Economics 313: Intermediate Microeconomics II. Sample Final Examination. Version 1. Instructor: Dr. Donna Feir

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1 Last Name: First Name: Student Number: Economics 313: Intermediate Microeconomics II Sample Final Examination Version 1 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 10 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 A is worth 50 points in total and consists of 10 multiple choice questions. Each question is worth 5 marks. Section B is worth 60 points in total and consists of three problems of varying length. Section A: Multiple Choice

2 1. Which of the following are barriers faced by governments in attempting to solve the free -rider problem in the provision of public goods? a. Completely self-interested behavior b. crowding-out of private provision c. measuring the costs and benefits of public goods d. all of the above e. both b and c 2. National defense is a a. Public good b. Private good c. Mixed good d. Pareto good e. Common good 3. Which of the following utility functions implies risk aversion? a. U(w) = 2w b. U(w) = 1 2 w c. U(w) = w 2 d. U(w) = w 1 2 e. U(w) = 1 w 1 4. Ariel produces aluminum cubes, facing costs of c(a) = A2, where A is the number of cubes produced, and selling them on the competitive market for $10. Bjorn grows beets next to Ariel s factory, facing costs of c(b) = B + B 2 + A2, where B is the number of beets produced, and 2 selling them for $5 on the competitive market. Because aluminum pollution is harmful to beet production, the town council decides to impose a tax on aluminum cubes. If the socially optimal production levels are A = 200 and B = 500, what is the tax (per aluminum cube) that would induce efficiency? a. $30 b. $15 c. $10 d. $25 e. $20 20 We want to set the tax on aluminum such that Ariel will chooses A = 100. When maximizing her utility, Ariel sets MB = MC With a tax MB = 10 T where T is the tax and MC = 2A/20 MC = MB 10 T = 2A/20 10 T = 2A /20 10 T = 400/20 10 T = 20 T = 10

3 5. Fortuna, California has 500 people. Every year a fireworks show is held. Each resident of Fortuna is willing to pay $4 for fireworks. If the cost of providing the fireworks (f) is c(f) = 2f 2, what is the Pareto Efficient amount of fireworks? a b c d. 500 e. 250 The efficient amount will set the social marginal benefit equal to the social marginal cost MB = MC = 4f = 4f f = Which of the follow is NOT a necessary condition for the first fundamental theorem of welfare economics to hold? a. Symmetric information b. No uncertainty c. No externalities d. No public goods e. Firms are price takers 7. Consider an economy in which x is a public good and y is a private good. There are two identical consumers who are each endowed with 300 units of the private good and no units of the public good. Each consumer has the utility function U = xy. Assume p x = p y. What is the efficient level of public good provision in this economy? a. 100 units b. 200 units c. 300 units d. 400 units e. There is insufficient information to answer this question MRS A + MRS B = P x P y = 1 y A x A + x B + y B x A + x B = 1 (300 x A ) + (300 x B ) = x A + x B 600 = 2(x A + x B ) x A + x B = 300

4 8. Consider the indifference curve drawn below. Suppose the consumer s MRS at point A is (in absolute value) equal to three. This means that: a. The consumer must pay three units of y for an additional x. b. The consumer is willing to give up three units of y for an additional x. c. The consumer must pay one-third of a unit of x for an additional y. d. The consumer is willing to give up 1/3 of a unit of y for an additional x. e. The consumer should buy more x and less y. 9. Movement from an inefficient allocation to an efficient allocation in the Edgeworth Box will a. Increase the utility of all individuals b. Increase the utility of at least one individual, but may decrease the level of utility of another person c. Increase the utility of one individual, but cannot decrease the utility of any individual d. Decrease the utility of all individuals e. Take the solution off the contract curve 10. Alex is a high quality mate and he is considering online dating. However, he is concerned that there are a lot of low quality mates who use online dating sites and thus chooses not to do online dating. This is an example of a. The absent markets hypothesis b. Statistical discrimination c. Adverse selection d. Moral Hazard e. A missing market due to uncertainty

5 Section B: Long Answer 1. To what extent can highways be considered a public good? Explain and justify your answer. 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. 2. How can the adverse selection problem explain why you are more likely to make a loan to a family member than to a stranger? Because you know your family member better than a stranger, you know more about the borrower s honesty, propensity for risk taking, and other traits. There is less asymmetric information than with a stranger and less likelihood of an adverse selection problem, with the result that you are more likely to lend to the family member. 3. Consider the following model of public goods. Assume that there is no production, and that the economy consists only of a representative consumer and the government. The representative consumer has no choice about how to use his or her time, and simply receives an exogenous quantity of goods, Y. The government collects a lump-sum tax, T, and transform it into public goods as follows: G = qt. The tax is an amount of Y that will be converted into the public good. a. Suppose that preferences over private consumption C and public goods G are such that these two goods are perfect substitutes, with the marginal rate of substitution of public goods for private goods equal to 1. Determine the optimal quantity of public goods that the government should provide, and interpret your results. So the marginal rate of substitution of a public good is MRS = 1. Since the PPF is given by G = qt and T is just some amount of Y, it implies the rate at which Y can be converted into G is given by 1 q or in other words the marginal rate of transformation (MRT) is equal to 1 q. If q > 1, then the optimal choice is G = qy and C = 0. This means that when the government can convert Y into G at a lower marginal cost than the marginal benefit to consumers, (the government is relatively efficient at producing the public good), than all production should be carried on by the government to produce the public good. If q < 1, then the optimal choice is G = 0 and C = Y. This means that when the government is relatively inefficient, then all production should be carried on by the private sector.

