(Stackelberg) In the market for soft drinks, two major competitors are PepsiCo and The Coca-Cola Company. Suppose they are the only producers of soft drinks and they face an world- market inverse demand of P = 200 – 0.5Q, where Q represents the total demand for soft drinks (QP + QC). If PepsiCo’s per-unit cost is $40, and Coca-Cola’s per-unit cost is $30, and neither firms have fixed costs. Suppose The Coca-Cola Company is the leader (makes its output decision before PepsiCo) and PepsiCo is the follower (makes its output decision after The Coca-Cola Company).
a. (20 pts) What are the Nash equilibrium price and quantities in this game?
b. (10 pts) What are the profits for the two competitors?
You have one item for sale in your store. The marginal cost of production is MC=$10, the probability of getting a high value customer who is willing to pay $25 is 30% and the probability of getting a low value customer willing to pay $15 is 70%. Compute the expected profit under the following different scenarios:
a. (10 pts) You choose a unique price to post and find your expected profit. Which price maximizes your expected profits?
b. (10 pts) You organize an auction (2nd price, sealed) and two people show up. Find your expected auction profit.
c. (10 pts) Go back to part b. You impose a reservation price (minimum you are willing to accept to sell the good) for the auction. The winner of the auction has to pay at least the reservation price of the seller. What is your expected profit is your reservation price is $20?