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Simple Pricing

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CHAPTER

Aggregate demand or market demand is the total number of units that will be purchased by a group of consumers at a given price.

Pricing is an extent decision. Reduce price (increase quantity) if MR > MC. Increase price (reduce quantity) if MR < MC. The optimal price is where MR = MC.

Price elasticity of demand: e = (% change in quantity demanded) ÷ (% change in price)

Estimated price elasticity is used to estimate demand from a price and quantity change.

[(Q1 - Q2)/(Q1 + Q2)] ÷ [(P1 - P2)/(P1 + P2)]

If |e| > 1, demand is elastic; if |e| < 1, demand is inelastic.

%ΔRevenue ≈ %ΔPrice + %ΔQuantity

Elastic Demand (|e| > 1): Quantity changes more than price.

Inelastic Demand (|e| < 1): Quantity changes less than price.

MR > MC implies that (P - MC)/P > 1/|e|; in words, if the actual margin is bigger than the desired margin, reduce price

Equivalently, sell more

Four factors make demand more elastic:

Products with close substitutes (or distant complements) have more elastic demand.

Demand for brands is more elastic than industry demand.

In the long run, demand becomes more elastic.

As price increases, demand becomes more elastic.

continued

Income elasticity, cross-price elasticity, and advertising elasticity are measures of how changes in these other factors affect demand.

It is possible to use elasticity to forecast changes in demand:

%ΔQuantity ≈ (factor elasticity)*(%ΔFactor).

Stay-even analysis can be used to determine the volume required to offset a change in costs or prices, which is how businesses often implement marginal analysis.

continued

Hot Wheels

Mattel introduced Hot Wheels in 1968

They kept price below $1.00 for 40 years, even as production costs rose

Finally tested a price increase, experienced profit increase of 20%

Why? Profit=(P-C)xQ

Businesses tend to focus on C and Q, neglect P

In many instances, companies can make money by simply raising price

Simple Pricing

In this chapter, we consider “simple pricing”:

A single firm selling a single product at a single price

Most firms sell: in competition with rivals; multiple products, and at different prices, so this is rare

Important to understand simple pricing first though

Simple pricing has become part of business vernacular

When your boss says that “demand is elastic,” she often means that price is too high.

Background: Consumer Surplus and Demand Curves

First Law of Demand - consumers demand more (purchase more) as price falls, assuming other factors are held constant.

Consumers make consumption decisions using marginal analysis, consume more if marginal value > price

But, the marginal value of consuming each subsequent unit diminishes the more you consume.

Consumer surplus = value to consumer - price paid

Definition: Demand curves are functions that relate the price of a product to the quantity demanded by consumers

Consumer Surplus and Demand Curves Example

Pizza consumer

Values first slice at $5, next at $4 . . . fifth at $1

Note that if pizza slice price is $3, consumer will purchase 3 slices

Pizza Demand Schedule

Pizza Example (cont.)

For the first slice, the total and marginal value are the same at $5

For the second, the marginal value is $4, while the total value is $9 = $5 + $4

Pizza Value Table

Background: Aggregate Demand

Aggregate Demand: the buying behavior of a group of consumers; a total of all the individual demand curves.

To construct demand, sort by value.

Pizza Consumer Surplus

Aggregate Demand (cont.)

Demand curves describe buyer behavior and tell you how much they will buy at a given price.

If something other than price causes an increase in demand, we say that “demand shifts” to the right or “demand increases” such that consumers purchase more at the same prices

Pricing Trade-Off

Pricing is an extent decision

Profit= Revenue - Cost

Demand curves turn pricing decisions into quantity decisions:

“what price should I charge?” is equivalent to “how much should I sell?”

Fundamental tradeoff:

Lower priceg sell more, but earn less on each unit sold

Higher priceg sell less, but earn more on each unit sold

Tradeoff created by downward sloping demand

Marginal analysis of pricing

Marginal analysis finds the profit increasing solution to the pricing tradeoff.

