Please answer all questions. Briefly explain your answers.
Question No. 1 (30%)
A profit maximizing firm produces three products X, Y and Z. The firm has no costs. There are three customers 1, 2 and 3. Each customer is willing to purchase at most one unit of each of the three products. The firm cannot price discriminate between customers. The following table presents the willingness to pay of each of the three customers for each of the three products:
Product X Y Z Customer 1 10 12 5 2 8 14 0 3 4 16 7
So, for example, Customer 1 is willing to pay no more than $10 for purchasing one unit of product X and Customer 3 is willing to pay no more than $7 for purchasing one unit of product Z.
Which of the two alternatives above is better for each of the three customers?
Question No. 2 (30%)
You run a sport club that offers fitness guidance by the hour.
Your cost is $40 per hour and you have no other costs.
You serve 2 types of customers in equal number: 100 youngsters and 100 seniors.
The weekly demand by each youngster is: where q is the number of hours per week and p is the price per hour.
Each senior customer is willing to pay no more than $50 per hour, for the first 3 hours, and zero thereafter.
Question No. 3 (40%)
Consider a monopolist seller (with no production costs) and two buyers,such that buyer 1 makes her buying decision first. Each buyer wants to purchase exactly one unit of the supplier’s product. The buyers’ actual valuation of the product, , is either 6 or 2. The two realizations are thought to be equally likely by the buyers (and the seller) without any additional information. Neither the buyers nor the seller know about the buyers’ true values before any such information.
Assume that the seller can costlessly provide additional private information to the buyers through advertising, which may alter their expected valuation of the product. Upon viewing the advert, the buyers receive one of the two equally likely signals, or . The signal provides information about the product’s true value or desirability. The accuracy of the signal is denoted by . Remember from your lectures that the accuracy of the signal determines how precise is the information contained in the advert about the true value – a buyer’s assessment of her valuation is less precise the smaller is (for any given signal). Let and denote how a buyer updates the probability of her true valuation given a particular signal she receives of accuracy.
Consider the following stage game:
Stage 1: The seller chooses. (The seller’s choice becomes publicly observable.)
Stage 2: The buyers observe their private signal, and updates their assessment of valuation.
Stage 3: The seller sets a single uniform price for both the buyers.
Stage 4: Buyer 1 makes the purchase decision. If she buys, she gives a perfectly informative signal to buyer 2. If she does not, the only information available to buyer 2 is the advertisement.
Stage 5: Buyer 2 makes the purchase decision.