Sample final exam 2 with answers

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Feb 20, 2024

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1 Sample Final Examination FIN 501 Please read the following statement of integrity carefully and sign below. Statement of Integrity I agree to take this exam in an honest manner. By signing below, I am certifying that I will not cheat on this exam in any way, including but not limited to, looking at my classmates’ answers or consulting any resources/notes (including cell phones). I understand that the penalty for violating this agreement may range from getting a 0 on the exam to failing the course. Signature ________________________________________ Date Instructions: You have 180 minutes to complete the following examination. The exam consists of 25 multiple choice questions and 4 additional questions. The answers to the multiple choice questions must be recorded on the scantron answer sheet using a pencil. For the other 4 questions, write your answers in the spaces provided in this packet. You may use the back pages if you need extra space for calculations or explanations. Answer all parts of all questions. If you believe that the question is ambiguous, explain why and state what assumption you are making to resolve the ambiguity, and then answer the question given that assumption. When explanations or work are required, they will count for most of the answer. Numerical answers are not necessarily whole numbers. The exam has 140 points . Numbers in square brackets at the start of each question tell how many points that question (or part of a question) is worth. You may use a calculator. However, it should be used for simple arithmetic only. No other materials are allowed. Please write your name and your NETID in the space below. NAME: ____________________________________________________________ NETID: ____________________________________________________________ ON THE SCANTRON ANSWER SHEET: Please enter your name and NETID and fill in the appropriate bubbles for each. Do not proceed until instructed to do so.

2 NAME:_________________________________ NETID: ___________________________ SCORE Question Points Multiple Choice (Total) / 75 #26 / 18 #27 / 15 #28 / 20 #29 / 12 Total / 140 NO TEST MATERIALS ON THIS PAGE Do not proceed until instructed to do so.

3 Multiple Choice. [3 points each] Select the best answer to each question. Write the letter corresponding to your answer on the scantron answer sheet using a #2 pencil . If you do not write your answer on the scantron answer sheet using a #2 pencil, if you select more than one answer, or if it is ambiguous which answer you have selected, you will not receive credit. 1. Which of the following is NOT a property that the optimal consumption bundle must satisfy in a standard utility framework? a. The consumer’s budget line is tangent to the indifference curve. b. The consumer’s budget constraint holds with equality. c. There is no bundle that would make the consumer better off. d. The consumer cannot afford a bundle that would give her higher utility. 2. A consumer’s utility function exhibits a (strictly) decreasing marginal rate of substitution. Suppose that there are two goods, pizza and soda, and that the consumer is indifferent between bundle A, which contains 0 pizzas and 10 sodas and bundle B, which contains 8 pizzas and 0 sodas. What can be said of bundle C, which contains 4 pizzas and 5 sodas? (Hint: it will help to draw a graph) a. Bundle A is strictly preferred to bundle C. b. Bundle C is strictly preferred to bundle B. c. The consumer is indifferent between bundles A, B and C. d. None of the above is correct. 3. If the price of a normal good decreases: a. The income effect is positive and the substitution effect is positive. b. The income effect is positive and the substitution effect is negative. c. The income effect is negative and the substitution effect is positive. d. The income effect is negative and the substitution effect is negative. 4. Which of the following CANNOT happen when the interest rate increases, for someone who is initially a saver ? a. Consumption in period 0 falls. b. Consumption in period 0 rises. c. Consumption in period 1 falls. d. Consumption in period 1 rises. 5. A decision maker has utility function 𝑢𝑢 ( 𝑤𝑤 ) = √𝑤𝑤 . The decision maker has initial wealth w = $400 and faces a 10% chance of losing $39. The most this decision maker will pay for full insurance against this risk is approximately: a. $3.90 b. $3.99 c. $6.24 d. $19.9

