on procedure on eBay or similar auc�on-based websites.

Auc�ons are typically used where it is difficult to decide what is the appropriate price for the item that the seller wishes to sell, and the auc�on mechanism allows the best price (on the day, given the a�endance of all interested poten�al buyers) for the seller to be achieved. Alterna�vely, it allows the buyer to get a bargain if no one else is interested in bidding the price higher. All poten�al buyers have a reserva�on price, which is the maximum price they would be willing to pay for the item. As the bid price moves above their reserva�on prices the poten�al buyers drop out of the bidding un�l only one is le�. As long as the highest bid exceeds the seller's reserve price, which is the minimum that the seller is prepared to accept for the item, then a sale is made.

A Dutch auc�on sees the price level offered by the seller move downward from an unrealis�cally high level un�l a point where one of the poten�al buyers jumps in and accepts the latest price offered by the seller. This is how flowers are sold by the Dutch at the flower auc�ons in Holland, hence the name. Other large markets, such as fish markets, also use the Dutch auc�on method since it is an efficient way to sell large quan��es of product in the shortest possible �me. But how does it work? Again, all buyers need to form a personal view, before the bidding starts, as to the highest price they would pay (their reserva�on price). This, in turn, is based on how much the item is worth to them in revenue or in intrinsic terms. For example, suppose a New York flower merchant knows that he or she can sell 40 dozen roses at $30 each and that buying them at $15 per dozen in Amsterdam would provide an acceptable profit margin a�er airfreight and other costs. The New Yorker is thus unwilling to jump in as the price �cks down from $20 to $19, $18, $17, and $16, but jumps in when the price �cks down to $15. If that buyer were to wait any longer, someone for whom $14 is a sa�sfactory price would jump in, and the New York

merchant would miss out on the opportunity to make profit.10

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In ordinary markets where the market clearing price (i.e., the one that causes supply to equal demand) is received by all sellers and paid by all buyers, this price is less than the reserva�on price for all except the marginal buyer—who is the buyer willing to pay no more than the market price. All other buyers were willing to pay more than the market price but did not have to (assuming a downward- sloping demand curve, i.e., differen�ated products). Note that a demand curve is, a�er all, simply a line joining the reserva�on prices of all the buyers in the market.Processing math: 0%

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Prices Based on Urgency of Demand

Second-degree price discrimina�on involves discrimina�ng among groups of buyers on a �me or urgency basis. Those who want to buy the product soonest pay a higher price than those who are willing to wait un�l later. The sale of innova�ve new electronic and so�ware products typically involve higher prices at first for the pioneer's product, with lower prices subsequently as the pioneer's AVC curves shi� downwards due to the learning curve and as new rivals enter the market with compe��ve prices for their own version of the new product. Another example is the pricing of �ckets for new movie releases. First runs in city theaters are priced substan�ally above the second runs in suburban and rural theaters. Later, the movie is typically shown on cable television (for a subscrip�on fee) and, finally, it is shown on free-to-air television (supported by adver�sing revenue). Another common example is provided by passenger airfares—business users usually book flights at rela�vely short no�ce whereas tourists and people visi�ng family members can plan ahead— hence, airlines discriminate on the basis of how urgently you want to fly.

Some rural and suburban moviegoers certainly do go to the city to see first-run movies. They do this because their reserva�on price to see a par�cular movie is above the price asked by the city movie theater. But, city markets are rela�vely thick markets, while suburban and rural markets are rela�vely thin markets, meaning that there is a rela�vely large number of buyers willing to pay the first-run price in the city compared to a rela�vely small number of buyers willing to pay the first-run price in suburban and rural markets. Accordingly, it is profit-maximizing for the movie producer to show a new movie first in larger city theaters for a higher price and later in smaller suburban and rural theaters for a lesser price.

Figure 8.9: Pricing based on urgency of demand

Figure 8.9 demonstrates the circumstance in which the demand for the new product in period 1 (e.g., first-run movies), shown as D1, is rela�vely strong, and

the profit-maximizing price and sales, P1 and Q1 respec�vely, are found where MC = MR1.The demand for the product in period 2 is less strong, shown as

D2. The buyers represented here include those who did not buy the product in period 1 (those whose reserva�on prices are less than P1) plus new buyers

who have entered the market as a result of reading favorable reviews or listening to word-of-mouth endorsements for the new movie or new product in general. The profit-maximizing price in period 2 is thus P2. Similarly in period 3, the demand curve D3 is made up of those who did not purchase in period 1

or 2 because their reserva�on price is below P2, as well as new buyers who have now entered the market a�er learning about the new product and the

benefits it offers. Thus, the price level is reduced period by period as the seller discriminates among buyers based on their reserva�on prices which reflect their urgency to purchase the new product.

