Any Questions from Last Class?

Chapter 6Simple Pricing

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Chapter 6 – Take Aways

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 = [(Q1 - Q2)/(Q1 + Q2)] ÷ [(P1 - P2)/(P1 + P2)] is used to

estimate demand from a price and quantity change. 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.

Chapter 6 – Take Aways

MR > MC implies that (P - MC)/P > 1/|e|; that is, the more elastic demand is, the lower the price.

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.

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.

Review of Chapter 5

Break-even quantity and entry decision Q=F/(P-MC)

Break-even price and shut-down decision Profit=Q(P-AC)

Sunk costs are vulnerable to postinvestment hold-up

Discount rates indicate willingness to trade future for current dollars

Introductory Anecdote In 1994, peso devalued by 40% in Mexico

Interest rates and unemployment shot up Overall economy slowed dramatically and consumer income fell

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

Surveys revealed decline mostly confined to premium hot dogs And, consumers using creative substitutes Lower priced brands took off but were priced too low

Failure to understand demand and to price accordingly was costly

Background: Consumer Surplus and Demand Curves First Law of Demand - consumers demand

(purchase) more as price falls, assuming other factors are held constant

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

Consumers attempt to maximize their surplus by using marginal analysis

Consumer surplus = value to consumer less price paid

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

Background: Consumer Surplus and Demand Curves (cont.) Hot dog consumer

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

Note that if hot dogs priced at $3, consumer will purchase 3 hot dogs, not 5

Background: Aggregate Demand Aggregate Demand: each consumer wants one unit; arrange them by what

they are willing to pay. To construct demand, sort by value.

Discussion: Why do aggregate demand curves slope downward? Role of heterogeneity? How to estimate?

Price Quantity RevenueMarginal Revenue

$7.00 1 $7.00 $7.00$6.00 2 $12.00 $5.00$5.00 3 $15.00 $3.00$4.00 4 $16.00 $1.00$3.00 5 $15.00 -$1.00$2.00 6 $12.00 -$3.00$1.00 7 $7.00 -$5.00

$0.00

$2.00

$4.00

$6.00

$8.00

$0.00 $2.00 $4.00 $6.00 $8.00

Marginal Analysis of Pricing

Pricing is an Extent Decision Profit=Revenue-Cost Lower prices mean higher sales Demand curves help us make decisions to

increase profits by modeling revenue Particularly marginal revenue Should I sell another unit?

Pricing Tradeoff

Lower pricesell more, but earn less on each unit sold

Higher pricesell less, but earn more on each unit sold

Tradeoff created by downward sloping demand

Marginal Analysis of Pricing

Marginal analysis finds the right solution to the pricing tradeoff. But only direction, not magnitude.

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

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

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

Proposition: Profits are maximized when MR=MC

Example Start from the top

If MR>MC for next step, reduce price

Continue until the next price cut would result in MR<MC

Price Quantity Revenue MR MC Profit $7.00 1 $7.00 $7.00 $1.50 $5.50 $6.00 2 $12.00 $5.00 $1.50 $9.00 $5.00 3 $15.00 $3.00 $1.50 $10.50 $4.00 4 $16.00 $1.00 $1.50 $10.00 $3.00 5 $15.00 –$1.00 $1.50 $7.50 $2.00 6 $12.00 –$3.00 $1.50 $3.00 $1.00 7 $7.00 –$5.00 $1.50 –$3.50

How do We Estimate MR?

Price elasticity is related to MR.

Definition: price elasticity= (%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.

Estimating Elasticities

Definition: Arc (price) elasticity=[(q1-q2)/(q1+q2)] [(p1-p2)/(p1+p2)].

Discussion: price changes from $10 to $8; 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%.

Estimating Elasticities (cont.)

3-Liter Coke Promotion Instituted to meet Wal-Mart promotion

Initial Final % Change Elasticity3 Liter Q 3-liter 210 420 66.67% -3.78

P of 3-liter $1.79 $1.50 -17.63%

2 Liter Q 2-liter 120 48 -85.71% 4.86P of 3-liter $1.79 $1.50 -17.63%

Total Liters Q liters 870 1356 43.67% -2.69P liters $0.60 $0.51 -16.23%

Product

Intuition: MR and Price Elasticity %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↓

Discussion: In 1980, Marion Barry, mayor of the District of Columbia, raised the sales tax on gasoline sold in the District by 6%.

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|

Discussion: e= –2, p=$10, mc= $8, should you raise price?

Discussion: mark-up of 3-liter Coke is 2.7%. Should you raise price?

Discussion: Sales people MR>0 vs. marketing MR>MC.

What Makes Demand More Elastic? 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.

Describing Demand with Price Elasticity First law of demand: e<0 (price goes up,

quantity goes down). Discussion: Do all demand curves slope

downward?

Second law of demand: in the long run, |e| increases. Discussion: Give an example of the second law of

demand.

Describing Demand (cont.)

Third law of demand: as price increases, demand curves become more price elastic, |e| increases. Discussion: Give an example of the third law of demand.

Sugar Price

HFCS Quantity

HFCS Price

HFCS Demand

Other Elasticities Definition: income elasticity=(%change in quantity demanded)

(%change in income)

Inferior (neg.) vs. normal (pos). 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 (pos.) vs. complement (neg.). Definition: advertising elasticity=(%change in quantity)

(%change in advertising) .

Discussion: The income elasticity of demand for WSJ is 0.50. Real income grew by 3.5% in the United States. Estimate WSJ demand

Stay-Even Analysis Stay-even analysis tells you how many sales you

need when changing price to maintain same profit level

Q1 = Q0*(P0-VC0)/(P1-VC0) When combined with information about elasticity of

demand, the analysis gives a quick answer to the question of whether changing price makes sense

To see the effect of a variety of potential price changes, we can draw a stay-even curve that shows the required quantities at a variety of price levels

Stay-Even Curve Example

Note that if demand is elastic, price cuts increase revenue

When demand is inelastic, price increases will increase revenue

$16

$18

$20

$22

$24

$26

$28

$30

300 400 500 600 700 800 900 1000

Elastic Demand (e = -4.0)

Inelastic Demand (e = -0.5)

Alternate Intro Anecdote 1993 Snickers was first Western-style candy

bar in Russia Priced the same as in Great Britain Distributor marked up 600% and pocketed the difference Mars did not appreciate how novel their product was and

how much customers would be willing to pay; the distributor, however, did understand.

By the time Mars figured understood this, competitors had entered and the novelty had decreased dramatically

The purpose of this chapter is to teach you how to price products and to avoid mistakes like this.

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.