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4 6. Suppose that A and B represent two inputs into a firm’s production function, F(A,B) = 2A + 3B. Let w A and w B denote the prices of inputs A and B, respectively. Under what conditions will a profit- maximizing firm choose to use a positive amount of A? a. w A ≤ w B . b. w A ≤ 2/3 w B . c. w A ≤ 3/2 w B . d. w B ≤ w A . 7. Part of a firm’s production process requires using an open flame to melt metal. Government regulations require that a fire warden be present in the factory any time the flame is in use. The firm pays the fire warden’s salary. This cost is best described as: a. Variable and avoidable. b. Variable and unavoidable. c. Fixed and avoidable. d. Fixed and unavoidable. 8. Imposition of a binding minimum wage: a. Always benefits workers, always harms firms and increases social surplus. b. Always harms both firms and workers and decreases social surplus. c. May benefit or harm workers, always harms firms, and incurs a deadweight loss. d. May benefit or harm firms, always harms workers, and incurs a deadweight loss. 9. Which of the following will definitely NOT cause a shift in the demand curve for good X? a. A tax imposed on a complementary good Y. b. Increases in the cost of producing good X. c. An increase in consumer utility from the good, all else equal. d. None of the above will cause the demand curve for good X to shift. 10. A tax is imposed to reduce a negative externality in a perfectly competitive market. Assume that the tax is set such that it brings the output of the good in question ( 𝑞𝑞 ) to the socially optimal level ( 𝑞𝑞 ∗ ) . Let 𝑞𝑞 𝑀𝑀 be the output prior to the introduction of the tax. Which of the following statements is true? a. Because 𝒒𝒒 = 𝒒𝒒 ∗ , there is no deadweight loss after the tax is imposed. b. Because 𝑞𝑞 ∗ ≠ 𝑞𝑞 𝑀𝑀 , there is deadweight loss after the tax is imposed. c. Because the price consumers pay is not equal to the price producers receive, there is deadweight loss after the tax is imposed. d. If the tax revenue is not used to compensate producers and consumers in this market, there is deadweight loss after the tax is imposed. 11. Which of the following statements about policies to reduce negative externalities is true? a. A uniform non-tradable production quota is not Pareto efficient/Pareto optimal unless all regulated firms are identical. b. Firms will always prefer tradable permits to taxation. c. Taxation to reduce negative externalities will create deadweight loss. d. It is not necessary to tax a monopolist who produces a negative externality because the monopolist always produces less than the socially optimal quantity.

5 12. A monopolist gets a subsidy of $2 per unit produced and sold and faces demand curve 𝑄𝑄 = 20 − 𝑃𝑃 . What is the monopolist’s marginal revenue? a. 20 − 𝑄𝑄 b. 20 − 2 𝑄𝑄 c. 22 − 𝑄𝑄 d. 𝟐𝟐𝟐𝟐 − 𝟐𝟐𝟐𝟐 13. What is true about monopolistically competitive industries? a. Firms make positive profits in the short-run and in the long-run. b. Firms can make either negative or positive profits in the short run c. There are high barriers to entry d. Firms charge prices equal to marginal cost 14. The Stackelberg outcome differs from the Cournot equilibrium because: a. In the Stackelberg game, the leader chooses a quantity that is not on its Cournot best response function. b. In the Stackelberg game, the follower chooses a quantity that is not on its Cournot best response function. c. In the Stackelberg game, threats to produce large quantities do not need to be credible. d. In the Stackelberg game, the players choose prices instead of quantities. For the next two questions, consider the sequential game represented below. Player 1 chooses from actions “Top” and “Bottom”; player 2 then chooses from actions “Up” and “Down”. Then player 1 chooses from “T” and “B” Assume that players 1 and 2 are companies and payoffs (in boxes) are in millions of dollars. (2,2) T B (1,3) Up Player 1 T Top Down (2,6) B Player 1 Player 2 (4,8) Bottom Up T (5,2) B (3,4) Down Player 1 T (9,1) B (1,9)

