Homework

Question 1. Exercise 4 and 5 from Chapter 5 in Shy (page 93)

Question  2. Exercise 3 and 5 from Chapter 6 in Shy (pages 128-129)

Question 3. Two firms have technologies for producing identical paper clips. Assume that all paper clips are sold in boxes containing 100 paper clips. Firm A can produce each box at unit cost of cA = $6 whereas firm B (less efficient) at a unit cost of c_B = $8.

a. Suppose that the aggregate market demand for boxes of paper clips is p = 12 -Q/2, where p is the price per box and Q is the number of boxes sold. Solve for the Nash-Bertrand equilibrium prices p^b_A and p^b_B, and the equilibrium profits ∏_A^b and ∏_B^b.

Question 4. The demand function for concert tickets to be played by the Seattle symphony orchestra varies between nonstudents (N) and students (S). Formally, the two inverse demand functions of the two consumer groups are given by

p_N = 12 - q_N and p_S = 6 - q_S.

Thus, at any given consumption level nonstudents are willing to pay a higher price than students. Assume that the orchestra's total cost function is C(Q) = 10 + 2Q where Q = q_N + q_S is to total number of tickets sold. Solve the following problems.

a. Suppose the orchestra is able to price discriminate between the two consumer groups by asking students to present their student ID cards to be eligible for a student discount. Compute the profit-maximizing prices p_N and p_S, the number of tickets sold to each group of consumers, and total monopoly profit.

b. Suppose now the local mafia has distributed a large number of fake student ID cards, so basically every resident has a student ID card regardless of whether the resident is a student or not. Compute the profit-maximizing price, the number of tickets sold to each group of consumers, and total profit assuming that the monopoly orchestra is unable to price discriminate.

c. By how much the orchestra enhances its profit from the introduction student discounted tickets compared with the profit generated from selling a single uniform ticket price to both consumer groups.

Question 5. In Tacoma, WA there are two suppliers of distilled water, labeled as firm Aqua and firm Blue. Distilled water is considered to be a homogenous good. Let p denote the price per gallon, q_A quantity sold by firm Aqua, and q_B the quantity sold by firm Blue. Both firms are located close to a spring so the only production cost is the cost of bottling. Formally, each firm bears a production cost of c_A = c_B = $3 per one gallon of water. Tacoma's aggregate inverse demand function for distilled water is given by p = 12-Q =12-q_A-q_B, where Q = q_A +q_B denotes the aggregate industry supply of distilled water in Tacoma. Solve the following problems:

a) Solve for firm A's best-response function, q_A = R_A(q_B). Also solve for firm B's best-response function, q_B = R_B(q_A). Show your derivations.

b) Solve for the Cournot equilibrium output levels q^c_A and q^c_B. State which firm sells more water (if any) and why.

c) Solve for the aggregate industry supply and the equilibrium price of distilled water in Tacoma.

d) Solve for the profit level made by each firm, and for the aggregate industry profit. Which firm earns a higher profit and why?