Homework Problem Set #15 KEY
E303
Davis, Spring 2006
1. Joe Holiday is a monopoly provider of Fishing Reels in a remote fishing village on a barrier island off the Gulf Coast. Currently he is selling is BassMaster reels for $50 each. Joe doesn’t know the precise demand function for fishing reels, but he estimates price elasticity of demand to be -2. If the reels cost Joe $30 each, is he maximizing profits? If not, what would be the profit maximizing price?
Is $50 a profit maximizing price? Y/N (circle one)
Profit Maximizing Price______P = MC/(1+1/h) = 30/(1-1/2) = 60
2. Consider the inverse demand relationship P = 21-Q. The total cost function is TC = 50 – Q.
a. What is the optimal price, quantity and maximum profits available to the seller, if the seller can post only a single price to all consumers?
MR = 21-2Q = 1 implies that Q = 10, so P = 21-10 = 11 and profits are
($11(10) – [50-$1(10)] = $55.
Optimal Price______11______
Optimal Profits ____50______
b) Illustrate in the coordinate axes provided below the maximal profits available to this seller, if the seller is forced to post a single price.
P$6
$1 /
5 Q
3. Now suppose that the seller is free to post consider post different prices to each different consumer.
a) Identify the profit maximizing quantity and maximal profits for the seller under these circumstances.
The firm would charge a different price to each consumer equal to their marginal valuation. Profits would equal .5(21-1)(20) = 200
Maximum Profits with Perfect Price Discrimination_$150 (take out fixed cost)
b) Shade in the appropriate area in the figure below.
P11
1 /
10 Q
c) What are the two conditions must be satisfied in order for a seller to realize maximum profits with perfect price discrimination? Why is each condition necessary?
Condition 1: - No resales: Low value sellers will drive price down via resales
Condition 2:- Ability to size up willingness to pay______.
4. Consider again the demand relationships in (2) and (3) above, but suppose that the demand relationship was for a single consumer who was considering joining a health club. Describe the membership and access fee structure that would optimize profits. (Be explicit)
Membership Price: $200 (equal to consumer surplus)
Access Fee: $1 per unit (marginal cost).
5. Suppose that Handsome Joe Hedley needs a new summer suit. He is willing to pay up to $300 for a first linen suit, and $200 for a second. If suits cost Smith & Co. Fine Clothiers $100 each, identify the sales quantity from setting price equal to $300 and $200 what pricing structure would maximize profits?
Quantity Profits
Price $300: 1 $200
Price $200 2 $200
How might Smith use Second Degree price discrimination to increase profits? What are the maximum profits available?
Pricing Strategy: Charge a high price for a first suit, but then a lower price for
additional suits.
Maximum Profits: Charging $300 for the first suit and $200 for the second, Smith
earns $300.
6. Suppose that an airline can divide travelers into economy class and business class. The price elasticity of demand for the business class is -1.5, and for the economy class is -3. If the marginal cost of a seat on an flight from Richmond to New York is $20, what are the optimal prices for each group?
P1 = 20/[1+1/-1.5] 60
P2 = 20/[1+1/-3] 30