6 15. Assuming firms can make payments to each other, what is one of the Pareto efficient outcomes of the above game? a. Top, Down, B. b. Bottom, Up, T. c. Bottom, Up, B. d. Top, Down, T. 16. What is the sequential equilibrium of the above game? a. Top, Down, B. b. Bottom, Up, T. c. Bottom, Down, T. d. Top, Down, T. 17. Which of the following is included in the standard calculation of GDP? a. The value of all intermediate goods. b. The value of used cars sold. c. The rental rate of housing, even if it’s occupied by the owner. d. The approximate value of household production. 18. If a U.S. resident buys a television made in Korea by a Korean firm, then: a. U.S. net exports (NX = X-M) decrease and U.S. GDP decreases. b. U.S. net exports (NX = X-M) are unaffected and U.S. GDP decreases. c. U.S. net exports (NX = X-M) are unaffected and U.S. GDP is unaffected. d. U.S. net exports (NX = X-M) decrease and U.S. GDP is unaffected. 19. Which of the following is a reason for why unexpected inflation is harmful? a. Firms must incur menu costs. b. Wealth is redistributed from lenders to borrowers. c. Consumers want to hold less money on average, requiring more trips to the bank. d. All of the above 20. What is included in the US monetary base? a. Only currency. b. Only currency and commercial banks’ deposits at the Federal Reserve. c. Everything listed in part b plus demand deposits and travelers checks. d. Everything listed in part c plus savings deposits, short-term time deposits, and money market mutual funds. 21. Which of the following accurately describes the effect of government policies on savings and investment in a closed economy ? The interest rate refers to the rate paid by borrowers. a. If the government runs a deficit, both the interest rate and equilibrium savings will fall. b. Changes in government spending have no effect on either the interest rate or equilibrium savings. c. If the government taxes interest income from savings, both the interest rate and equilibrium savings will fall. d. If the government offers an investment tax credit, both the interest rate and equilibrium savings will rise.

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7 22. Which of the following effects materialize if the government of a small open economy increases spending? a. Domestic investment falls. b. Net exports fall. c. The domestic interest rate increases. d. All of the above. 23. In the Solow Growth model: a. An increase in the savings rate can increase long-run consumption per capita. b. An increase in the savings rate can increase short-run consumption per capita. c. An increase in the rate of population growth will increase long-run consumption per capita. d. An increase in productivity may increase or decrease long-run consumption per capita. 24. Suppose that, in the GDP equation, consumption is equal to 5000+0.7(Y-T) and investment is equal to 10,000+0.1Y. Everything else does not depend on Y. What is the fiscal multiplier in this economy? a. 2.5 b. 3.3 c. 5 d. 10 25. If cash accounts for 10% of deposits held and banks lend out 90% of the deposits, what is the money multiplier? a. 10 b. 5.5 c. 1.1 d. 0.18

8 Computational/Short Answer Questions: Please write your answers in the space provided. Partial credit will be awarded for partially correct work. So, write legibly and show your work. Full credit will not be given for a correct answer without showing supporting work. 26. A consumer can invest in an asset that returns 50% with a 40% probability and returns -15% with an 60% probability. There is also a safe asset that pays 5% for sure. The consumer’s utility function in each state of the world is 𝑙𝑙𝑙𝑙 ( 𝑤𝑤 ) and his wealth is $1000 . [18 points] a. Let 𝑎𝑎 be the amount of the consumer’s wealth invested in the risky asset. What choice of 𝑎𝑎 maximizes the consumer’s utility? [9 points] The consumer’s problem is to choose 𝑎𝑎 such to maximize: 0.4 ∗ 𝑙𝑙𝑙𝑙 ( 𝑎𝑎 ∗ 1.5 + (1000 − 𝑎𝑎 ) ∗ 1.05) + 0.6 ∗ 𝑙𝑙𝑙𝑙 ( 𝑎𝑎 ∗ 0.85 + (1000 − 𝑎𝑎 ) ∗ 1.05) Simplifying: 0.4 ∗ 𝑙𝑙𝑙𝑙 (1050 + 0.45 𝑎𝑎 ) + 0.6 ∗ 𝑙𝑙𝑙𝑙 (1050 − 0.2 𝑎𝑎 ) Take derivative with respect to a, set equal to zero. 0.4 ∗ 0.45 1050 + 0.45 𝑎𝑎 − 0.6 ∗ 0.2 1050 − 0.2 𝑎𝑎 = 0 0.18 1050 + 0.45 𝑎𝑎 = 0.12 1050 − 0.2 𝑎𝑎 189 − 0.036 𝑎𝑎 = 126 + 0.054 𝑎𝑎 0.09 𝑎𝑎 = 63 𝑎𝑎 = $700 Note to grader: 𝑎𝑎 = 0.7 is ok too (i.e., it’s ok if they calculated the share of wealth rather than the number of dollars if calculation is correct) 𝑎𝑎 = $700

