1. Chapter 6 Simple Pricing
Managerial Economics: A Problem Solving Approach (2nd Edition)
Luke M. Froeb,
Brian T. McCann,
Website, managerialecon.com
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2. Chapter 6 – Summary of main points
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.

3. Chapter 6 – Summary (cont.)
MR > MC implies that (P - MC)/P > 1/|e|; in words, if the actual markup is bigger than the desired markup, 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.
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.

4. Introductory anecdote: Gas prices
US: From early 2007 to mid 2008 gas prices rose in the US.
Gas prices caused people to find alternate methods of work and travel to avoid using gas.
Some farms began using mules instead of tractors
India: In Rajasthan, the rising gas prices caused many farmers to switch from tractors to camels on farms.
As oil prices rose, demand for camels increased.
Prices for camels tripled over a two-year period.
A US company, NNS, that produces potash fertilizer experienced an increase in input costs due to their use of petrochemicals.
NNS doubled the price of the generic fertilizer, and priced it’s branded fertilizer at a 35% premium above the generic price.
Costs increased rapidly over the first two quarters combined with NNS’s policy of quarterly price revision led to stockouts and a price that ended up being 25% below the generic – NNS could have earned $13 million but failed to maintain their premium

5. Background: consumer surplus and demand curves
First Law of Demand - consumers demand (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

6. Background: consumer surplus and demand curves (cont.)
Hot dog consumer
Values first dog at $5, next at $ fifth at $1
Note that if hot dogs price is $3, consumer will purchase 3 hot dogs
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7. 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.
Discussion: Why do aggregate demand curves slope downward?
Role of heterogeneity?
How to estimate?
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8. 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 price sell more, but earn less on each unit sold
Higher price sell less, but earn more on each unit sold
Tradeoff created by downward sloping demand

9. Marginal analysis of pricing
Marginal analysis finds the profit increasing solution to the pricing tradeoff.
It tells you only whether to raise or lower price, not .
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

10. Example: finding the optimal price
Start from the top
If MR > MC, reduce price (sell one more unit)
Continue until the next price cut (additional sale) until MR<MC
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11. How do we estimate MR? Price elasticity is a factor in calculating 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.
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12. Estimating elasticities
Definition: Arc (price) elasticity=
[(q1-q2)/(q1+q2)]  [(p1-p2)/(p1+p2)].
Discussion: Why, when price changes from $10 to $8, does quantity changes from 1 to 2?
Example: On a promotion week for Vlasic, the price of Vlasic pickles dropped by 25% and quantity increased by 300%.
Is the price elasticity of demand -12?
HINT: could something other than price be changing?
Note that in many examples, the arc price formula is not used for simplicity
Answer: In the Vlasic example, price of Heinz is coming off promotion and the Vlasic price is being advertised in the newspaper, in store coupons, and end of aisle displays.

13. Estimating elasticities (cont.)
3-Liter Coke Promotion (Instituted to meet Wal-Mart promotion)
Compute price elasticity of 3 liter coke; cross price elasticity of 2 liter coke with respect to 3 liter price;
Extra credit: aggregate elasticity of demand for 2 and 3 liter coke. (compute change in price index and change in liters consumed.
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14. Intuition: MR and price elasticity
Revenue and price elasticity are related.
%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%. What happened to gas sales and availability of gas? Why?
ANSWER to question: tax revenue declined by 40% because demand for gasoline in the district of columbia is very price elastic.

15. 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?

16. 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 prices?
Discussion: mark-up of 3-liter Coke is 2.7%. Should you raise the price?
Discussion: Sales people MR>0 vs. marketing MR>MC.

17. 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.

18. Describing demand with price elasticity
First law of demand: e < 0 ( as 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.

19. 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.
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20. Other elasticities Estimate WSJ demand
Definition: income elasticity measures the change in demand arising from a change in income
(%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; a change in demand arising form a change in advertising
(%change in quantity)  (%change in advertising) .
Discussion: The income elasticity of demand for WSJ is Real income grew by 3.5% in the United States.
Estimate WSJ demand

21. Stay-even analysis
Stay-even analysis tells you how many sales you need when changing price to maintain the same profit level
Q1 = Q0*(P0-VC0)/(P1-VC0)
When combined with information about the elasticity of demand, the analysis gives a quick answer to the question of whether or not 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.
Derivation of formula
Profit0 = P0*Q0 – VC0*Q0 – FC0
Profit1 = P1*Q1 – VC0*Q1 – FC0
Set equal and solve for Q1

22. Stay-even curve example
Note that if demand is elastic, price cuts increase revenue
When demand is inelastic, price increases will increase revenue
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23. 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?

24. 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.

25. Alternate introductory anecdote
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
Substitution to cat food mixed with eggs and rolled up in a tortilla.

26. Managerial Economics - Table of contents
1. Introduction: What this book is about
2. The one lesson of business
3. Benefits, costs and decisions
4. Extent (how much) decisions
5. Investment decisions: Look ahead and reason back
6. Simple pricing
7. Economies of scale and scope
8. Understanding markets and industry changes
9. Relationships between industries: The forces moving us towards long-run equilibrium
10. Strategy, the quest to slow profit erosion
11. Using supply and demand: Trade, bubbles, market making
12. More realistic and complex pricing
13. Direct price discrimination
14. Indirect price discrimination
15. Strategic games
16. Bargaining
17. Making decisions with uncertainty
18. Auctions
19. The problem of adverse selection
20. The problem of moral hazard
21. Getting employees to work in the best interests of the firm
22. Getting divisions to work in the best interests of the firm
23. Managing vertical relationships
24. You be the consultant
EPILOG: Can those who teach, do?
Managerial Economics - Table of contents