Prices Based on Differing Elas�ci�es of Demand

Third-degree price discrimina�on is a situa�on whereby a seller can simultaneously charge two or more different prices to customers who have differing price elas�ci�es of demand for the same product or service. Examples of third-degree price discrimina�on are the telephone and electricity price differen�als between household users and business users of these services. Telephone companies may also charge different amounts for long-distance calls according to whether they are made during business hours or in the evenings and on weekends. When signing up for these services in the first instance, the seller wants to know whether it is a business account or a private (household) account. Sellers charge businesses a higher price because their demand is less elas�c—the business must use the phone and use electricity in the normal conduct of their business, and employees will be less interested in saving electricity or in shortening their phone calls than will householders who, a�er all, have to pay their own bills. Also, businesses need to make calls in business hours because people may resent receiving business calls a�er hours, or because they only have a work phone number and want to reach the other personProcessing math: 0%

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Telephone service is an example of third-degree price discrimina�on. Telephone companies o�en charge different rates for long-distance calls according to the �me and day of the week they are placed.

at their desk. Householders can wait un�l the evening or weekends to call friends or family at their homes (or on their cell phones).

Another common situa�on is that the firm has both a domes�c market and an export market for its output (see Figure 8.10). Its domes�c price can be somewhat higher than its export price because the price elas�city of demand in the export market is typically much higher, due to the greater presence of subs�tutes and rival suppliers, and also customer income levels in export markets may be lower than domes�c customers' incomes. In Figure 8.10, we demonstrate how the firm should choose two different prices for two different groups of customers such that it maximizes its overall profit.

Figure 8.10: Third degree pricing discrimina�on

Note in Figure 8.10 that demand is shown to be rela�vely more inelas�c in market 1 and rela�vely more elas�c in market 2. The manager's task is to choose the total output level and then allocate it between markets 1 and 2 such that MC = MR in both markets. To do this we need to find an aggregate measure of marginal revenue; we do this by the horizontal addi�on of the MR1 and MR2 curves. In the third panel of Figure 8.10 we show the ΣMR curve (Σ is the

Greek le�er sigma) which connotes the horizontal sum of the two MR curves. Note that it follows MR1 un�l MR2 "kicks in" at which point it kinks and

represents the sum of both MR1 and MR2. The ΣMR curve falls to intersect the MC curve at the total output level shown as ΣQ in the right-hand part of

Figure 8.10, where ΣQ is necessarily the sum of Q1 and Q2. Thus, the firm should set price P1 in market 1 and price P2 in market 2 to maximize its profit. 11

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While a firm may suspect that the price elas�city of demand differs significantly between two main groups of customers that demand its product, it will typically require significant expenditure on search ac�vity to es�mate those price elas�ci�es with any great accuracy. We have seen that if managers do know the firm's AVC = MC level, or, more generally, the shape of the MC curve, they can make "informed guesses" about the price elas�ci�es based on their knowledge of the customers from previous market experience. Given these es�mates managers can derive the demand and marginal revenue curves that are needed to find the profit-maximizing price and output levels. While these es�mates may contain substan�al errors, we know that there is scope for error due to the avoidance of more expensive search processes that are not invoked by making educated guesses. Managers who believe that one group of their customers is substan�ally more price elas�c than the rest might find a way to isolate these two groups of customers and tenta�vely raise the price against the more inelas�c group and lower the price faced by the more elas�c market. Before too long the result of this market experiment would be clear —sales in the more elas�c market would expand more than the sales in the less elas�c market fell and profits would increase, or not. If it seems to be working the manager might push the experiment a li�le further to see if profit can be increased s�ll further. If the experiment fails, the manager could revert to the former pricing strategy.

