Explain the following

4. A country which does not tax cigarettes is considering the introduction of a $3 per pack tax. The estimated demand and supply lnctions for cigarettes are given as: QD = 160,000 10,000P Qs = - 20,000 + 5,000P, where Q = daily sales in packs of cigarettes, and P = price per pack. The country has hired you to provide the following information regarding the cigarette market and the proposed tax. a. What are the equilibrium values in the current environment with no tax? b. What price and quantity would prevail after the imposition of the tax? What portion of the tax would be borne by buyers and sellers respectively? c. Calculate the deadweight loss from the tax. Could the tax be justied despite the deadweight loss? What tax revenue will be generated? 1. The following market demand and firm cost conditions describe a perfectly competitive industry p = 1000 - 0.001Q TO = 20q - 0.2q2 + 0.001q where TC is total cost. All firms are identical. Determine the long-run equilibrium price (p), market output (Q), firm output (q) and number of (identical) firms. (Hint: marginal cost is MC = 20 - 0.4g + 0.003q?) (10 marks) 2. The City of Calgary has a more or less free market in taxi service. Any respectable firm can provide taxi service as long as the drivers and cabs satisfy certain safety standards. Let us suppose that there is a constant marginal cost and average cost per trip of a taxi ride equal to $5 and that the average taxi has a capacity of 20 trips per day. Let the market demand function for taxi rides be given by Q = D(p) = 1100 - 20p, where demand is measured as rides per day and price is measured in dollars. Assume that the industry is perfectly competitive (a) What is the competitive equilibrium price per ride? What is the equilibrium number of rides per day? What is the minimum number of taxi cabs in equilibrium? (5 marks) (b) During the Calgary Stampede, the influx of tourists raises the demand for taxi rides to D(p) = 1500 - 20p. Find the following magnitudes, based on the assumption that for these 10 days in July, the number of taxicabs is fixed and equal to the minimum number found in part (a): equilibrium number of rides per day and profit per cab per day. (4 marks) (c) Now suppose that the change in demand for taxicabs in part (b) is permanent. Find the new equilibrium price, equilibrium number of rides per day, and profit per cab per day. How many taxi cabs will be operating in equilibrium? How does the new equilibrium compare to the equilibrium found in part (b). Explain why the answer found here in part (c) differs from the answer found in part (b). (4 marks) 3. Suppose that there are four identical firms in the market, each having a marginal cost given by: MC(q) = where q is the output of an individual firm. The market inverse demand is given by: P = 200 - .5Q where Q is the total amount sold in the market. (a) What is the supply curve of the industry when there is competition between the four firms? (3 marks)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]