6 b. Suppose that preferences over private consumption C and public goods G are such that these two goods are perfect complements. Assume the representative consumer always wishes to consume private consumption goods and public goods in fixed proportions of 1 to 1. Determine the optimal quantity of public goods that the government should provide, and interpret your results. Solve C and G from the following two equations: C = G (this comes from wanting to consumer private and public goods one to one perfect complements) C + G q = Y (this comes from the budget constraint C + T = Y) From these equations we can solve C + G = Y qc + G = qy G = qc + qy q And using C = G C = qc + qy C + qc = qy (1 + q)c = qy C = qy 1 + q = G Consumer wishes to consume private consumption goods and public goods in fixed proportions. When the government because more cost effective at producing the public good, both the private consumption goods and public goods increase. When the government becomes less cost efficient, both the private consumption goods and public goods decrease. 4. A bakery and coffee shop operate next to each other downtown. The bakery sells bags of donuts (d) for $30 each and the coffee shop sells bags of coffee (k) for $15. Making donuts and coffee is costless, but each shop needs to advertise to attract customers. Some of the customers lured by the advertising from one shop will also make a purchase at the other shop. Specifically, the bakery needs to spend c(d) = d2 dk on advertising in order to sell d bags of donuts and the coffee shop must spend c(k) = k2 dk on advertising in order to sell k bags of coffee

7 a. What is the bakery s marginal private benefit of selling a bag of donuts and the marginal private cost? What is the coffee shop s marginal private benefit of selling a bag of coffee and the marginal private cost? MPB d = p d = 30, MPC d = 2d 15 k 30 ; MPB k = p k = 15, MPC k = 2k 15 d 30. b. How many bags of donuts and coffee will be sold in the competitive marketplace? MPB d = MPC d 30 = 2d 15 k 30 MPB k = MPC k 15 = 2k 15 d 4k 30 = d 30 Two equations and two unknowns! (do you notice a theme in this course?) 30 = 4k 15 2d 30 = 2d 15 k 30 8k 30 + k 30 = 4d d 30 9k 30 = 6d 30 3k = 2d d = 3 2 k 2 3k 15 2 k 5k 30 = = k k = 180 d = 3 (180) = c. The city looks out for its business owners and hires a consultant to determine how much the two shops should advertise in order to maximize total profits. What level of d and k does the consultant recommend? π d + π k = 30d c(d) + 15k c(k) Maximize this function get the first derivative and set it equal to zero For d: 30 c(d) d c(k) = 0 30 = (2d d 15 k 30 ) + ( k 30 ) 30 = 2d 15 2k 2d 30 = k 450 = 2d k 15

8 For k: 15 c(d) k c(k) k 2k = 0 15 = 15 d 30 d 2k 15 = d = 2k 15 d 225 = 2k d 15 2d k = 4k 2d 4d = 5k d = 5 4 k 450 = 2 ( 5 4 k) k 450 = 5 2 k 2 2 k 450 = 3 2 k k = 300 d = 5 (300) = d. The city decides to subsidize d and k so as to induce the owners to choose the amounts recommended by the consultant. What should be the subsidy per bag of donuts, s d, and the subsidy per bag of coffee, s k? 30 + s d = 2(375) (300) s d = s d = = s k = 2(300) (375) s k = = There are two people in this economy who both get utility from the consumption of goods X and Y. The graph below shows the production possibility frontier for goods X and Y, and one indifference curve of person 1. At point B, the slope of the indifference curve is equal to -2.

9 Good X a. Is point A production efficient? Explain briefly. Point A is production efficient because it is on the PPF b. Complete above graph to make point B consumption efficient if the total amounts of good X and Y are given by point A. See graph: The IC of person 2 is tangent to person 1 s (MRS 1 = MRS 2 c. Make adjustments if necessary to your graph in b) such that point B is Pareto efficient. See graph: The new point is on the PPF but also the slope of the PPF is equal to the slopes of the ICs at point B. In other words, the marginal cost of x in terms of y (MRT) is equal to the marginal benefit of x in terms of y