Answer the following questions

The simultaneous-move game (shown below) is played twice, with the outcome of the first stage observed before the second stage begins. There is no discounting. The variable x is greater than 4, so that (4, 4) is not an equilibrium payoff in the one-shot game. What are the Nash equilibria in the one-shot game (Hint: there are 7 and no Nash equilibrium involves either picking Qi with positive probability)? For what values of x is the following strategy (played by both players) a subgame-perfect Nash equilibrium? Strategy for player i: Play Q in the first stage. If the first stage outcome is (Q1, Q2) then play Pi in the second stage. If the first stage outcome is (y, Q2) with y # Q1 then play R; in the second stage. If the first stage outcome is (Q1, z) with z # Q2 then play S; in the second stage. If the first stage outcome is (y, z) with y # Q1 and z # Q1 then play Pi in the second stage. P2 Q2 R2 S2 PI 2,2 x,0 1,0 0.0 Q1 0, x 4.4 -1,0 0.0 R 0,0 0.0 0,2 0,0 0.-1 0,-1 -1,-1 2.0l4. I-IrConsider a perfectly competitive market. Suppose that all rms are identical and have the same cost function G (q) = 4g. 32 (a) What is the equilibrium price, 310, facing a rm? Compute the market equilibrium quantity demanded if the market demand is g = 10 p. [In what follows, consider the monopolist's problem facing the demand q = 10 p. Cost is the same as above] (b) Compute the monopolist's optimal output, q\1. Suppose the market demand for your good is given by P=120-(1/5)0. The cost function for each firm is identical, and is given by c(q)=10+(1/10)g. a) If all firms in this market have the same technology and are price-takers, how many units should each firm produce if the market price for the firm's product is $20? b) Assuming the market clears, how many firms are in the market? ") If there is only one firm in the market (i.e. it is a monopoly), what price should it charge and how many units should it sell to maximize profits? 2. Suppose a monopolist having constant marginal cost equal to I (ie. c(Q)=Q) sells to two consumers. Consumer I has an inverse demand given by P (q,) = 3 - 3q, and Consumer 2 has an inverse demand of P2 (q2) = 4 - 4q2. Resale between the two consumers is not allowed. a) Assume the monopolist has to use uniform pricing. Calculate the monopolist's profit maximizing price and quantity. How much will each consumer consume at that price? b) Graphically show the outcome in part (a). ") Now assume that the monopolist can engage in third degree price discrimination. What are the profit maximizing prices that the monopolist should charge? Calculate the profits and compare them to part (a). 3. A monopolist has a single production plant in California with a total cost function of c(Q) = = Q2. where Q is total output. The good can be sold to two separate markets, those on the west coast and those on the east coast. There is no resale between coasts. The inverse demand function for the east coast is given by p = 100 - q, and the inverse demand function for the west coast is given by p = 80 - =qw. a) Calculate the monopolist's profus if he uses standard uniform pricing. b) The monopolist can build a second plant in Massachusetts (ice. an east coast plant) that is identical to the California plant (ice. west coast plant), and plans on producing output for each region at their respective plant. He will then treat these markets as separate, charging different prices to each market. If the cost of constructing the plant is $1200 should the monopolist build the second plant? How much should the monopolist be willing to pay for the plant? Explain.30 - Marginal cou Market demand Marginal revenue 35 50 70 235-35 Q 17.5.35 Figure 10.5 12) Suppose that Figure 105 shows a monopolist's demand curve, marginal revenue, and its cost. The 127 A monopolist would maximize its profit by producing a quantity of and by charging a price AT8, 165 151 50; 550 () 70: $30 D) There is not sufficient information. 13) Suppose that Figure 105 shows a monopolist's demand curve, marginal revenor, and its cast. At 13) the profit maximizing output level and price, the consumer surplus would be B) $1,235. (746125. 14) Suppose that Figure 10.5 shows an industry's market demand, its marginal revenue, and the 14) production costs of a representative firm. If the industry was perfectly competitive, it will produce a quantity of and charge a price of AJ 35: 565 B) 50, 450 () 70, $30 D) There is not sufficient information. 15) Suppose that Figure 10.5 shows an industry's market demand, its marginal revenue, and the 15) production costs of a representative firm. If the industry was perfectly competitive, the consumer surplus would be: Aj $2,450. B) $1,225. C) $6125. D) $262 5. 16) Refer to Figure 10.5. The deadweight loss associated with the monopoly would be: 16) A) $787.5. B) $612 5. () $762.5. D) There is not sufficient information