Luiggi Donayre Summer 2009 Department of Economics Economics 104 Washington University Session 2. Exam 2 Suggested Solutions

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1 uiggi Donayre Summer 2009 Department of Economics Economics 104 Washington University Session 2 Exam 2 Suggested Solutions Name (Print Clearly!) This is a 108 point exam. There are 25 multiple choice questions worth 2 points each and 4 short answer questions worth a total of 50 points. At the end, there is a bonus question worth 8 points. Make sure you read every alternative for the multiple choice questions carefully before writing the letter of the alternative you think is best in the blank. Take your time with the multiple choice questions; they require careful thought. Write legibly in the space provided for the short answer questions. Your score may be lower if your answer cannot be easily read. Be concise and use sound economic reasoning, not just common sense. Make a special effort to be clear in your writing; the grade you receive on the questions depends in part on how well you communicate. Important Note: You may use your calculator for growth rate and compounding questions on this exam. You may not refer, however, to any saved information in your calculator. Accessing any inappropriate information, in your calculator or from any other source, is a serious breech of academic integrity and will be treated as such. GOOD UCK! Multiple Choice Short Answer #1 Short Answer #2 Short Answer #3 Short Answer #4 Bonus Question /50 /9 /15 /13 /13 /8 Total Score /100 1

2 MUTIPE CHOICE (2 points each): Write the letter of the alternative that best answers the question in the blank. Make sure you read all four alternatives before making your choice. A 1. What would happen to the equilibrium price and quantity of coffee if the wages of coffee-bean pickers fell and the price of tea fell? a. Price would fall and the effect on quantity would be ambiguous. b. Price would rise and the effect on quantity would be ambiguous. c. Quantity would fall and the effect on price would be ambiguous. d. Quantity would rise and the effect on price would be ambiguous. B 2. Sarah. and Sarah S., together with thousands of music fans, risk their lives by rushing to buy tickets for a Jason Mraz concert at the Scottrade Center. This behavior indicates a. the ticket price was above the equilibrium price. b. the ticket price was below the equilibrium price. c. the ticket price was at the equilibrium price. d. nothing about the equilibrium price. D 3. Assume Bisbirudolph buys computers in a competitive market. It follows that a. Bisbirudolph has a limited number of sellers to turn to when he buys a computer. b. Bisbirudolph will find himself negotiating with sellers whenever he buys a computer. c. if Bisbirudolph buys a large number of computers, the price of computers will rise noticeably. d. None of the above is correct. C 4. Which of the following statements is not correct? a. The catch-up effect is based on the assumption of diminishing returns to capital. b. Investment in poor countries by citizens of rich countries is one way poor countries can learn new technologies. c. Malthus argued that charity and government aid was an effective way to reduce poverty. d. Peace and justice are keys to growth. A 5. Other things the same, which of the following could explain an increase in productivity? a. either an increase in human capital or an increase in physical capital b. an increase in human capital but not an increase in physical capital c. an increase in physical capital but not an increase in human capital d. neither an increase in human capital nor an increase in physical capital D 6. Real GDP per person is $30,000 in Qingland, $20,000 in Drewland, and $11,000 in Pauland. Saving per person is $1,000 in all three countries. Other things equal, we would expect that a. all three countries will grow at the same rate. b. Qingland will grow the fastest. c. Drewland will grow the fastest. d. Pauland will grow the fastest. A 7. Compared to stocks, bonds offer the holder a. lower risk and lower potential return. b. lower risk and higher potential return. c. higher risk and lower potential return. d. higher risk and higher potential return. 2

