Economics 313: Intermediate Microeconomics II. Sample Final Examination. Version 2. Instructor: Dr. Donna Feir

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1 Last Name: First Name: Student Number: Economics 33: Intermediate Microeconomics II Sample Final Examination Version Instructor: Dr. Donna Feir Instructions: Make sure you write your name and student number at the top of this page. You have 50 minutes to complete this exam. In order to minimize distractions to others, you are not permitted to leave in the last 0 minutes of the exam. Materials allow: simple (non-programmable) calculator You should answer all questions. Write your answers in the space provided. Use the backside of your exam for scrap paper if you wish, but only information written in the space provided will be considered for grading. You may also tear off the last page of the exam and use it for scrap paper. Use your time wisely. If you get stuck on a question move onto the next question and return if time permits. There are two sections to the exam: Section is worth 50 points in total and consists of 0 multiple choice questions. Each question is worth 5 marks. Section B is worth 50 points in total and consists of 5 problems of varying length.

2 Section : Multiple Choice. producer has a PPF given by y = 00 x. If the price of good x is $0 per unit and the price of good y is $ per unit, then which of the following output choices maximizes the producer s profit? a. x = 0, y = 00. b. x = 0, y = 50. c. x = 50, y = 0. d. x = 00, y = 0. e. None of the above. consumer has utility function U = xy. If this consumer is maximizing his utility by consuming 50 units of good x and 00 units of good y, then which of the following could be the prices of each good? a. p x = $ and p y = $. b. p x = $ and p y = $4. c. p x = $4 and p y = $. d. p x = $4 and p y = $4. e. None of the above. 3. Positive externalities are created when a. consumers reduce their demand for coffee and price thereby declines b. farmers spray pesticide in their fields and it washes into the local river c. your neighbor plants beautiful flowers in her yard and you enjoy looking at them d. None of the above e. ll of the above 4. The second fundamental theorem of welfare economics states. a. under certain conditions, a competitive equilibrium is Pareto optimal b. a competitive equilibrium is always Pareto optimal c. under certain conditions, a Pareto optimum is a competitive equilibrium d. a Pareto optimum is always a competitive equilibrium e. the competitive equilibrium will result in inequity 5. ssume an economy with no market power, externalities, or asymmetric information. Which of the following statements about is TRUE? I. From the first welfare theorem, we know that the equilibrium allocation in such an economy will be efficient. II. From the second welfare theorem, we know potential Pareto improvements are possible as long as property rights are well-defined and negotiation is costless.

3 III. From the Coase theorem, we know that lump sum redistribution prior to trade will allow potential Pareto improvements, relative to the original equilibrium. a. I only. b. II only. c. III only. d. II and III only. e. I, II, and III. 6. Which of the following statements is FLSE?. ny move from an allocation that is not on the contract curve to one that is on the contract curve is a potential Pareto improvement.. If we are at an allocation on the contract curve, then no Pareto improvements are possible. 3. ny move from an allocation that is not on the contract curve to one that is on the contract curve is a Pareto improvement. a. None of the statements are false. b. I only. c. II only. d. III only e. II and III only. 7. You have $9 and preferences given by U(w) = w. Which of the following options is most attractive? a. Get a free lottery ticket that has a in 3 chance of winning $9 b. Pay $5 for a lottery ticket that has a chance of winning $ c. Do nothing d. Pay all your money ($9) for a lottery ticket that has a in 4 chance of winning $00 e. Take a gamble where you lose 9 dollars with probability 0.5 and win 9 dollars with 0.5 a) (00) + 00 (9) = + 8 = 8 = b) = 5 + = 7 c) 9 d) 00 = 5 4 e) 8 = 9 8. The free-rider problem is encountered when

4 a. all individuals who consume a public good pay for it b. someone benefits from a public good without paying his or her full share c. all individuals are willing to pay for what they consume d. all goods consumed and produced are private goods e. when there are scarce resources and prices are high 9. The rate at which one good can be converted technologically into another is called a. the marginal rate of transformation b. the marginal rate of substitution c. the marginal product of labor d. the rate of conversion e. the marginal rate of technology 0. riel produces aluminum cubes, facing costs of c() =, where is the number of cubes produced, and selling them on the competitive market for $30. Bjorn grows beets next to riel s factory, facing costs of c(b) = B + B + 0 4, where B is the number of beets produced, and selling them for $5 on the competitive market. Because aluminum pollution is harmful to beet production, but riel has the right to produce aluminum. There are no transactions costs and property rights are firmly established. What will be the amount of aluminum produced? a. 00 b. 00 c. 400 d. 5 e. 0 MSC = + = 30 = MB 3 60 = 30 = 3 = 0 Section B: Long nswer. ll along the coast of British Columbia foghorns operate to protect ships from hitting rocky parts of the coastline during periods of heavy fog. These foghorns are located on dangerous stretches of the coast and sound loud alarms that passing ships and other coastal traffic can hear. Most often, foghorns are owned and operated by the government. Suppose that the BC provincial government has decided to stop funding foghorns. government spokesperson has argued that there is no good reason for government involvement. While it is true that the foghorns provide a valuable service, the private market is perfectly capable of providing this service efficiently.