Simple rules o�en suffice; for example, airlines simply charge less for airfares if the dura�on of the return trip involves a Saturday night. They reason that most business travelers want to be home for the weekend and, thus, charge more for flights between any par�cular two ci�es if the trip does not include a Saturday night stopover. Similarly, textbook publishing companies charge more for textbooks sold in the wealthier U.S. market than they do for the same textbooks sold in less-wealthy foreign countries, with the price being different according to the shipping address. Cheaper U.S. textbooks sold in Asia are o�en labeled: "Not for resale in the U.S.," and legal ac�on is threatened if a bookseller were to buy books at export prices and a�empt to resell them in the United States at domes�c prices. Given the knowledge managers should have about the firms' markets, they should be able to devise a decision rule that effec�vely separates their customers into two or more discrete groups based on differing price elas�city of demand, and then set different prices for different subgroups of customers.Processing math: 0%

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"Buy one get one free" and "25% off your next purchase" are examples of bundle pricing, which is used to en�ce consumers to spend more than they ini�ally intended and thus increase overall revenue for the business.

Bundle Pricing

Bundle pricing is the prac�ce of combining two or more products and selling them at a single "package" price that is less than the combined prices of the products if sold separately. The purpose of bundle pricing is to induce the buyer to spend more than they would have if they had only bought one unit of the product, and thus increase the overall revenue of the firm. You have likely seen many examples of bundle pricing. A coffee shop might offer coffee for $3 and a croissant for $1.50 if sold separately, or offer both for $3.95 as a package deal. Computer so�ware is typically bundled with computer hardware at a single price. Restaurants offer fixed-price menus that include, for example, soup, main course, and dessert for a single price that is less than the a-la-carte menu prices of these items added together. Retailers offer free parking if you buy something at their store. Professional sports teams and symphony orchestras offer season �ckets that are less than the total price of �ckets to all the individual performances.

Bundling Complementary Goods

As long as the incremental revenue accruing to the firm from the bundle price exceeds the incremental costs of producing and selling the two or more products, the firm will increase its profits by prac�cing bundle pricing. Let's consider the example of the offer of a pair of complementary goods, such as coffee and a croissant, for $3.95. Assume that the average variable cost of each is constant and, thus, equal to marginal costs, and that there are no incremental fixed costs, so that the marginal cost of each is equal to the incremental cost of each, as shown in Table 8.2.

Table 8.2: Bundle pricing example—coffee and croissant for $3.95 Coffee sold separately Croissant sold separately Coffee and croissant bundle

Incremental revenue $3.00 Incremental costs Direct materials $0.30 Direct labor 0.50 Variable overhead 0.20 Total incremental costs $1.00 Contribu�on margin = $2.00 Units sold before were 50 Total contribu�on before = $100 Units sold a�er will be 30 Total contribu�on a�er = $60

Incremental revenue $1.50 Incremental costs Direct materials $0.40 Direct labor 0.15 Variable overhead 0.05 Total incremental costs $0.60 Contribu�on margin = $0.90 Units sold before were 20 Total contribu�on before = $18 Units sold a�er will be 10 Total contribu�on a�er = $9

Incremental revenue $3.95 Incremental costs Direct materials $0.70 Direct labor 0.65 Variable overhead 0.25 Total incremental costs $1.60 Contribu�on margin = $2.35 Units sold before were 0 Total contribu�on before = $0 Units sold a�er will be 60 Total contribu�on a�er = $141

In this case, we can see that the coffee and croissant bundle makes a lesser contribu�on margin (i.e., $2.35) than the sum of the two component items (i.e., $2.90) but offering them in combina�on sells more coffees and croissants than before, such the total contribu�on rises from $118 before the introduc�on of bundle pricing to $210 a�er the introduc�on of bundle pricing. This happens because some customers who previously bought only coffee or only a croissant now see the bundle as a superior value proposi�on, and in addi�on some new buyers are a�racted into the coffee shop because the bundle offers them a superior value proposi�on. No�ce also that some buyers con�nue to buy just coffee or just a croissant at the a-la-carte prices. These extra 30 coffees contribute an addi�onal $60 and the extra 10 croissants contribute an extra $9 to the $141 contributed by the bundle to make the total contribu�on from coffee and croissants $210.

From the customer's perspec�ve, the bundle price offers an addi�onal item for an addi�onal amount of money that may be less than the customer's reserva�on price for that addi�onal item. In this case if a customer who regularly buys coffee has a reserva�on price for a croissant of, say $1.25, that customer would not buy a croissant at the a-la- carte price of $1.50, but would buy one when it is included in the bundle price because it costs only an addi�onal $0.95 over the cost of a coffee alone. Oppositely, a regular customer who buys only croissants and has a reserva�on price for coffee of say, $2.50, would not buy a coffee at the a-la-carte price of $3.00 but would buy one in the bundle because the addi�onal cost of the coffee is effec�vely only $2.45 more than the croissant alone. Similarly, people whose reserva�on price for coffee is below $3 (say $2.75) and for a croissant is below $1.50 (say $1.25) would not be customers of this coffee shop at the a-la-carte prices but would now find the "coffee plus croissant" bundle price an a�rac�ve proposi�on because the bundle price of $3.95 is less than their combined reserva�on price of $4.00. Finally, some customers who currently buy both coffee and croissants at other coffee shops would be a�racted to this par�cular coffee shop because it has effec�vely reduced its price for this combina�on of products.