3 D 8. In a small closed economy investment is $20 billion and private saving is $22 billion. What are public saving and national saving? a. $24 billion and $2 billion b. $20 billion and -$2 billion c. $2 billion and $24 billion d. -$2 billion and $20 billion B 9. If the nominal interest rate is 5 percent and the rate of inflation is 2 percent, then the real interest rate a. 7 percent. b. 3 percent. c. 2.5 percent. d..4 percent. B 10. Which of the following would not be a result of replacing the income tax with a consumption tax so that interest income was no longer taxed?? a. The interest rate would decrease. b. Investment would decrease. c. The standard of living would eventually rise. d. The supply of loanable funds would shift right. B 11. Imagine an economy in which: (1) pieces of paper called yollars are the only thing that buyers give to sellers when they buy goods and services, so it would be common to use, say, 50 yollars to buy a pair of shoes; (2) prices are posted in terms of yardsticks, so you might walk into a grocery store and see that, today, an apple is worth 2 yardsticks; and (3) yardsticks disintegrate overnight, so no yardstick has any value for more than 24 hours. In this economy, a. the yardstick is a medium of exchange but it cannot serve as a unit of account. b. the yardstick is a unit of account but it cannot serve as a store of value. c. the yardstick is a medium of exchange but it cannot serve as a store of value, and the yollar is a unit of account. d. the yollar is a unit of account, but it is not a medium of exchange and it is not a liquid asset. C 12. In which of the following sets of assets are the assets correctly ranked from most liquid to least liquid? a. bonds, money, cars, houses b. bonds, cars, money, houses c. Money, bonds, cars, houses d. Money, cars, houses, bonds D 13. Imagine that the federal funds rate was below the level the Federal Reserve had targeted. To move the rate back towards it s target the Federal Reserve could a. buy bonds. This buying would increase the money supply. b. buy bonds. This buying would reduce the money supply. c. sell bonds. This selling would increase the money supply. d. sell bonds. This selling would reduce the money supply. C 14. If the public decides to hold less currency and more deposits in banks, bank reserves a. decrease and the money supply eventually decreases. b. decrease but the money supply does not change. c. increase and the money supply eventually increases. d. increase but the money supply does not change. 3

4 A 15. If the Fed makes open market purchases of bonds, a. the money supply increases by more than the amount of bonds purchased. b. the money supply increases by less than the amount of bonds purchased. c. the money supply decreases by more than the amount of bonds purchased. d. the money supply decreases by less than the amount of bonds purchased. C 16. When the money market is drawn with the value of money on the vertical axis, if the Federal Reserve sells bonds, then the money supply curve a. shifts rightward, causing the value of money measured in terms of goods and services to rise. b. shifts rightward, causing the value of money measured in terms of goods and services to fall. c. shifts leftward, causing the value of money measured in terms of goods and services to rise. d. shifts leftward, causing the value of money measured in terms of goods and services to fall. D 17. Which of the following is not implied by the quantity equation? a. If velocity is stable, an increase in the money supply creates a proportional increase in nominal output. b. If velocity is stable and money is neutral, an increase in the money supply creates a proportional increase in the price level. c. With constant money supply and output, an increase in velocity creates an increase in the price level. d. With constant money supply and velocity, an increase in output creates a proportional increase in the price level. B 18. Chai deposits money into an account with a nominal interest rate of 6 percent. He expects inflation to be 2 percent. His tax rate is 20 percent. Chai s after-tax real rate of interest a. will be 2.8 percent if inflation turns out to be 2 percent; it will be higher if inflation turns out to be higher than 2 percent. b. will be 2.8 percent if inflation turns out to be 2 percent; it will be lower if inflation turns out to be higher than 2 percent. c. will be 3.2 percent if inflation turns out to be 2 percent; it will be higher if inflation turns out to be higher than 2 percent. d. will be 3.2 percent if inflation turns out to be 2 percent; it will be lower if inflation turns out to be higher than 2 percent. A 19. High and unexpected inflation has a greater cost a. for those who save than for those who borrow. b. for those who hold a little money than for those who hold a lot of money. c. for those whose wages increase by as much as inflation, than those who are paid a fixed nominal wage. d. for savers in low income tax brackets than for savers in high income tax brackets. D 20. When inflation rises, people a. make less frequent trips to the bank and firms make less frequent price changes. b. make less frequent trips to the bank while firms make more frequent price changes. c. make more frequent trips to the bank while firms make less frequent price changes. d. make more frequent trips to the bank and firms make more frequent price changes. 4