5 Do you agree with the BC spokesperson? Based on what you have learned in Economics 33, do you think that it is desirable to leave the provision of foghorn services entirely up to the private market? To get full credit for this question, you would have to explain why it is that we might think that the services provided by foghorns are non-excludable and non-rivalrous, and hence are PUBLIC GOODS. Public goods tend to be under-provided by private markets so leaving foghorn provision to private markets is not likely to lead to the efficient level of provision.. Under what circumstances can peopling gain from sharing their risks through risk pooling agreements? What types of people will enter into risk sharing agreements? Individuals sharing their gains or losses when they face independent risks results reducing the variance of a gamble while preserving its expected value. This works because of the law of large numbers. This means the gamble without risk pooling is a mean preserving spread of the gamble with risk pooling. risk averse person will always prefer to pool risks in these circumstances. 3. Suppose the utility functions of two roommates are given by u = x G u = x G where x and x denotes the consumption of the private good for person and, respectively, and G denotes the public good. The price of the private good is $ and the price of the public good is equal to p G =. Both roommates have an income of $80, that is I = 80, I =80. a. Solve for the efficient quantity of the public good G MRS + MRS = p g = x p x x G + = 4(G + G ) x x G = x G + x G = x + x = 4G x + x BC: 80 = x + G, 80 = x + G x = 80 G, x = 80 G Plugging into above 80 G + 80 G = 4(G + G ) 60 = 4G + G + 4G + G 60 = 6(G + G ) = G + G

6 Now suppose both people try to maximize their utility given the contribution of the other person to the public good and their own budget constraint. That is, we want to find each person s best response function. b. Solve for person and s best response functions. Person : MRS = p x G = and then substituting into for x using the budget constraint. ( 80 G (G +G ) ) =. Now get G in terms of G 80 G = 4G + 4G 80 4G = 6G G = G Since Person faces the same BC and has the same utility as Person G = G c. Find the Nash equilibrium contributions to the public good Since we know the equilibrium is symmetric, either we can sub the best response function of Person into Person or get G equal to G. Using the second method: G = G 3 G G = G = 40 3 G = 40 5 G = 8, G = 8 so total pubic good provided would be 6 units as opposed to the efficient amount which is d. Show the what would happen if the government provided the short fall in the public good provision 80 G If the government provided the short fall of 0.66 units: ( ) = 4G (G +G +0.66) + 4G = 80 G 0G = G = , G = Donations to the public good go down. 4. Consider an exchange economy consisting of two people, and B, endowed with two goods, and. Each person is initially endowed with 5 of each good. Their preferences are given by U (x, x ) = x x and U B (x, x ) = x x. ssume that p =. a. Find the MRS for each consumer when x is on the vertical axis. MRS = x x x = x x ; and MRS B = x B x B xb = x B x B b. Write the equation of the contract curve MRS = MRS B

7 nd we know that 0 = x + x B and 0 = x + x B x x x = x B B x x = 0 x (0 x ) x [(0 x )] = (0 x )x 40x 4x x = 0x x x 40x 3x x = 0x x (40 3x ) = 0x x = 0x 40 3x c. Find the budget constraint for each consumer. P x + x = P P x + x = P d. Could the p = and the allocations (x, x ) = ( 0 3, 0 3 ) and (x B, x B ) = ( 0 3, 0 3 ) constitute a competitive equilibrium? This amounts to finding whether you are on the contract curve at this point and both consumers BC bind. You could also check to see if the MRSs are equal to at this allocation and that total demand equals total supply. 5. Smith & Co., a well-known producer of hand tools, wishes to hire a researcher to speed the development of the next generation of left-handed screwdrivers. If the researcher works hard, there is an 80% chance that she will make the crucial breakthrough and allow her firm to earn $50,000 in revenues and only a 0% chance that she ll make no breakthrough in which case the firm will not earn any additional revenue. If the researcher shirks her duties, there is only a 40% chance that she ll be able to make the breakthrough. Smith & Co. cannot observe the effort level of the researcher. Researches can earn $0,000 in other jobs without exerting effort and hard effort by a researcher at Smith & Co is equivalent to a cost of $0,000 and shirking is equivalent to a cost of $0. The researcher has a utility equal just to the amount received in dollars minus the cost of working hard if they work hard. a. Write down the incentive compatibility constraint that induces high effort when researchers are paid w G if they make the breakthrough and w B if they don t. The incentive compatibility constraint: (the worker must be better off by or at least as well off to work hard): 0. 8w G + 0. w B 0, 000 > 0. 4w G w B b. Write down the relevant participation constraints for this contract meant to induce high effort.

8 The participation constraint for the researcher: (he utility of providing high effort when paid w G when the breakthrough is made and w B if they do not, must be greater than the utility of not participating.) 0. 8w G + 0. w B 0, 000 > 0, 000 The participation constraint for the firm: (profits are at least greater than zero) (50, 000 w G )(0. 8) + ( w B )(0. ) > 0