Page 1 Economics 281 B1 Winter 2014 Final Exam The University of Alberta Instructor: Scott Beesley This exam has 18 MCs and 42 marks in short answers, for a total of 60 marks. You have 2.5 hours. Please mark your name and student number on the booklet and scantron sheet immediately. Please mark MC answers on the Scantron sheet as you go along... Good Luck. 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 cross-price elasticity for two goods is positive. The two goods are A) normal goods B) substitutes C) complements D) inferior goods 2. Suppose that a consumer has utility function U(x, y) with MUx = 5y 2 x and MUy = 2x 2 y. What is the marginal rate of substitution? A) 10y 3 x 3 B) 2x/5y C) 5y/2x D) 5y 2 x 2 3. Assume that we are modeling inter-temporal consumption for a typical consumer. Further assume that we measure current consumption on the horizontal axis and future consumption on the vertical axis. A market exists where borrowing and lending can occur for a fixed interest rate, r. Now identify the statement that is false. A) When a consumer can lend or borrow at the same interest rate, the consumer's budget constraint is a straight line. B) When the rate at which a consumer can borrow is higher than the rate at which the consumer can lend, the consumer's budget constraint is composed of two straight lines with different slopes. C) When a consumer cannot borrow money or earn an interest rate for saving money, the consumer's budget constraint is a straight line. D) When a consumer has access to financial markets so that he/she can lend or borrow money, his/her budget constraint is expanded when compared to his/her budget constraint without access to financial markets. 4. Diminishing marginal returns occur when the total product function is A) decreasing. B) increasing at a decreasing rate. C) increasing at a constant rate. D) increasing at an increasing rate. Page 2 5. Suppose a firm's total cost curve can be written TC(Q) = Q - .5Q 2 + Q 3 , with marginal cost MC(Q) = 1 – Q + 3Q2. This cost function exhibits: A) economies of scale B) diseconomies of scale C) neither diseconomies nor economies of scale. D) economies of scale for output levels less than some level, Q1 = 1/4, and diseconomies of scale thereafter. 6. In a constant cost industry, which of the following statements is true? A) The long run market supply curve and the long run firm supply curve are both horizontal. B) While the long run market supply curve is horizontal, the long run firm supply curve generally is upwards-sloping. C) The long run market supply curve and the long run firm supply curve are both upwards-sloping. D) While the long run market supply curve is upwards-sloping, the long run firm supply curve is horizontal. 7. Suppose that a market is initially in equilibrium. The initial demand curve is 90 dP Q . The initial supply curve is 2 sP Q . Suppose that the government imposes a $3 tax on this market. What is the change in consumer surplus due to the tax? A) $450. B) $420.50. C) $29.50. D) $0.50. 8. In a perfectly competitive market, a tariff A) is another term for an excise tax imposed on any good. B) sets the price of an imported good. C) is a tax on an imported good. D) is the same as an import quota. 9. Consider a perfectly competitive market with inverse market supply 5 3 sP Q and inverse market demand 50 2 dP Q . Suppose the government subsidizes this market with a subsidy of $5 per unit. What is the equilibrium quantity traded after imposition of the subsidy? A) Q = 10 B) Q = 12.5 C) Q = 9 D) Q = 7.5 10. Consider a perfectly competitive market with market supply 2sQ P and market demand 30dQ P . Suppose the government imposes an excise tax of $4 per unit on this market. What is the deadweight loss from this tax? A) 2 B) 4 C) 6 D) 8 Page 3 11. Which of the following statements regarding a monopolist's profit maximizing condition is false? A) The monopolist's profit-maximizing price will be greater than marginal cost for the last unit supplied. B) A monopolist can earn positive economic profit. C) Because monopoly price is above marginal cost and a monopoly earns positive economic profit, there are no benefits to consumers in the monopoly market. D) Price equals average revenue at the profit-maximizing quantity of output. 12. Inverse demand for a monopolist's product is given by 300 6P Q while the monopolist's marginal cost is given by 3MC Q . The profit-maximizing quantity of output for this monopolist is A) 33.33 B) 100 C) 50 D) 20 13. The inverse elasticity pricing rule says that the optimal markup of price over marginal cost expressed as a percentage of price A) is equal to ½ the inverse of the price elasticity of demand. B) is equal to - ½. C) is equal to the opposite of the inverse of the price elasticity of demand. D) is equal to the inverse of the price elasticity of demand. 