Page 1 Economics 281 B3 Winter 2015 Final Exam The University of Alberta Instructor: Scott Beesley *** 14 MC and 40 SA marks, for a total of 54.*** You have 2.5 hours. Good Luck. Note that all work must be shown in order to obtain full (or any!) marks on the short answer questions. NOTE: If you have a Revenue or Cost function of Q, and you need the marginal revenue or cost, use the following: If F(Q) = a + bQ + cQ 2 , then marginal F(Q) = b + 2cQ 1. Suppose the price of A is $3, the price of B is $5, the consumer's income is $30, and the consumer's level of satisfaction is measured by A B . The consumer's income constraint is A) max 3A +5B B) max A+B C) A+B 30 D) 3A+5B 30 2. Suppose demand is given by Q d = 1000 – 25P and supply is given by Qs = 75P. At the equilibrium price and quantity, the price elasticity of demand is A) –3 B) –25 C) –1/3 D) –10 3. Suppose that a consumer has the utility function U = 5X + 7Y. The MRSx,y is A) 7/5 B) 5/7 C) 1.00 since X and Y are perfect substitutes. D) 0 since X and Y are perfect complements. 4. Given the production function Q = L 2 , calculate the average product of labor for L = 2, and also calculate the marginal product of labor between L = 1 and L = 2. A) The average product of labor is 2 and the marginal product of labor is 2. B) The average product of labor is 1 and the marginal product of labor is 3. C) The average product of labor is 3 and the marginal product of labor is 2. D) The average product of labor is 2 and the marginal product of labor is 3. 5. A firm has a Cobb-Douglas production function for its inputs of capital and labor. The firm is currently paying $10 per labor hour and $5 per machine hour. The firm is currently at an efficient production level, employing an equal number of machines and workers. What can we infer about the marginal productivities of capital and labor at this point? A) MPK = MPL B) MPK = 2MPL C) MPL = 2MPK D) MPL = .5MPK Page 2 Use the following to answer questions 6-8: Use the figure to answer the following. 0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 0 200 400 Quantity Price 75 150 225 375 25 50 75 1 0 125 Demand Supply 6. Determine the level of consumer surplus at the market equilibrium. A) 16,875 B) 11,250 C) 7,500 D) 3,750 7. Determine the level of producer surplus at the market equilibrium. A) 16,875 B) 11,250 C) 7,500 D) 3,750 8. Suppose the government sets a price ceiling of $50 in this market. What is the minimum level of deadweight loss with the price ceiling? A) 7,500 B) 3,750 C) 1,875 D) 937.50 9. The inverse elasticity pricing rule tells us the monopolist's optimal mark-up of price over marginal cost. In general, A) the more price elastic the monopolist's demand, the smaller the mark-up will be. B) the less price elastic the monopolist's demand, the smaller the mark-up will be. C) price equals marginal revenue for the monopolist. D) marginal revenue equals average revenue for the monopolist. Page 3 10. To compute the optimal monopoly price with a linear demand curve, the monopolist A) should set MC = MR, which would determine the optimal quantity and price would equal MC and MR as well. B) should set MC = MR, which would determine the optimal quantity and price would be found by inserting the optimal quantity into the monopolist's demand curve. C) should set MC = MR, which would determine the optimal quantity and price would be found by doubling the marginal cost. D) should set output where total revenue would be the greatest. 11. A monopsonist maximizes profit when A) marginal revenue equals marginal cost. B) marginal revenue product of labor equals marginal cost. C) marginal revenue product is set equal to zero. D) its marginal revenue product of labor equals its marginal expenditure on labor. 