5 C 21. Julie puts money into an account. One year later she sees that she has 5 percent more dollars and that her money will buy 6 percent more goods. a. The nominal interest rate was 11 percent and the inflation rate was 5 percent. b. The nominal interest rate was 6 percent and the inflation rate was 5 percent. c. The nominal interest rate was 5 percent and the inflation rate was -1 percent. d. None of the above is correct. C 22. If an economy with no population growth or technological change has a steady state MPK of 0.1, a depreciation rate of 0.1, and a saving rate of 0.2, then the steady state capital stock: a. is greater than the Golden Rule level. b. is less than the Golden Rule level. c. equals the Golden Rule level. d. could be either above or below the Golden Rule level. B 23. In the context of the Solow model, the fact that the U.S. exhibits a saving rate well below sustainable levels would allow us to infer that the capital stock in the U.S. is a. well above the Golden Rule level b. well below the Golden Rule level c. about equal to the Golden Rule level d. increasing at exponential rates towards its steady state value A 24. If the per worker production function is given by then the steady state ratio of capital to labor is: a. 8. b. 8. c. 16. d / 3 y k, the saving ratio is 0.4, and the depreciation rate is 0.1, D 25. In the Solow growth model of an economy with population growth, the break-even level of investment must do all of the following except: a. offset the depreciation of existing capital. b. provide capita for new workers. c. keep the level of capital per worker constant. d. equal the MPK. 5

6 SHORT ANSWER QUESTIONS. Read all parts of each question carefully and answer in the space provided. Use clear economic reasoning and make sure you write legibly. 1. (9 points) Use the table below to answer the following questions. Stock Yld % PE Vol 100s Hi o Close Net Chg Burger King , Coca Cola , Mc Donalds Pepsi , Sprint , Verizon , a) (5 points) Explain what dividends are and determine which company paid the highest dividend per share. How much was dividend per share in this company? Dividends refer to the part of profits paid by firms to their shareholders. Dividend yield equals dividend per share over the price of the share. You can use this definition to calculate dividends for each of the firms in the table. Doing so yields that the firm with the highest dividend per share is Pepsi: Pepsi (dividend per share) = 0.021(62.45) b) (6 points) Ben is a risk-averse investor. That is, he does not like risk. If he had $100,000, how should he allocate his wealth among the stocks above to create his portfolio? Explain (hint: do not state how many stocks he should buy from each company. Only state which companies he should buy stocks from and based on what criteria). As discussed in class, stocks are risky. Therefore, investors want to find ways to avoid the risk. The main way in which they do so is by diversifying it. As we talked in class, investors do not want to allocate all shares in one firm because if that firm collapses, their wealth will be seriously harmed. Hence, investors will diversify their portfolios. There are basically three broad categories of firms: fast food, beverage and communication. There is no unique way to diversify the portfolio. In general, fast food companies seem to be in a negative streak in terms of their price changes. Despite this issue, it might be a good idea to get shares from McDonald s since, given they re relatively stable PE ratio, you would expect the price to increase in the future (though the volume trade is not too high). You would not expect to make that much a profit with these shares, though, since the variation between low and high price is not that big (but then again, Ben cares more about risk than returns, so he wouldn t mind this too much). In terms of beverage companies, both seem to be overvalued. Their price changes have been relatively high. Both exhibit relatively high dividend yields. Either not buying shares from beverage companies or buying a small fraction of the portfolio in either one would be appropriate. Regarding communication companies, Sprint seems to be a good company to buy shares from. It has a low PE ratio, which would lead you to believe the price will increase in the future (note, as well, the negative chance in price, consistent with the low PE ratio). Even though the dividend yield is not so high, it is likely to increase as the price increases in the future. 6

7 2. (15 points) Suppose the Gorman Bank (GB) holds $500 million in deposits and that the reserve requirement is 10 percent. a) (3 pts.) Assume GB does not hold any excess reserves initially. If Maggie, GB s largest depositor, withdraws $50 million in cash from her account and this makes GB hold $75 million in excess reserves, show both T-accounts for GB, before and after Maggie withdrew her money. Initial T-account Assets iabilities Reserves Deposits oans 450 T-account after withdrawal Assets iabilities Reserves Deposits oans 330 b) (5 pts.) Suppose now that Katie deposits $15 million in GB. What is the maximum amount that the money supply could increase? What are you assuming for this to happen? If Katie deposits $15 million in GB then, assuming that all banks hold the minimum amount of reserves necessary and that all money given out in loans will be deposited in other bank accounts, the money supply would be given by: MS = 15 (1/R) = 15(1/0.1) = 150 However, since the question is asking for the maximum amount that the money supply can increase (i.e., change), we need to take into account the fact that currency is reducing by $15 million. So, the maximum amount MS can change is = $135 million. c) (7 pts.) If the Fed lowers the reserve requirement to 5%, but banks choose to hold another 7.5% of deposits as excess reserves, what is the overall change in the money multiplier and the money supply from Katie s deposit as a result of these actions? If the Fed lowers the RR to 5%, and banks choose to hold another 7.5% as excess reserves, then the $15 million deposited by Katie will generate required reserves equal to 15(0.05)=$0.75 million and excess reserves equal to 15(0.075)=$1.125 million. Hence, banks will keep =$1.875 million as reserves. Therefore, the relevant ratio of reserves to deposits is 1.875/15 = Then, the money supply will be given by 15(1/0.125) = 15(8) = $120 million. Since the initial money supply was $135 million, the (negative) change in the money supply is $15 million. 7

