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1 . Perfect Competition Consider a market that faces the following market supply and demand functions Q3 = 2+2p Q\" = 16-39 where identical rms face the total cost function of 1 TC : s + 3:; + Eg? a) What is the market price? b) Derive the average variable cost, average total cost, and marginal cost functions. 0) In the short run, how much does each rm produce? (:1) In the short run, how much economic prot or loss will be obtained? e) Based on the results in part ((1), will rms want to enter or exit the market? Why? f) In the long run, what is the market price? (Hint: You can nd the long run rm quantity by setting two of the cost functions equal to one another) 2 . General Equilibrium Consider a market with two goods, 3: and z, and two consumers, A and B. The utility functions for consumers A and B are as follows 5:4: (73: E9 5% mum {3.le N which- Dam: and the initial endowments for each consumer are 6A : (4,2) 63 : (2,6) where consumer B is endowed with 2 unit of good :5 and 6 units of good z, respectively. a) Draw the Edgeworth Box (Don't worry about the shape of the utility curves. Just pick a general shape that we have used before). b) Derive the contract curve. 3. Monopoly Consider a situation where a monopolist faces the following inverse market demand curve p = 132 2g and the following cost function T0 = 12g + 2132 a) Derive the marginal revenue and marginal cost functions. b) What are the equilibrium price and quantity if this market behaved as if it were perfectly competitive? 0) Calculate the Consumer Surplus, Producer Surplus and Welfare levels under perfect com- petition. d) What are the equilibrium price and quantity when the monopolist produces as a monop- olist? e) Calculate the Consumer Surplus, Producer Surplus and Welfare levels under monopoly. f) How much deadweight loss does the monopolist create? g) What could the government do to regulate the monopolist? 4. Price Discrimination Let's assume that you are a manager for an amusement park. Your company has just found new evidence that your market demand can be broken into two separate groups. These two groups, students and non-students, have two different demand functions. Those inverse functions are given below 1 Students: p = 8 1'3 Non-Students: p = 13 q [if you aggregated those functions, you would obtain 3) = 13 q if p > 8 and p = 9 q if p S 8). You also know that the total and marginal cost functions for the resort are T0 = 6+2q+-2 M0 = 2+9r a) Plot the inverse demand curve; for students and non-students. Include both marginal revenue curves and supply curves on the same graph. Make sure to label graphs clearly. b) Assume that you can only charge one price for tickets. What is the equilibrium price, quantity and prots if you choose to act as a monopolist? c) Now, let's assume that you choose to price discriminate. What is the equilibrium price and quantity for students and non-students? What is your new total prot? Round answers to two decimal places. d) Do the prices in part (c) make sense? Why would the price for one group be higher than the price for the other group? e) What kind of price discrimination is this? Is there any way you can prevent arbitrage in this case? If so, how? Why is it important to prevent arbitrage in price discrimination