9 b. A money manager comes along and offers to buy the risky asset holdings in exchange for an asset that pays 10% for sure. That is, after the trade, the manager would own the 𝑎𝑎 dollars of the risky asset (where 𝑎𝑎 is what you calculated in the last part) and the consumer would own 𝑎𝑎 dollars of an asset that returns 10% for sure (with the rest in the asset that returns 5% for sure). Will the consumer agree to this trade? Explain how you arrived at your answer (Hint: it requires calculations). [9 points] We need to compare the expected utility from 𝑎𝑎 = $700 in the risky asset from the certain utility of putting $700 in the new asset that pays 10% for sure plus holding the rest in the other safe asset. Expected utility from risky asset: 0.4 ∗ 𝑙𝑙𝑙𝑙 (1050 + 0.45 ∗ 700) + 0.6 ∗ 𝑙𝑙𝑙𝑙 (1050 − 0.2 ∗ 700) 0.4 ∗ 𝑙𝑙𝑙𝑙 (1365) + 0.6 ∗ 𝑙𝑙𝑙𝑙 (910) ≈ 6.9756 Utility from holding $280 in an asset that pays 10% for sure and the rest ($720) in an asset that pays 5% for sure: 𝑙𝑙𝑙𝑙 (700 ∗ 1.1 + 300 ∗ 1.05) ≈ 6.989 Because utility when holding the asset offered by the manager is higher, the consumer will agree to the trade. Note to grader: if the student just writes down that the consumer will agree to the trade without providing adequate explanation (or writes a vague explanation such as “consumer doesn’t like risk”), they should get no credit.

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10 27. The supply of gold is given by 𝑄𝑄 𝑆𝑆 = max (0, 𝑃𝑃 − 5) . The demand for gold is given by 𝑄𝑄 𝐷𝐷 = max(0,500 − 4 𝑃𝑃 ). [15 points] a. What is the equilibrium price and quantity of gold? [2 points] 𝑃𝑃 − 5 = 500 − 4 𝑃𝑃 5 𝑃𝑃 = 505 𝑃𝑃 = 101 𝑄𝑄 = 96 b. To combat speculation, the government imposes a price ceiling of $60 . Calculate the new price and quantity [2 points] , the change in consumer surplus [5 points] , and the deadweight loss of this policy [6 points] . New price is $60 . 𝑄𝑄 𝑆𝑆 = 55 Consumers gain a rectangle with the size 55*41=2255 through paying a lower price. They lose a triangle equal to 0.5*(96-55)*41=840.5. So on net, they gain $1414.5 ($1415 is ok). No need to penalize if they forget the dollar sign. They can also calculate the old surplus, the new surplus and take the difference. Deadweight loss is the triangle whose height is the difference between new quantity and old quantity and whose width is the difference between marginal cost and willingness to pay at Q=55. Willingness to pay is 111.25, marginal cost is 60. Calculation: 0.5*(96-55)*(111.25-60)=$1050.625 ($1051 is ok too). No need to penalize if they forget the dollar sign. Equilibrium price: 101 Equilibrium quantity: 96 New price: $60 New quantity: 55 Change in consumer surplus Deadweight loss: $1050.625 $1414.5

11 28. Consider the following simultaneous move game. Starbucks and Espresso Royale are considering how many new stores to open in a country they’re expanding into. After they simultaneously make their decisions, they compete and earn the additional profits (in millions) given in the cell corresponding to the number of stores each firm opened. [20 points] Starbucks 0 1 2 3 Espresso Royale 0 (0,0) (0, 15) (0,20) (0, 23 ) 1 (20,0) (15,12) ( 12 ,15) ( 4 , 20 ) 2 (30,0) (23,10) (5,10) (0, 15 ) 3 ( 37 ,0) ( 30 ,9) (2,2) (-5, 10 ) a. Identify each firm’s best response to each of the other firm’s actions by circling the firm’s payoff associated with its best response (as we did in class). [ 7 points ] (see bold underlines above) b. Is there a weakly/strictly dominant strategy for either of these firms? Are there any weakly/strictly dominated strategies? Explain. [ 5 points ] a. Starbucks has a strictly dominant strategy – to open 3 stores. This strategy always does better than any other strategy. For this reason, all other strategies are strictly dominated. b. Espresso Royale has no dominant strategy because there is no strategy that always does better than/at least as well as any other strategy (best responses are not in the same row). It has one strictly dominated strategy – to open zero stores. Opening one store always does strictly better than zero stores. Note to grader: not necessary to say “strictly” to get full credit. Points off if they say “weakly”. If they only state the strategies without explaining, -3 points. It’s also ok if they say that Espresso Royale opening two stores is dominated because it’s never a best response. c. What is/are the Nash equilibrium/equilibria of this game? [2 points] Espresso Royale opens 1 store, Starbucks opens 3 stores. d. Prior to the entry decisions being made, Espresso Royale is considering whether to buy Starbucks’ rights to operate in the new country. This would enable Espresso Royale to control how many Starbucks stores are opened and keep all the profits from those stores. Assume that the profits corresponding to each store combination are unchanged. How many Starbucks and Espresso Royale stores will Espresso Royale choose to open if it buys the rights from Starbucks? Explain. [2 points] The highest sum of profits is 39, so Espresso Royale will open 1 Starbucks store and 3 Espresso Royale stores.