Discounts for Larger Volumes

It may surprise you that discounts for larger volumes are another form of bundle pricing. Many firms offer a product in different sized packages and rather than mul�plying the unit price by the number of units, o�en say things like "20% off the second meal"; or "three for the price of two"; or "pay for 4 nights, get the 5th night free" and so on. Similarly, Coca-Cola prac�ces bundle pricing by offering its product in containers of various sizes—note that bo�les that hold twice as much cola cost less than twice as much as the smaller bo�le, for example. The larger sizes can be viewed as bundles, or mul�ples, of the smallest size offered for sale and the buyer is effec�vely given a discount per unit (per fluid ounce) for purchasing larger quan��es.

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Again, the customer will choose to buy the larger size container, or the greater number of units in the bundle, if the incremental cost to the buyer is less than the sum of his or her reserva�on prices for the extra volume or units provided. We illustrate this in Table 8.3 where we show the results of a market experiment where several different sizes of liquid detergent are offered at the prices indicated, as well as the reserva�on prices of three different buyers.

Table 8.3: Quan�ty discounts and reserva�on prices for three customers Size of container (fluid ounces)

Seller's price for each size

Customer A's reserva�on prices

Customer B's reserva�on prices

Customer C's reserva�on prices

10 $2.00 $2.80 $2.50 $1.80

20 $3.50 $3.60 $3.30 $3.40

30 $5.00 $4.80 $4.20 $4.90

40 $6.25 $6.00 $5.00 $6.20

50 $7.50 $7.00 $5.50 $7.55

The shaded prices show where the customer's reserva�on price is greater than the seller's asking price. We see that customer A would buy either of the first two sizes because the bundle price is less than this customer's reserva�on price for each of these sizes. Customer B would only buy the smallest size because the bundle price of larger sizes exceeds his or her reserva�on price. Customer C would not buy any of the smaller sizes but would enter the market and buy the 50-ounce container if it is available at the price of $7.55 or less. If these three customers are representa�ve of the market as a whole, this seller might decide to offer the product in the 10-, 20-, and 50-ounce sizes since it would sell a total of 90 ounces of detergent (rather than only 20 ounces if offering only the smallest size) for every three customers like these.

Whether the detergent firm will want to do that depends on the incremental costs of producing the larger-sized containers and filling them with detergent, of course. The rule, as you know, is that if the incremental revenue is greater than the incremental cost, then the firm should do it. In the simple example here with only three buyers, the incremental revenue of selling an addi�onal 20-ounce container and a 50-ounce container is $11. If the market is made up of 100,000 buyers like these three, the incremental revenues would be $1.1 million, all other things being equal. So, if the incremental fixed costs of se�ng up addi�onal filling lines, plus the incremental costs of the direct materials, labor, and variable overhead costs, are less than $1.1 million, it would appear to be a profit-making decision to go ahead with the three different sized containers of detergent.

10. "Ticks down" is the appropriate wording because Dutch auc�ons typically use a large clock-like dial and the single hand is first ratcheted around to start �cking down from a very high price. Each �ck is followed by a very short pause (like a cheaper watch) or in some cases (like a Rolex) the hand slides smoothly around the dial. The buyers either yell when they reach their reserva�on price, or to avoid arguments about who was slightly faster, the auc�on house provides bu�ons to push so that the buyer might win by milliseconds. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.3#return10) ]

11. In the case where MC is an upward sloping curve, this curve should be superimposed on the ΣMR curve in the third panel of Figure 8.10, and at the MC level where it intercepts the ΣMR curve, a horizontal line would be drawn back across the other two panels to find the output levels at which the MR curves (MR1 and MR2, respec�vely) fall to meet that MC level

in each of the two markets. To demonstrate that you understand this, visualize the upward sloping MC curve in the right-hand panel of Figure 8.10 that would cause the prices and outputs shown to be profit maximizing. Hint: it needs to cut the ΣMR curve at output level ΣQ. [return (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/sec8.3#return11) ]

