Answer key to the Second Midterm Exam Principles of Macroeconomics Professor Adrian Peralta-Alva University of Miami October 20, 2007 I Multiple Choice Questions (78 points total, 3.25 points each) Select what you think is the best answer to each of the following questions. YOU MUST ANSWER ALL MULTIPLE CHOICE QUESTIONS USING THE BUBBLE SHEET PROVIDED. 1. The time series of TFP for Solowland is illustrated in the graph below. The y-axis denotes the valueoftfp,andthex-axisdenotesyears. TFP of Solowland 120 100 80 60 40 20 0 2007 2027 2047 2067 2087 2107 2127 2147 2167 We can see that the TFP of Solowland increases as time goes by. According to the Solow model, Solowland will experience sustained economic growth during the period 2007-2167 (a) true (b) false 2. Consider a country that has reached its long run equilibrium. TFP and capital depreciation are not expected to change but the saving rate goes up permanently. This country will experience sustained economic growth. 1
(a) true. (b) false. 3. A higher level of efficiency or TFP translates into a higher long-run GDP, and also into higher long-run consumption. (a) true. (b) false. 4. Consider two countries with the same work force, saving rates, efficiency levels, capital depreciation rates, and values for parameter α. Country 1 has one-tenth of the capital stock of country 2. Country 2 is very close to its long-run equilibrium. Thus, Country 1 is poor while Country 2 is rich(er). According to the Solow model (a) Country 1 will grow fast for some years and it will eventually catch up with Country 2 (in terms of GDP levels). (b) Country 1 is poor. Poor countries tend to stay poor and thus it will reach its own long-run equilibrium where GDP is lower than that of Country 2. 5. One implication of the Information Technology Revolution is that computers, semiconductors, etc. constitute now a large proportion of the total capital stock of the United States. Information Technologies have a very high rate of depreciation. Thus, the Information Technology revolution resulted in a sudden increase in the depreciation rate of physical capital in the United States. According to the Solow model, this increase in capital depreciation (holding everything else constant) (a) should translate into a lower long-run capital stock, and thus lower long-run GDP (b) should translate into a higher long-run capital stock, and thus higher long-run GDP 6. The U.S. economy experienced one of its strongest economic expansions during the 1990-2000 period. Some people attribute this economic expansion to the massive introduction of Information Technologies. Based on your answer to the previous question, and using a Solow diagram, it is possible to say (a) that the increase in TFP associated to the use of information technologies more than compensated for the negative impact of higher depreciation, which can help explain why the economy ended up with a higher GDP (b) that the increase in GDP attributed to the higher depreciation of capital was further expanded by the increase in TFP associated to the use of information technologies 7. If Pfizer Pharmaceuticals is considering building a new research facility at a cost of $8 million, with expected profit from the facility of $2 million, then the expected profit rate is. If inflation equals 3% and if the risk free real interest rate equals 20% then we can expect Pfizer to. 2
(a) 25%; build the new research facility (b) 25%; invest its money in a different, more profitable project, or at best to put it in a corporate savings account (c) 125%; build the new research facility (d) CANCELED 8. Which of the following explains why investment demand is negatively related to the real interest rate? (a) A lower real interest rate makes more investment projects profitable and hence undertaken. (b) Consumers are willing to spend less and hence save more at higher real interest rates. (c) Interest rate flexibility in financial markets assures an equilibrium in which saving equals investment. (d) All of the above are correct reasons why investment demand is negatively related to the real interest rate. 9. Which of the following may have a negative relationship with household saving? (a) the real interest rate (b) expected future income (c) a and b. 3
