Problem 1. Exercise 4 and 5 from Chapter 5 in Shy (page 93)
Problem 2. Exercise 3 and 5 from Chapter 6 in Shy (pages 128-129)
Problem 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 cB = $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 pb A and pb B, and the equilibrium profits ∏A b and ∏B b .
Problem 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 pN = 12 - qN and pS = 6 - qS
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 = qN + qS 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 pN and pS, 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.
Problem 5. In Pittsburgh, PA there are two suppliers of spaghetti, labeled as firm Topo and firm Gigio. Spaghetti is considered to be a homogenous good. Let p denote the price per package, qT quantity sold by firm Topo, and qG the quantity sold by firm Gigio. Formally, each firm bears a production cost of cT = cG = $2 per package
Pittsburgh’s aggregate inverse demand function for distilled water is given by p = 12-Q = 12-qT-qG, where Q = qT +qG denotes the aggregate industry supply of spaghetti in Pittsburg. Solve the following problems:
a. Solve for firm Topo's best-response function, qT = RT(qG). Also solve for firm Gigio's best-response function, qG = RG(qT). Show your derivations.
b. Solve for the Cournot equilibrium output levels qc T and qc G. State which firm sells more spaghetti (if any) and why.
c. Solve for the aggregate industry supply and the equilibrium price of spaghetti in Pittsburgh.
d. Solve for the profit level made by each firm, and for the aggregate industry profit. Which firm earns a higher profit and why?