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Summary

In this chapter, we have applied theore�cal concepts learned in the preceding chapters to the pricing decisions of the firm in prac�cal situa�ons where

1. the cost of informa�on about the cost and revenue func�ons might be low enough to allow es�mates to be made of the cost and revenue func�ons such that the manager can proceed to use the "marginalist pricing" rule of MC = MR and

2. the informa�on search costs is expected to be higher such that the managers make the business decision to forego any further informa�on search ac�vity and use a markup pricing rule whereby a percentage markup over average variable costs is used to arrive at the price level to be charged.

Instead of obtaining es�mates of the underlying demand func�on, we saw that an es�mate of the price elas�city of demand provides enough informa�on, given current price and quan�ty demanded data, to derive expressions for the firm's demand and marginal revenue curves. Par�cularly, if average variable costs are expected to be constant at the current observed level, it then becomes a simple ma�er to apply the marginalist pricing rule to find the profit- maximizing price and output level.

We saw that the marginalist pricing rule and the markup pricing rule can be reconciled—that for every price obtained by the MC = MR rule there is a corresponding markup rate that would arrive at the same price. We found that the profit-maximizing markup rate is determined by the price elas�city of demand, and that the size of the profit-maximizing markup is inversely propor�onal to the (absolute) value of the price elas�city; that is, the higher the price elas�city in absolute terms, the lower is the profit-maximizing markup rate. Thus, products with more and closer subs�tutes and for which price is a larger propor�on of customers' incomes should be expected to carry smaller markup rates than products with few close subs�tutes and which are rela�vely inexpensive compared to customers' incomes.

Next, we showed that the avoidance of search cost provides a margin for error for the markup rate. This margin for error is wider the larger are the expected costs of informa�on search necessary to gain reliable es�mates of the cost and revenue curves. Thus, the actual markup rate u�lized can diverge significantly from the true (but unknown) profit-maximizing rate, such that the actual price and quan�ty demanded are quite different from the profit- maximizing levels. Despite this, the firm can make a larger profit as compared to first incurring the search costs and then se�ng the profit-maximizing price and output. Further, demand shi�s that are iso-elas�c, or roughly so, will poten�ally leave the current markup rate as the profit-maximizing one and not require a recalibra�on of the markup rate. Also, shi�s of the cost and demand curves due to infla�on are also likely to leave the current markup rate as op�mal if the curves are equally affected by infla�on.

Finally, in this chapter we considered ways to increase profits by se�ng different prices for different customers, discrimina�ng against those with higher reserva�on prices, more urgent demand, and less elas�c demand. We also considered bundle pricing, which allows the firm to extract more revenue from customers and increase profits as long as the incremental revenue exceeds the incremental costs associated with this pricing strategy.

In the following two chapters, we con�nue to examine the pricing decision of business firms in the context of new products (Chapter 9) and compe��ve bidding and price tendering (Chapter 10).

Ques�ons for Review and Discussion

Click on each ques�on to reveal the answer.

1. If the regression equa�on that best fits the TVC data collected for a firm is a linear equa�on, does that mean that the diminishing returns to the variable factors of produc�on is not applicable to that par�cular firm? Why or why not? (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/boo

The regression analysis of a limited range of output levels may show constant returns to variable inputs over that range of output levels without meaning that diminishing returns would not be observed at higher output levels. A linear line of best fit is compa�ble with a situa�on in which there are ini�ally increasing returns and later diminishing returns, but the data has been collected only from output levels around the point of inflec�on in the TP (or TVC) curve.

2. Explain in words (and some symbolic nota�on) how knowledge of the current price and quan�ty demand levels, combined with an es�mate of the price elas�city of demand at that price and quan�ty combina�on, can be used to derive an equa�on for the demand curve. (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/boo

The demand curve can be expressed as P = a + bQ, so if we already know the current values of P and Q we would need to find only the values of a and b. We can deduce the values of a and b if we know the price elas�city at the current price. Since ε = (1/b) . (P/Q) and we know ε, P, and Q, we can solve for b and subsequently solve for a in the demand curve since it is now reduced to one equa�on with only one unknown value.

