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2. Consider a competitive industry with several identical rms. The long run av erage cost of a firm producing q units of output is given by Acm) = 10 sq + 12. Suppose factor costs are constant and there is free entry and exit. Suppose man ket demand is (206') = 31 P. where P denotes market price. Determine the number of firms in the industry in the long run equilibrium. A monopolist produces output Q at a cost of C(Q) = 4Q+ Q2 The market demand function is P(Q) = 12 - Q (a) Suppose the monopolist can only charge a single price. Calculate the mo- nopolist's profit-maximising price and quantity. [5 marks] (b) Calculate the deadweight loss under monopoly. [5 marks] (c) Suppose a regulator imposes a per unit tax of t on the deadweight loss under monopoly. The monopolist's profit is now given by P(@)Q - c(Q) - D(Q) where D(Q) is the deadweight loss at quantity Q. Suppose t = 4. Calculate the optimal quantity produced by the monopolist under this policy. [5 marks] (d) Suppose the monopolist can charge a two-part tariff consisting of a lump- sum fee and a per-unit price. In this case, what is the tax revenue from the [5 marks] policy in part (c)?QUESTION FOUR QUESTION FOUR (A) Give the following hypothetical end- of - period prices for shares of the Drill -on- Corporation, and assuming a current price of sh. 50 per share Probability 0.15 0.1 0.3 0.2 0.25 End of Period Price per Share 35 42 50 55 60 i) Calculate the rate of return for each probability; what is the expected return? The variance of end- of- period return; The range and semi-interquartile range ii) Suppose forecasting is refined such that probabilities of end- of- period prices can be broken down further, resulting in the following Page 4 of 5 Probability 0.01 0.05 0.07 0.02 0.1 0.3 0.2 0.15 0.05 0.05 End of period price per share 0 35 38.57 40 42 50 55 57 60 69 a) Calculate and explain the change in the expected returns, the range of returns and the semi- interquartile range of returns. b) Calculate the semi variance of the end - of period returns. Why might some investors be concerned with semi variance as a measure of risk QUESTION FOUR (B) Given two random variables x and y State of Nature Probability variable x variable y I 0.2 18 0 II 0.2 5 -3 III 0.2 12 15 IV 0.2 12 V 0.2 6 (i) Calculate the mean and variance of each of these variables and the covariance between them (ii) Suppose x and y represent the returns from two assets. Calculate the mean and variance for the following part folios. in x 125 100 75 50 25 0 -25 % in y -25 0 25 50 75 100 125 (iii) Find the portfolio that has the minimum variance. (iv) Let portfolio A have 75% in x and portfolio B have 25% in x. Calculate the covariance between the two portfolios. (v) Calculate the covariance between the minimum variance portfolio and portfolio A.A risk neutral principal hires a risk averse agent to work on a project. The agent' 5 utility function is V(w.-i) = WT: - 3(a). where w is wage, 303,-) is the disutility associated with the effort level 3,- exerted on the project. The agent can choose one of two possible effort levels, 814 or 31,, with associated disutility levels 3(EH) = 4, and 3(a) = 2. 0 If the agent chooses effort level 61.1, the project yields 80 with probability 1/ 2, and 0 with probability 1 / 2. e If the agent chooses q, the project yields 80 with probability 1/4 and 0 with probability 3 /4. The reservation utility of the agent is 0. Let {wH,wL} be an outputcontingent wage contract, where am is the wage paid if the project yields 80, and am is the wage if the yield is U. The agent receives a xed wage if :0 H = wL. (a) If effort is observable, which effort level should the principal implement? What is the best wage contract that implements this effort? [5 marks] (b) Suppose effort is not observable. What is the optimal contract that the principal should offer the agent? What effort level does this contract im- plement? [8 marks] (c) Compare the optimal contract in part (a) with that in part (b) and provide intuition for any similarity or difference in the income risk they impose on the agent and in the principal's payoff. ['2' marks]