14. A monopolist owns two plants in which to produce product A. The marginal cost of producing A is increasing, but currently is lower in plant 1 than in plant 2. How should the monopolist allocate production? A) Produce all output in plant 1. B) Produce all output in plant 2. C) Produce 50 percent in plant 1 and 50 percent in plant 2. D) Produce in plant 1 up to the point where marginal costs are equated across the plants. (In other words, reallocate production so that 1 2MC MC .) 15. Let a monopolist face consumer group A with inverse demand PA = 100 – 2QA and consumer group B with inverse demand PB = 80 – QB. The monopolist can conduct third degree price discrimination, but faces a capacity constraint that QA + QB 100. What will be the amount supplied to each of the customer groups? A) QA = 50; QB = 50. B) QA = 60; QB = 40. C) QA = 33.67; QB = 66.33 D) QA = 36.67; QB = 63.33 Page 4 16. A monopolist faces inverse demand 400 4 dP Q and has constant marginal cost 80MC . If this monopolist engages in first-degree price discrimination, total output will equal A) 20 units B) 40 units C) 60 units D) 80 units 17. What is the difference between uniform pricing and price discrimination? A) Uniform pricing and price discrimination are the same. B) With uniform pricing firms charge different prices for the same good or service and with price discrimination firms charge the same price for the same good or service. C) With uniform pricing firms charge the same price for the same good or service and with price discrimination the firms charge different prices for the same good or service. D) The uniform price is always higher than the discriminated price. 18. 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. 19. (7 marks) Given: U(x,y) = x 2/3 y 1/3 MUX = (2/3) (y/x) 1/3 MUY = 1/3 (x/y) 2/3 Income = $300 Px=4 Py=2 a) (1 mark) Find the optimal bundle and the utility it yields. b) (1 mark) Now assume that both prices change to 3 and find the new utility level. c) (3 marks) Find the income and substitution effects for the above change. d) (2 marks) Find the compensating and equivalent variations for the above change. 20. (7 marks) You have this production function Q(L,K) = 100 L 0.6 K 0.8 MPL = 60 L -0.4 K 0.8 MPK = 80 L 0.6 K -0.2 w=3 r=4 a) (3 marks) Find the cost function. b) (1 mark) What is the cost to produce 1,000 units? c) (1 mark) What is the cost to produce 4,000 units? d) (2 marks) Show in detail this production functions' returns to scale. Page 5 21. (9 marks) Given: Demand; P = 500 - Q and Supply; P = 200 + 0.5 Q a) (1 mark) Find the standard unconstrained equilibrium. b) (1 mark) Find, CS, PS and TS in part a). c) (3 marks) Now impose a tax of $30 per unit. Find Qtax, Pincluding tax, Pnet of tax, Tax dollars collected, and the DWL created by the tax. Who pays more, buyers or sellers? d) (2 marks) Starting from the part a) result, assume open trade is allowed when the world price is $250. How many units will be imported? e) (2 marks) In response to the imports found in part d), a tariff is imposed. What tariff would cut imports to 120 units? Show your work! 22. (9 marks) Consider a monopoly with: TC(Q) = 625 + 3 Q + 0.25 (Q) 2 MC(Q) = 3 + 0.5 Q And Demand is P = 63 - 0.05 Q so, MR = 63 - 0.10 Q a) (3 marks) Find the monopoly outcome, giving price, quantity and profit. b) (3 marks) Assume the government enforces competitive pricing on the firm. Find the resulting price, quantity, and use those results to obtain the deadweight loss of monopoly. c) (3 marks) Finally, presume that the monopolist can make copies of the cost function. Find the profit-maximizing price, total quantity, and the resulting profit. NOTE: All calculations must be shown - correct figures that "appear out of nowhere" will not be credited, and that might also apply to later calculations based on the unsupported number! Page 6 23. (10 marks) A monopoly firm sells into two markets, where: P1 = 2000 - 2 Q1 so MR1 = 2000 - 4 Q1 P2 = 800 - Q2 so MR2 = 800 - 2 Q2 and TC = 100,000 + 500 Q, MC = 500 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 a) (4 marks) Find the standard unconstrained solution (i.e. price discrimination is allowed) (P1, Q1, P2, Q2, Revenue, costs, profit and average cost) b) (3 marks) Now remove the ability to price discriminate. Find P, Q, and profit. Show all the work to confirm that both markets buy, or don't buy! c) (3 marks) From the part a) situation, impose a quantity limit of 450. What does profit fall to?
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