12. A monopolist faces linear inverse demand P = a – bQ and constant marginal cost, c. Which of the following gives a correct formula for the monopolist's profit maximizing price? A) P = (a/b – c) B) P = a/2. C) P = (a+c)/2 D) P = a/2 + c. 13. Let the inverse demand curve for a monopolist's product be P = 100 – 2Q and the marginal cost of production be constant at MC = 10. Suppose that the firm considers moving from a uniform pricing strategy to a two-block tariff where the first block provides 15 units at a price of P1 = $70 and the second block provides an additional 15 units at a price of P2 = $40. How much does the monopolist's profit rise with this scheme? A) $225 B) $337.50 C) $450.50 D) $512 14. All consumers are alike and each has an inverse demand curve for a monopolist's product of P = 100 – 2Q. The marginal cost of production is constant at MC = $10. Let the monopolist charge a price of $10 per unit purchased and a subscription fee of $2025 that must be paid by each purchaser. What is the amount of consumer's surplus generated by this scheme? A) 0 B) $2025 C) $2025 multiplied by the number of consumers in the market. D) $90 multiplied by the number of units purchased. Page 4 15. (6 marks) Given: U(x,y) = x 0.60 y 0.40 MUX = 0.60 x -0.40 y 0.4 MUY = 0.40 x 0.6 y -0.6 Income = $1,000 Px=6 Py=2 a) (2 mark) Find the optimal bundle and the utility it yields. b) (2 mark) Now assume that the price of y increases to 4; find the new bundle and its utility level. c) (2 marks) Find the income and substitution effects for the above change. 16. (3 marks) Let Q = 10 minimum (L/2, 2K) w = 15, r = 30 a.) (1) Find the cost function. b.) (1) Say w increases to 30 and find the resulting new cost function. c.) (1) Assume that for some reason L = 400 and K = 50. What are MPL and MPK at that point? 17. (4 marks) Given: Q = 8 L 3/8 K 1/8 w = 30 r = 20 MPL = 3 L -5/8 K 1/8 MPK = L 3/8 K -7/8 a) (2 marks) Find the factor demands. b) (2 marks) Find the cost function. Page 5 18. (9 marks) Given: Demand; P = 200 - 2 Q & Supply; P = 50 + Q a) (1 mark) Find the standard unconstrained equilibrium P and Q, as well as Consumers' Surplus and Producers' Surplus. b) (4 marks) Begin from the part a) result. Assume a tax of $30 per unit is imposed. Find the gross and net of tax prices, total tax dollars collected, consumers' surplus and producers' surplus. c) (4 marks) Again, begin from the part a) result, which is assumed to be for a closed small economy. Now assume open trade is allowed when the world price is $150. Find the resulting volume of exports, consumers' surplus, producers' surplus, and the gain from trade. 19. (8 marks) You are running a monopoly firm which can operate any number of factories, where for each factory: TC(Qf) = 2,000 + 5 Qf + 0.05 (Qf) 2 MC(Qf) = 5 + 0.1 Qf And Demand is P = 105 - 0.02 Q so, MR = 105 - 0.04 Q a) (2 marks) For the given cost function, find QMES and ACMIN. (needed to do b), of course!) b) (4 marks) Find the multiple-plant outcome (Price, Market Quantity, Revenue and Profit). c) (2 marks) Assume the antitrust authorities decide to regulate this firm such that Price = MC. (1/2 mark each) Calculate the resulting outcome (Price, Market Quantity, Number of factories and Profit). Page 6 20. (10 marks) (plus 2 possible bonus marks!!!) A monopoly firm sells into two markets, where: P1 = 32 - 0.001 Q1 so MR1 = 32 - 0.002 Q1 P2 = 24 - 0.0005 Q2 so MR2 = 24 - 0.001 Q2 and TC = 10,000 + 20 Q, MC = 20 a) (2 marks) Find the standard unconstrained solution (i.e. price discrimination is OK, no quantity limit) (marks for: Revenue and profit) b) (4 marks) Now remove the ability to price discriminate. (marks for: Price, Q1, Q2, and profit) c) (4 marks) Now, allow P. D. again, as in a), but assume that production is capped at 7,000 units. (marks for: P1, P2, Revenue and profit) d) Bonus Time for 2 marks extra... What does profit fall to if both the "No P.D." and "Quantity limit" constraints are imposed?
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