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1. Assume that the market for steel 1s competitive. The inverse demand curve for steel 13 P 12ll- Q and its inverse supply (i. e. ,industry marginal cost) curve is P: Q + 20, where P is price and Q 15 quantity. (a) Depict these inverse demand and supply curves in a diagram and use algebra to calculate the market equilibritun values of price, Pc, quantity, QC, and price elasticity of demand, EC. [ll]I points] (1)) In the above context, also calculate consumer surplus, CSC, producer surplus, PSE, and social welfare, SWc. [ll] points] 2. Suppose that the industry in Question 1 is taken over by a monopolist. (a) Depict the monopolist's prot maximization problem in a diagram and use algebra to solve for the values of price, Pm, quantity Q1], and price elasticity of demand, Em. [ll]| points] (b) Calculate the impacts of monopolization in terms of the resulting changes in consumer surplus, producer surplus, and social welfare. [1!) points] 3. (a) Return to the scenario in Question 1 and assume that the process of producing steel causes air and water pollution, which result in marginal external cost NIEC = 21']. Taking this externality into consideration, calculate the socially optimal level of steel production, Q5, and illustrate its determination in a diagram like the one for Question 1(a) by using any additional curve that may be needed. Also calculate social welfare, SW5. [ll] points] (b) If the competitive market fails to account for external costs and continues to produce at Q: {'om Question 1(a)), what would be the resulting loss in social welfare? Explain your calculation with the help of a diagram. [5 points] (c) Calculate a per unit tax that could correct the market failure in part (b). If this tax is implemented, what would be the resulting values of social welfare, consumer surplus, producer surplus, total external costs, and total tax revenue? Also illustrate these areas in a diagram. [15 points] 1. Below is strategic form for Grading on the Curve when players make their choices simultaneously. We constructed this strategic form in Lecture 3. Recall that a > c > f 2 0 and u > v 2 0 in this game. COL's Strategy many few ROW's many strategy C-u, C-u a-u, f-v few f-v, a-u c-V, C-V (a) Find specific values for the parameters a, c, f, u and v such that (few , few) is a strong dominant strategy equilibrium. Given the values you chose: is (few , few) a Nash equilibrium; is (few , few) a strict Nash equilibrium? (b) Think about this problem from part a) in a more general way. Find inequality restrictions on the parameter values such that (few , few) is a strong dominant strategy equilibrium, and provide an intuitive inter- pretation of the inequalities. (c) Find specific values for the parameters a, c, f, u and v such that both (many , many) and (few , few) are strict Nash equilibria. (d) Attack the problem from part c) in more general way, by finding in- equality restrictions on the parameter values such that both (many , many) and (few , few) are strict Nash equilibria, and provide an intu- itive interpretation of the inequalities.18. (5 points) You are the Chief Investment Officer of Rookie Life Insurance Company (RLIC). The company is only 2 years old, but has had enormous success in writing new annuity business. The company has sold $1 billion in deferred payout annuities. A deferred payout annuity is a single premium contract sold to 30 year old individuals and begins making monthly payments at age 65. The company is risk adverse, wishes to maximize surplus, and wants to duration match when the contracts are in their payout period. The liability duration will initially be 25, but will be 8 in the payout stage. You have decided on the following initial investment mix: Expected Asset Class Weight Return Duration Common Stock 20% 7.5% Private Preferred Stock 30% 5.0% 15.0 Municipal Bonds 30% 5.0% 20.0 Short Term Bonds 20% 2.5% 2.0 Total 100% 5.3% 10.9 (a) (1.5 points) Explain what aspects of the portfolio should be monitored for changes in RLIC's circumstances and constraints, and how each will likely change over time. (b) (1.5 points) If the stock market decreases by 30%, explain the benefits and costs of rebalancing the portfolio. (c) (2 points) You are considering the following rebalancing disciplines . Calendar rebalancing Percentage of portfolio rebalancing (i) Explain why the calendar rebalancing might be more appropriate during the deferral period. (ii) Explain why the percentage of portfolio rebalancing might be more appropriate during the payout period.Question 1 (total 15 points}. A rm has a production function: f (K . L} = EDLKD'E + LEE 2 LEKE a. What is its short-run production function if capital is xed at K=4'? b. What are the fum's marginal product of labour and average product of labour in the short run? c. Calculate the elasticity of output with respect to labour. Question 2 (total 16 points} . Do the following functions exhibit increasing, constant, or decreasing retiirns to scale? Explain you: answers. a. The production ftmction Q = Wigwam, where M is materials, K is capital and L is laboUr. b. q = L + 0.5K c. u = DELHI\" I d. if = M.3 + 4K Question 3 (12 points]. Find the Marginal Rate of Technical Substitution for the following production functions: 1 | a. 'FLEKE 11 q = L.5 + [(0.5 o. q = L + K Question 4 (Total It} points). Suppose a fum's cost uiction is C = 2q3 lql + Slq. average cost curve is described by the equation AC = 2432 lq + 94). At what output level does the marginal cost curve cross the average cost curve? Question 5. (16 points, 8 points each} For the following, please answer \"True" or "False" and explain why. a. When buying a piece of equipment, it is always bed for the rm to pay cash instead of borrowing the funds since this mnders the equipment less costly. b. University of Tomato is choosing a location for a new building. The university has campuses at Downtown1 Scarborough and Mississauga. A large parcel of land would have to be purchased at Scarborough or Mississauga if the building were to Jugs L be built there. So it is cost-effective to locate the new building at downtown because the university already owns the land. Independent random samples of size n, and n, are taken from the normal populations N(1,of) and N(#2,02 ) respectively. (i) Write down the sampling distributions of X, and X2 and hence determine the sampling distribution of X1 - X2 , the difference between the sample means. (ii) Now assume that of = o} = 02 (a) Express the sampling distribution of X - X, in standard normal form. (b) State the sampling distribution of (m - D)S/ + (12 - 1)S] (c) Using the N(0,1) distribution from (a) and the x- distribution from (b), apply the definition of the / distribution to find the sampling distribution of X - X, when o is unknown