3. Suppose a firm chooses the price of its product by applying a 50% markup to its average variable costs, which are constant over the relevant range. Suppose also that top management agree that a 10% price increase would cause sales to fall by about 15%. What should they do now (if they want to maximize short-run profits)? (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/boo

For the 50% mark-up to be profit maximizing, that would imply the price elas�city is −3.0, using the formula for the profit-maximizing mark-up, X = [−1/(ε +1)]. But top management agree that price elas�city is −15%/10% = −1.5. Subs�tu�ng for ε in the mark-up equa�on, we would find X = [−1/(−1.5 +1)] = −1/−0.5 = 2, which implies that a 200% mark-up over AVC would be profit maximizing. Management should raise prices to confirm their elas�city data and subsequently their mark-up rate.

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4. Explain why the demand for some products is more elas�c than it is for other products. (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/boo

Price elas�city is higher if there are more and closer subs�tutes, and/or if the price is rela�vely high and represents a larger propor�on of consumers' incomes. The closer the subs�tutes are the more likely it is that the consumer will switch to a subs�tute if the price of X rises, and the more income it takes to purchase the product, the more likely the consumer is to switch to a cheaper subs�tute.

5. Explain in your own words why the magnitude of search costs (that would be required to ascertain the demand and costs curves) is posi�vely related to the range of prices (and markup rates) that allow the firm to make more profit than it could if it first incurred search costs and then set the price where MC = MR. (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/boo

The higher the search costs are the more wrong you can be about the mark-up rate. Search cost avoided is opportunity revenue that can be added to the sales revenue at the current price. If search was undertaken and revealed that the price should be changed, the contribu�on from sales would need to rise by more than the search costs incurred before the "search then change price" strategy would be worthwhile.

6. Explain why an outward shi� of the demand curve that causes the value of price elas�city to be more or less unchanged at the current price level would not cause managers to want to raise the price. (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/boo

An iso-elas�c demand shi� that leaves the price elas�city at about the same level would cause managers to leave price at the same level if they are happy that the current price level was previously profit maximizing (given the prospect of large search costs). Unless search costs are small the managers are unlikely to want to re-examine price elas�ci�es or demand curve es�ma�on, since the search costs would be expected to outweigh any subsequent improvement in profits.

7. If infla�on causes the firm's costs to rise by a higher percentage than it causes customers' incomes to rise, explain whether the firm should raise or lower its markup rate to maximize its profit. (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/boo

If infla�on impacts the firm's costs more than it does the consumers' incomes, managers would want to raise prices to maximize profits because the intersec�on of the MC and MR curves would occur at a lower output level, and demand curves are downward sloping. Thus they would want to increase their mark-up rate. In a kinked-demand-curve oligopoly situa�on they would expect their rivals to also raise prices since the cost increase is likely to be suffered by all firms.

8. Suppose I own a valuable oil pain�ng (e.g., the Mona Lisa) and wish to sell it. For a given group of poten�al buyers, which auc�on method, English or Dutch, would deliver the highest price, and why? (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/boo

In theory, the Dutch auc�on would garner the higher price, equal to the reserve price of the person or organiza�on that values the pain�ng most highly (whereas the English auc�on price might be only $1 above the reserve price of the person or organiza�on that values it second-most highly). This assumes that all poten�al bidders are present at the auc�on, that they have a clear idea of their reserva�on price, and that they all understand that in the Dutch auc�on they will lose the item if they are not the first to bid and stop the clock.

9. What is the difference between first-degree, second-degree, and third-degree price discrimina�on? On what bases does the discrimina�on occur? (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/boo

First-degree price discrimina�on (PD) discriminates against buyers on the basis of their willingness to pay, inducing the person who is willing to pay the most to bid the highest. Second-degree PD discriminates against buyers based on their urgency of demand—those who want the product sooner pay more than others who are willing to wait longer. Third-degree PD discriminates against buyers based on their price elas�city of demand—those whose demand is more inelas�c pay more than others whose demand is more price elas�c.

10. Describe several ways that the firm might u�lize bundle pricing to increase its profit from the same group of poten�al customers. (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/boo

Bundle pricing can be prac�ced by offering the product in different sized containers where larger containers cost less than propor�onally more. Another bundling method is to offer 2 for the price of 1, or 11 for the price of 10, or frequent-buyer programs. A third method is to combine unlike but usually complementary products into a package deal that is priced at less than the simple sum of the prices of the products when sold separately.