10. In the above figure, if the real interest rate was 2, there would be. In this situation market forces will quickly push the interest rate until equilibrium is restored. (a) a shortage in available funds for investment; down (b) a shortage in available funds for investment; up (c) a surplus of saving; down (d) a surplus of saving; go up 11. You lend a friend $100 and he pays you back the $100 plus 5 percent next year, for a total of $105. You are (a) clearly better off because $105 is greater than $100. (b) better off only if the (nominal) interest rate is less than 5 percent. (c) better off only if the (nominal) interest rate is more than 5 percent. (d) None of the above answers are correct. 12. The saving supply captures the relation between total saving (private + government) and the interest rate. As you may know, the U.S. government had a nearly zero deficit by 1999 and now it has a large deficit (i.e. its tax revenue is now lower than its expenditures). Assuming private saving today is similar to that of 1999 and that the Investment demand curve today is also similar to that of 1999, (a) the real interest rate today should be higher than in 1999 and Investment should be lower (b) the real interest rate today should be higher than in 1999 and Investment should be higher (c) the real interest rate today should be lower than in 1999 and Investment should be lower (d) the real interest rate today should be lower than in 1999 and Investment should be higher 13. Frank Murphy is considering how many snowmobiles to purchase for his snowmobile rental business. Frank will have this business open for only one year. Below are his estimates of the number of snowmobile rentals per year, depending on the number of snowmobiles available. Number of Yearly Snowmobiles rentals 1 90 2 170 3 240 4 300 5 350 After paying all expenses Frank expects a profit of $10 per rental. Each snowmobile costs $15,000. What will be the total investment of Frank Murphy on snowmobiles if the interest rate is 5.5%? A) 0 B) 1 C) 2 D) 3 E) 4 4
14. Which of the following may have a negative relationship with corporate investment? I) the real interest rate, II) lower economic growth expectations, or III) lower taxes on corporate income (a) IandII. (b) II and III (c) II only. (d) I only. (e) III only. 5
15. Consider the market for unskilled workers in an automobile plan assembly line. Suppose this market is in equilibrium today. Suppose that starting tomorrow unskilled workers find better opportunities in a different industry sector and become less willing to do factory work. As a result, wages in the automobile assembly sector and employment. A) falls; falls B) falls;increases C) go up; declines D) go up; increases 16. A permanent increase in the fraction of women willing to work: A) increases the supply of labor. D) decreases the demand for labor. B) decreases the supply of labor. E) increases the demand for labor. C) increases the marginal product of labor. 17. The demand for labor in a certain industry is ND = 40-5w, where ND is the number of workers employers want to hire and w is the real wage measured in dollars per hour. The supply of labor in the same industry is NS = 10 + 5w, where NS is the number of people willing to work. If the minimum wage is $4 per hour, how many workers will be unemployed? A)5 B) 10 C) 15 D) 20 E) 0 18. If a firm hires up to N workers the marginal product of the N th worker equals 30 N bulbs per hour. Lightbulbs sell for $2 each, and there are no costs to producing them other than labor costs (i.e. other costs are negligible). If the wage is $30 per hour, how many workers should this firm employ (i.e. its demand at a wage of $30)? A) 0 B) 30 C) 15 D) The correct answer is neither A, nor B, nor C 19. Depart from the situation described in problem 18, but now assume that the price of lightbulbs increases to $3 each. How many workers should the firm hire if wages are still at $30 per hour (i.e. its demand at a wage of $30, when price of output is $3)? A) 0 B) 60 C) 20 D) The correct answer is neither A, nor B, nor C 20. Depart from the situation described in problem 18, but now assume that the supply of workers equals N s =15. Notice that supply does not depend on the wage rate. What will be the equilibrium wage of this market? A) $30 B) $20 C) there is not enough information to answer 6
21. The demand for and supply of labor in a certain industry are given by the equations N d = 400 2w N s = 240 + 2w Equilibrium wage is. In this case, a minimum wage of $50 destroys jobs (relative to equilibrium with no minimum wages). A) $160; 0 B) $40; 20 C) $40; 0 D) $40; 40 22. Suppose that a given firm buys new equipment and reorganizes its production practices in such a way that the marginal product of each worker increases (at any possible employment level). Also, assume that wages and the price of the good of the firm are unchanged. Given that the firm can produce the same as before with fewer workers, the labor demand will (a) shift to the left because the firm can now produce the same at a lower cost (b) shifttotherightbecausethefirmcanmakemoreprofits by hiring more workers 23. The marginal product of labor is the additional: A) wage paid for an additional hour of work. B) wage paid for an additional worker employed. C) labor employed to produce one more unit of output. D) output produced by one more worker. E) hour worked to produce one more unit of output. 