It tells you which direction to go (to raise or lower price), but not how far to go.

Definition: marginal revenue (MR) is change in total revenue from selling another unit.

If MR>0, then total revenue will increase if you sell one more.

If MR>MC, then total profit will increase if you sell one more.

Proposition: Profit is maximized when MR = MC

Example: Find the Optimal Price

Once you reach the 4th unit, total profit decreases by %0.50 because the MR from the 4th unit is only $1, which is less than $1.50 MC

Therefore, the profit maximizing quantity is 3 and we see that the price is $5.00 for 3 units to be sold

Optimal Price

How Do We Estimate MR?

Price elasticity allows us to calculate MR.

Definition: price elasticity of demand (e)

(%change in quantity demanded)

(%change in price)

If |e| is less than one, demand is said to be inelastic.

If |e| is greater than one, demand is said to be elastic.

Mistake in 3rd Edition

The Correct Answer

Elastic Demand implies |e|>1

Inelastic Demand implies |e|<1

The following figures are mis-labled (The inequality in parentheses should be reversed)

Elastic Demand [|e| < 1]

Inelastic Demand [|e| > 1]

Price Elasticity Example

Mayor Marion Barry increased taxes on gasoline sales in DC by 6%.

Before the tax, gas station predicted that the increase in a sales tax would reduce quantity demanded by 40%.

The gas station owners were indirectly arguing that gasoline revenue, and the taxes collected out of revenues, would decline because gasoline sales in DC has a very elastic demand.

Estimating elasticities

Definition: Arc (price) elasticity=

[(q1-q2)/(q1+q2)]

[(p1-p2)/(p1+p2)]

Discussion: Compute elasticity, when price changes from $10 to $8, and quantity changes from 1 to 2?

Example: On a promotion week for Vlasic, the price of Vlasic pickles drops by 25% and quantity increases by 300%.

Is the price elasticity of demand -12?

HINT: could something other than price be changing?

Intuition: MR and Price Elasticity

Revenue and price elasticity are related by the following approximation.

%Rev ≈ %P + %Q

Elasticity tells you the size of |%P| relative to |%Q|

If demand is elastic

If P↑ then Rev↓ • If P↓ then Rev↑

If demand is inelastic

If P↓ then Rev↑ • If P↑ then Rev↓

Formula: Elasticity and MR

Proposition: MR = P(1-1/|e|)

If |e|>1, MR>0.

If |e|<1, MR<0.

Discussion: If demand for Nike sneakers is inelastic, should Nike raise or lower price?

Discussion: If demand for Nike sneakers is elastic, should Nike raise or lower price?

Elasticity and Pricing

MR>MC is equivalent to

P(1-1/|e|)>MC

P>MC/(1-1/|e|)

(P-MC)/P>1/|e|

MR > MC means that (P-MC)/P > 1/|e|

The left side of the expression is the current margin = (P-MC)/P

The right side is the desired margin, or the inverse elasticity = 1/|e|

If the current margin is greater than the desired margin, reduce the price because MR>MC and vice versa.

Intuition: the more elastic demand becomes (1/|e| becomes smaller), the less you can raise price over MC because you lose too many customers

What Makes Demand More Elastic?

5 factors that affect demand elasticity and optimal pricing:

Products with close substitutes have elastic demand.

Demand for an individual brand is more elastic than industry aggregate demand.

Products with many complements have less elastic demand.

In the long run, demand curves become more elastic.

As price increases, demand becomes more elastic.

Factor 1

1. Products with close substitutes have elastic demand.

Consumers respond to a price increase by switching to their next-best alternative.

If their next-best alternative is a very close substitute, then it doesn’t take much change in price for them to switch.

When Mayor Barry raised the price of gasoline, DC commuters began buying gasoline in nearby Virginia and Maryland.