Decision Problems

1. You have been called in as a consultant to the manager of Smith's Bookstore who is wondering if the present price of $9.95 for paperback novels is profit maximizing. The firm has experimented with prices every week for the past six months and collected data on prices and quan��es demanded for paperback novels sold each week. You conduct regression analysis of the data and obtain the following results (where P is in dollars and Q represents thousands of books sold per week):

Regression equa�on Q = 49.147 − 2.941P

Coefficient of determina�on R

2 = 0.96

Standard error of es�mate Se = 0.128

Standard error of the coefficient

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Regression analysis of the firm's weekly total variable cost and sales levels over the same period provide the following informa�on:

Regression equa�on TVC = 102.35 + 0.025Q2

Coefficient of determina�on R

2 = 0.92

Standard error of es�mate Se = 0.232

Standard error of the coefficient

Sβ = 0.003

a. What is the profit-maximizing price for the paperback novels sold by this bookstore? b. What is your predic�on for the level of sales at that price, and what is your 95% confidence interval for sales at that price? c. What is the price elas�city of demand at the price you are recommending?

2. The Laura Ann Bou�que purchases a line of inexpensive dresses from an importer and pays $30 per dress regardless of volume. These dresses are marked up by about one-third to sell at $39.95 each and quan�ty demanded averages 300 dresses per week.

a. What would the price elas�city of demand have to be for that markup rate to be profit maximizing? b. Laura Ann wants to maximize profit and is wondering if she is using the appropriate markup rate. Suppose she pays $500 for a marke�ng student to

conduct a survey of customers and this results in an es�mate of price elas�city of ε = –3.5. What price is profit maximizing if this es�mate can be regarded as being reliable?

c. Was it worthwhile for Laura Ann to spend the $500 on search costs?

3. Archibald Tires buys car �res at an average price of $600 per set of four, applies a 25% markup, and sells them for an average price of $750 per set, regardless of volume. Archibald typically sells about 60 sets of �res per week at that price. Joe Archibald has conducted an informal survey of his customers and has es�mated that if he raised his price by 10% he would lose 1 out of every 9 customers.

a. Derive an expression for the demand curve for these �res. b. What is the profit-maximizing price and quan�ty demanded, based on Joe's es�mate of price elas�city? c. What do you advise Joe Archibald to do, and why?

4. The Thomas Tent Company has two markets for its mid-size tent, the domes�c market and the export market. The demand curve for the domes�c market is characterized by P = 100 − 15Q, while the demand curve for the export market is P = 60 − 2.5Q, where P is the price in U.S. dollars and Q represents thousands of tents. The firm has one produc�on facility that manufactures the tents, which has a total cost func�on characterized by TC = 10,800 + 20Q +

0.1Q2 in the relevant range of outputs. a. What is the profit-maximizing level of mid-size tent produc�on for the firm? b. How should Thomas Tent divide this output between the two markets? c. What price should be set in the domes�c market? d. What price should be set for the export market?

5. Greener Grass Company (GGC) competes with its main rival, Be�er Lawns and Gardens (BLG), in the supply and installa�on of in-ground lawn watering systems in the wealthy western suburbs of a major east-coast city. Last year, GGC's price for the typical lawn system was $1,995 compared with BLG's price of $2,100. GGC installed 9,130 systems, or about 55% of total sales, and BLG installed the rest. (No doubt many addi�onal systems were installed by do-it- yourself homeowners since the parts are readily available at hardware stores.) GGC has substan�al excess capacity—it could easily install 25,000 systems annually, as it has all the necessary equipment and can easily hire and train installers. Accordingly, GGC is considering expansion into the eastern suburbs, where the homeowners are less wealthy. In past years, both GGC and BLG have installed several hundred systems in the eastern suburbs but generally their sales efforts are met with the response that the systems are too expensive. GGC has hired you to recommend a pricing strategy for both the western and eastern suburb markets for this coming season. You have es�mated two dis�nct demand func�ons, as follows:

Qw = 1,035.548 − 6.07164Pgw + 2.83Pbw + 2,100Ag − 1,500Ab + 0.2348Yw

for the western market and

Qe = 49,714.29 − 30.7692Pge + 6.984Pbe + 1,180Ag − 950Ab + 0.0825Ye

for the eastern market, where Q refers to the number of units sold; P refers to price level; A refers to adver�sing budgets of the firms (in millions); Y refers to average disposable income levels of the poten�al customers; the subscripts w and e refer to the western and eastern markets, respec�vely; and the subscripts g and b refer to GGC and BLG, respec�vely. GGC expects to spend $1.5 million on adver�sing this coming year and expects BLG to spend $1.2 million on adver�sing. The average household disposable income is $55,000 in the western suburbs and $25,000 in the eastern suburbs. GGC does not expect BLG to change its price from last year, since it has already distributed its glossy brochures (with the $2,100 price stated) in both suburbs, and its TV

commercial has already been produced. GGC's cost structure has been es�mated as TVC = 755.363Q + 0.005Q2 where Q represents single lawn watering systems.