8 3. (16 points) Suppose that the market for loanable funds in Pittyburg is initially in equilibrium. a) (4 pts.) Molly, president of Pittyburg, decided to cut taxes as a way to gain popularity. Even though tax revenue falls, she continues spending as before because she thought she could use Pittyburg s central bank to monetize the deficit. Of course, since the central bank is independent, she was denied that possibility. If before the tax cut, she collected in taxes as much as her government spent, and tax revenue fell $350 billion after the tax cut, use a supply-and-demand diagram to analyze how Molly s decision changes the initial equilibrium in the market for loanable funds. What s the new equilibrium quantity? Make sure to show the graph and to explain what happens during the transition between the old and the new equilibrium. Since Molly collected in taxes as much as her government spent before the tax cut, the budget was balanced. However, after the tax cut, tax revenues fell in $350 billion. Hence, she incurred in a budget deficit, which reduces public savings and, thus, national savings. This shifts the supply of F leftwards (or, equivalently, upwards). At the prevailing interest rate, there is an excess demand (i.e, shortage) for F, which pushes the interest rate up until the market clears again. In the end, the quantity of F reduces and the interest rate rises. Graphically: b) (6 pts.) After the tax cut, Molly does not know what to do. She is concerned about the possibility of a crowding-out effect. Her advisor, Sarah S., tells her that she should provide investment tax credits if she wants to change this situation. Use a supply-and-demand diagram to show the effects of Sarah s advice, using the equilibrium after the tax cut as the new initial situation. Explain what effect is Molly exactly concerned about and why this crowding-out effect arises. Will this advice address Molly s concern? What is the new price and quantity of equilibrium in this case? The budget deficit crows out investment in the sense that there are less loanable funds available for firms to finance their new projects. That is, public investment crowds out private investment. This simply arises because the budget deficit increases the real interest rate, reducing the incentive for firms to take loans (since the higher interest rate makes them more expensive). 8

9 Sarah S. suggests implementing investment tax credits, which increases the incentives for firms to invest and, therefore, increases the demand for F. Therefore, this policy might counter-balance the budget deficit and promote private investment. The higher demand will unambiguously increase the interest rate even more, but the effect on the quantity of F depends on the magnitude of the supply and demand curves shifts. It is ok if you just assumed one of the three cases. Graphically: In this case, the shift in the demand curve is bigger than the shift in the supply curve so the quantity of F increases. c) (3 pts.) Paul, an expert government analyst, talks to Molly and tells her that independently of whether her advisor s recommendation solved her concern or not, the new situation does not promote long-term economic growth in Pittyburg. He tells Molly that it has actually created an unfavorable trade-off between the present and the future. What might Paul be talking about? Is he right? By increasing investment today, there will be a higher long-run growth in the economy. However, in order to finance the higher investment today, private savings need to increase. The higher interest rate (r 3 ) increases the quantity supplied of F along the S 2 curve. Therefore, consumption today is going down to finance a higher long-run growth in the future. There is a trade-off between present and future. 4. (13 points) The Solow model and the Golden Rule. Part I The Production function and the steady-state a) (3 pts.) A general class of production functions used in Economics is the so-called Constant Elasticity of Substitution (CES) production function: Y F 1/ ( K, ) K (1 ) where (0,1) is the share of capital (the percentage change in output due to a change in capital) and determines the degree of substitutability of inputs. This production function implies that the rate of substitution between capital and labor is constant. Does it exhibit constant returns to scale? Show that it does or that it doesn t. 9