12 e. Espresso Royale is considering offering $15 million for Starbucks business in the new country. Is this high enough to compensate Starbucks for lost profits (assume its profits is zero if it doesn’t enter the country, not including any payments made by Espresso Royale)? Is it low enough for Espresso Royale to be willing to pay? Explain. [4 points] [2 points] This is not high enough to compensate Starbucks because if it enters and firms play the Nash Equilibrium, Starbucks’ profits will be $20 million, which is more than $15 million. [2 points] This is low enough for Espresso Royale to be willing to pay because it gains $39-$4=$35 million from buying Starbucks’ right to operate. 29. An economy grows according to the Solow growth model we have studied in class. Assume that the economy starts out in a long-run equilibrium. Illustrate what happens in each of the following scenarios with graphs. Explain what happens to output per capita, consumption per capita, and capital per capita in the short run and the long run. Be as specific as possible. [12 points] a. The savings rate decreases from 10% of output to 5%. [6 points] 2 points for stating that 𝑠𝑠 1 = 0.1 and 𝑠𝑠 2 = 0.05 , either in the graph or in the explanation. Deduct points for not labeling the red and black lines in the graph and/or for not labeling the x- and y-axes. It’s fine if they don’t draw the f(k) line (but they should have the (n+d)k and the sf(k) lines). Savings per worker/investment per worker Capital-labor ratio, k 𝑠𝑠 1 𝑓𝑓 ( 𝑘𝑘 ) ( 𝑙𝑙 + 𝑑 ) 𝑘𝑘 𝑘𝑘 1 ∗ 𝑠𝑠 2 𝑓𝑓 ( 𝑘𝑘 ) 𝑘𝑘 2 ∗

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13 When the savings rate decreases from 𝑠𝑠 1 to 𝑠𝑠 2 , the 𝑠𝑠 ∗ 𝑓𝑓 ( 𝑘𝑘 ) line shifts down. This causes the steady- state capital per worker to decrease from 𝑘𝑘 1 ∗ to 𝑘𝑘 2 ∗ in the long run (capital per capita falls). Output per capita is unchanged in the short run, but falls in the long run. Consumption per capita increases in the short run but falls in the long run. Note: it’s also fine to say that consumption per capita may fall or increase in the long run. But saying it definitely increases in the long run is wrong. If they don’t specify what happens to capital per capita in the short run, that’s fine. Note: just because the savings rate decreases by 0.05 percentage points doesn’t mean that we can know the amount by which capital per capita or consumption per capita changes in the long run. If they try to make a definitive statement about these, take some points off. (we can say something specific about how consumption per capita changes in the short run, but don’t penalize students if they don’t give any specific numbers in this respect). b. A disease kills half (50%) of the population. [6 points] 2 points for making it explicit that capital per capita doubles in the short run (either labeling that in the graph or verbally). Minus points for incorrect or missing labels (again, it’s fine if they don’t draw the f(k) line). None of the curves shift. It’s fine if they don’t draw the new k on the graph, as long as 𝑘𝑘 ∗ is labeled and the written explanation is correct. Capital per capita, output per capita, and consumption per capita increase in the short run. In the long run, everything returns to the original equilibrium (i.e., nothing changes). Note that just because capital per capita doubles doesn’t mean that output per capita or consumption per capita double. If they say the latter, take some points off. f(k) Savings per worker/investment per Capital-labor ratio, k ( 𝑙𝑙 + 𝑑 ) 𝑘𝑘 𝑘𝑘 𝑠𝑠𝑓𝑓 ( 𝑘𝑘 ) 𝑘𝑘 ⬚ ∗

14 SCRATCH PAPER

15 SCRATCH PAPER

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