a. Derive the demand curves for GGC's product in each market.Processing math: 0%

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b. Plot graphically the demand and MR curves for each market, and also show GGC's combined marginal revenue curve (ΣMR) and its MC curve. Show graphically the quan��es that should be produced and sold, and the prices that should be charged, in each market.

c. Confirm your quan�ty and price results algebraically. d. Calculate the price elas�ci�es of demand in each market and discuss these in rela�on to the prices to be charged in each market. e. Add a short note to GGC management outlining any reserva�ons and qualifica�ons you may have concerning your price recommenda�ons.

Key Terms

Click on each key term to see the defini�on.

bundle pricing (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

The prac�ce of combining two or more products and selling them at a "package" price that is less than the combined prices of the products if sold separately. The purpose of bundle pricing is to induce the buyer to spend more and thus increase the overall revenue of the firm.

Dutch auc�on (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

A "reverse" auc�on where the seller's bidding begins at an unrealis�cally high price then drops down progressively un�l somebody accepts the asking price, and thereby wins the item.

English auc�on (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

An auc�on where the ar�cle's ini�al cost is set at a rela�vely low level, and then the poten�al buyers compete with each other, bidding the price higher un�l only one buyer with the highest bid price is le�, who then wins the item.

first-degree price discrimina�on (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

A system of pricing whereby the seller induces the winning buyer to pay at or near the maximum that the buyer is willing to pay for an item. Auc�ons are examples of first-degree price discrimina�on.

infla�on (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

A process by which the prices of goods and services in a given country con�nue to rise over a period of �me, which means that people can buy fewer goods and services with any given amount of money due to the deprecia�on of the monetary unit (dollar).

iso-elas�c demand shi�s (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

Shi�s of the demand curve where price elas�city stays the same at any given price level. Thus, if marginal costs are constant, the same markup rate con�nues to be the profit-maximizing rate, despite shi�s of the demand curve.

level of significance (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

The degree of confidence we can have that the regression analysis of data from a sample indicates the true rela�onship that exists between the variables in the whole popula�on.

marginalist pricing (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

A form of pricing where the firm sets price using the "marginal cost equals marginal revenue" rule, by using data obtained by firms based on their prior produc�on and market experience.

markup pricing (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

The prac�ce of se�ng price by adding an amount, calculated as a percentage of direct costs per unit (AVC), to the AVC, to determine the asking price of a product.

price discrimina�on (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

A pricing prac�ce where a firm (legally) charges its customers different prices for what is basically the same product (e.g., air travel) because that base product is delivered at different �mes or in different circumstances that contribute addi�onal value to some consumers who are prepared to pay a higher price.

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real terms (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

An assessment of the monetary value of an asset or other item that is expressed in constant-purchasing power dollars, as dis�nct from nominal (or monetary) terms where price is expressed in terms of the face value of a currency that is deprecia�ng due to infla�on.

reserva�on price (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

The maximum price that a buyer is willing to pay for a given item, or in the case of sellers, the minimum price for which they will sell an item.

second-degree price discrimina�on (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

A pricing prac�ce that involves charging higher prices to those whose demand is more urgent, and lower prices to those whose demand is less urgent, such as short-no�ce airfares cos�ng more than advance-purchase airfares.

seller's reserve price (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

The minimum price that the seller is prepared to accept for a given item in order for a sale to be made.

thick markets (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

Markets that are rela�vely dense with many poten�al buyers of a par�cular item within a given radius of the seller(s), such as exists for most products in large ci�es.

thin markets (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

Markets in which there are rela�vely few buyers in a given area, such as in rural and remote areas, or for products in dense areas of popula�on that very few buyers need or can afford. Examples are the market for hip replacements or uncut diamonds.

third-degree price discrimina�on (h�p://content.thuzelearning.com/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AUBUS640.12.1/sec�ons/fm/books/AU

A pricing prac�ce that involves charging higher prices to those whose demand is less price elas�c, and lower prices to those whose demand is more price elas�c, such as business class airfares cos�ng more than economy class airfares.

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