Factor 2

2. Demand for an individual brand is more elastic than industry aggregate demand.

Rough rule of thumb: brand price elasticity is approximately equal to industry price elasticity divided by brand share

Example:

elasticity of demand for all running shoes = -0.4

Market share of Nike running shoes is 20%

Price elasticity of demand for Nike running shoes is -0.4/.20 = -2

Using our optimal pricing formula, this would give Nike a desired margin of 50%

Factor 3

3. Products with many complements have less elastic demand.

Products that are consumed as a larger bundle of complementary goods have less elastic demand.

Example: iPhones have less elastic demand because of the number of apps run on them

If the price of an iPhone increases, you are less likely to substitute to another product due to the complementary apps

Factor 4

4. In the long run, demand curves become more elastic.

This can also be explain by the speed at which price information is spread; or the ability of consumers to find more substitutes in the long run.

Example: ATM fees

At a selected number of ATMs, a bank raised user fees from $1.50 to $2.00.

When informed of the fee increase, users typically completed the current transaction but avoided the higher-priced ATMs in the future.

Factor 5

5. As price increases, demand becomes more elastic.

Example: high-fructose corn syrup (HFCS)

Primary use is a caloric sweetener in soft drinks

Sugar is the perfect substitute for HCFS

Import quotas and sugar price supports have raised the US domestic price of sugar about twice that of HFCS.

Bottlers have shifted to HFCS.

Bottlers have no close substitute for low-priced HFCS, although as the price of HFCS approaches that of sugar, demand for HFCS becomes very elastic.

Other Elasticities

Definition: income elasticity measures the change in demand arising from a change in income

(%change in quantity demanded)  (%change in income)

Inferior goods (negative): as income increases, demand declines

normal goods (positive): as income increases, demand increases

Definition: cross-price elasticity of good one with respect to the price of good two

(%change in quantity of good one)  (%change in price of good two)

Substitute (positive): as the price of a substitute increases, demand increases

Complement (negative): as the price of a complement increase, demand decreases

Stay-Even Analysis

Stay-even analysis tells you how many sales you need when changing price to maintain the same profit level

How to implement marginal analysis of pricing using stay-even quantity:

%ΔQ = (%ΔP)

(%ΔP + margin)

Margin=40%, %ΔP=5%, then %ΔQ = 11.1%

In other words, a 5% price increase would be profitable if quantity went down by less than 11.1%.

Use elasticity estimates or marketing surveys to determine whether quantity would go down by 11.1%.

Cost-Based Pricing

Our expression for optimal pricing, MR=MC or (P-MC)/P= 1/|e|, takes into account the firm’s cost structure and its consumer demand

Often, the consumer side is ignored in pricing decisions, leading to cost-based pricing. Why?

Often, firms do not have the demand picture

They need to invest in a market research division to take profitability seriously

Extra: Quick and Dirty estimators

Linear Demand Curve Formula:

e= p / (pmax-p)

Discussion: How high would the price of the brand have to go before you would switch to another brand of running shoes?

Discussion: How high would the price of all running shoes have to go before you should switch to a different type of shoe?

Extra: Market Share Formula

Proposition: The individual brand demand elasticity is approximately equal to the industry elasticity divided by the brand share.

Discussion: Suppose that the elasticity of demand for running shoes is –0.4 and the market share of a Saucony brand running shoe is 20%. What is the price elasticity of demand for Saucony running shoes?

Proposition: Demand for aggregate categories is less-elastic than demand for the individual brands in aggregate.

Title?

In 1994, the peso devalued by 40% in Mexico

Interest rates and unemployment shot up

Overall economy slowed dramatically and consumer income fell

Concurrently, demand for Sara Lee hot dogs declined

This surprised managers because they thought demand would hold steady, or even increase, since hot dogs were more of a consumer staple than a luxury item.

Surveys revealed the decline was mostly confined to premium hot dogs

And, consumers were using creative substitutes

Lower priced brands did take off but were priced too low.

Failure to understand demand and to price accordingly was costly.