10 To show whether this production function exhibits CRS or not, you need to determine how much output increases when all inputs increase, say by a factor. Hence, if all inputs increase by this factor, the new production function is: F( K, ) 1/ ( K) (1 )( ) 1/ K (1 ) 1/ ( K (1 ) ) 1/ K (1 ) F( K, ) Since increasing all inputs by a factor increases the output (or F(K,)) by the same factor, then this function exhibits constant returns to scale. A special case of the CES function is the Cobb-Douglass function (when 0), that we studied in class. Suppose the share of capital is 1/3 and let 0. So, the production function in this case is: Y F 1/ 3 2 / 3 ( K, ) K b) What is the per-worker production function? The per-worker production function is simply the aggregate production function expressed in per worker units, Y/. Hence, for y Y /, the per worker production function is: y Y F( K, ) K 1/ 3 2 / 3 K 1/ 3 1/ 3 2 / 3 2 / 3 K 1/ 3 k 1/ 3 c) Assume that the country possesses 40,000 units of capital and 5,000 units of labor and suppose the depreciation rate is 10%. What saving rate is necessary to make the given capital-labor ratio the steady-state level of capital per worker? With K = 40,000 and = 5,000 then k = 40,000/5,000 = 8. The steady-state condition is given by 0.1 and k 8, then it follows that: sf ( k) k. With sk 1/ k s (8 1/ ) (0.1) 8 s 0.8 / d) If the government implements a policy that changes the saving rate to 50%, what would happen with the new steadystate level of capital per worker? How would the transition occur? Graph the initial steady-state and the transition to the new steady-state. If s 0. 5, then the new steady-state capital per worker will be given by: sk 1/ k 0.5( k 1/ 3 ) (0.1) k k As the savings rate increases, the investment curve shifts upwards, with a new, higher steady-state. Hence, the original steady-state level of capital per worker is now below the new steady-state, which implies that investment is higher than depreciation, and so capital per worker will accumulate over time until it converges to the new steady-state. Graphically: 10

11 Part II The Golden Rule In Ezeland, capital equipment depreciates at a much faster rate than it does in the Saranyaland. If the countries are otherwise identical, in which country will the Golden Rule level of capital per worker be higher? Show it graphically. The GR level of capital per worker will be higher in Saranyaland because, at the GR level, MPK. Since Saranyaland has a lower, then it must be the case that, at the GR level, the MPK is higher for Saranyaland than for Ezeland. With a higher MPK, the GR level of capital per worker is higher for Saranyaland. Graphically: 11

12 Bonus Question (8 pts.) We have seen in class that human capital is a key contributor to economic growth. In particular, research intensity and new ideas have been calculated to explain as much as 80% of recent U.S. growth (Jones, 2005). The following figure plots research intensity in the U.S. and the G-5 countries. Research intensity is measured as the number of scientists, R&D workers and engineers as a percentage of the labor force. What is worth noting from this figure is the magnitude of research intensity. In either the U.S. or G-5, less than 1% of the labor force is engaged in research according to the National Science Foundation. Given this information, how could you explain the apparent puzzle between the fact that the number of researchers is so small, relative to the size of the labor force, and their big contribution to economic growth? Do you think a Cobb- Douglass production function would be appropriate to explain this phenomenon? If so, explain why. If not, how would you modify the typical production function to explain this phenomenon? This is related to what we discussed in class about ideas (or technology, for that matter). Ideas are a public good in the sense that once researchers find a new, more efficient way to produce goods or services, then these are rapidly disseminated and everyone benefits from it. So, even though it is true that there are relatively few researchers and scientists vis-à-vis the size of the labor force, the scale effect associated with the nonrivalry of ideas operates at a global level. This is usually referred to as the social returns to ideas. Thus, social returns to ideas are positive externalities. This effect can be captured by assuming that the production function exhibits increasing returns to scale. That is, if all inputs increase by a factor, then output increases by a factor greater than. This assumption then would capture the notion that as the stock of ideas grow, output grows even more precisely because of the social returns to ideas. Because a Cobb-Douglass production function exhibits constant returns to scale, then it would not be a good assumption for this particular case. 12