24. According to the standard Solow model, in the long-run, an economy that does not save at all (i.e. s =0) will end up with ; while an economy that saves as much as possible (s =1) will end up with. A) a low level of capital but high GDP and consumption since expenditure motivates production; a very low GDP since high saving does not motivate GDP B) no capital and thus no GDP and no consumption; a relatively high GDP since high savings push the Solow curve up. However, they will also have zero consumption since consumption is the fraction of the GDP spent, and in this case such fraction is (1 s) =0 C) The Solow model cannot tell us what happens when s =0or s =1. 7
II Essay problems Answer, as concisely as possible, each one of the following problems. Limit youranswertothespace provided. 1. (10 points The engine of economic growth) Empirical studies document that the GDP per worker, denoted by Y L, of any given country can be related to its per worker stock of capital, denoted by K L, and to its level of total factor productivity (TFP) in the following way µ Y K α L = TFP t, t L t the time subindex t is measured in years and α is a constant between 0 and 1 that may vary from country to country. The Solow growth model, in turn, dictates that capital per worker evolves through time according to the recursive formula K L = s t TFP t K α L t +(1 δ) K L t, t+1 1+η where η is a number denoting the growth rate of the labor force, s denotes the savings rate and δ denotes the rate of depreciation of physical capital. Using a Solow diagram explain what is the only possible force that can generate sustained growth in GDP per worker (Hint: Try the different possibilities that push the Solow curve up and explain why only one of them can generate sustained economic growth) FOR SUSTAINED ECONOMIC GROWTH WE REQUIRE THE SOLOW CURVE TO EXPAND IN A SUSTAINED WAY (WITHOUT BOUNDS). HIGHER SAVING OR TFP, LOWER DEPRECIATION, AND LOWER POPULA- TION ALL RESULT IN A HIGHER SOLOW CURVE. HOWEVER, SAVING, DE- PRECIATION, AND LOWER POPULATION GROWTH CAN ONLY PUSH THE SOLOW CURVE WITH BOUNDS. (SAVING IS BOUNDED BY 1, DEPREC IS BOUNDED BY 0, ETC) TFP IS THE ONLY FORCE THAT CAN CONTINUOUSLY EXPAND THE SOLOW CURVE SINCE, A PRIORI, THERE ARE NO BOUNDS TO TFP IMPROVEMENTS. 2. (12 points total) A graphical analysis of the AK" model: The diagram below considers a growth model we studied in midterm one. Here we will study it from the graphical point of view. The most relevant part of the diagram is the forecasting equation for capital k t+1 = sak t +(1 δ) k t. It is assumed here that capital includes both, human and physical capital, and that production of 8
GDP using such type of capital is not subject to diminishing returns. In particular, GDP t = Ak t. In the above equations the values of the saving rate, TFP, and capital depreciation rate are all strictly positive, constant through time, and such that sa +(1 δ) > 1. Use the diagram below, and the same methods we developed in class to study the Solow diagram to answer the following questions: kt 1 kt 1 sakt 1 kt 45 degree line k 2009 k 2008 k 2007 k 2007 k 2008 k 2009 k t (a) (4 points) Illustrate on the x-axis" of the diagram, what will happen to capital as time goes by (do at least two forecasts using the modified Solow equation above)? capital will grow (b) ( 4points) If TFP, saving, and depreciation stay constant, will this economy stagnate or continue growing in the long-run? (justify your answer, and base your conclusions on what you learn from part a) SINCE THE EQUATION DRIVING THE BEHAVIOR OF CAPITAL IN THIS CASE IS, k t+1 = sak t +(1 δ) k t, WHICH IN THE GRAPH IS A LINE THAT IS ALWAYS ABOVE THE 45 DEGREE LINE, CAPITAL INCREASES CONTIN- UOUSLY. THIS ECONOMY CAN GROW AT A SUSTAINED RATE, EVEN IN THE LONG-RUN. (c) (4 points) Construct a new diagram (or draw on top of the one provided above) where you also study the behavior of capital through time for a different economy that has the same capital for 2007, TFP, and capital depreciation rate as the economy of the original diagram, but with 9
a higher saving rate. The one-period ahead forecasts for such an economy, and the curve for such an economy, should correspond to the following equation k country 2 t+1 = s 0 Ak country 2 t +(1 δ) k t, with s 0 > s. In summary, I am asking you to illustrate in a single diagram how capital evolves through time for two economies where one saves more than the other. AS WE CAN SEE BELOW, COUNTRY 2 WILL GROW ALWAYS FASTER THAN COUNTRY 1 country k 2 t 1 s country Ak 2 t 1 k t kt 1 count. 2 k 2009 kt 1 sakt 1 kt 45 degree line k 2009 count. 2 k 2008 k 2008 count. 2 k 2008 k2007 k 2008 k2009 count. 2 k 2009 kt 10