Econ 201 Macroeconomic Theory I Assignment 1 (Chapter 10, 11,12) 1. Label each of the following statement true, false, or uncertain. Explain briefly. a) In the long-run, capital accumulation affects the level of output, but not the growth rate of output per capita. True/Uncertain. If the production function satisfies the property of decreasing return to capital, as the one we discussed in Chapter 10 and 11, then in the long run capital accumulation will only affect the level of output per capita, but not the growth rate of output per capita. b) Output per capita in most countries in the world is converging to the level of output per capita in the United States. Uncertain/ False. Output per capita in OECD countries converges to the level of output per capita in the United States. But for some African countries, their output per capita remains in low level or even have negative growth rate since 1960. c) For much of the human history, any increase in output leads to a proportional increase in population, and therefore, there was stagnation of output per capita. True. See Pg 235 of textbook. d) A higher investment rate cannot sustain higher growth rate forever. True. Higher investment rate (higher saving rate) will only increase the capital accumulation. As illustrated in (a), if the production function satisfies the property of decreasing return to capital, then this will lead to positive growth rate for some time, but it cannot lead to higher growth rate forever. e) The golden rule capital stock is the capital stock that gives the highest steady state output per worker. False. The golden rule capital stock is the capital stock that gives the highest steady state consumption per worker. f) Education increases human capital, and so output. So increase education can sustain the long-run growth. False/Uncertain. If the production function is decreasing return to human capital, as physical capital, then increasing education, as accumulation physical capital, cannot sustain long-run growth 1
g) If the production function is in the form of constant return to capital, for example, like Y=AK, where K is capital and A is a constant productivity level, then capital accumulation can sustain economic growth. True. h) A higher saving rate implies a higher growth rate of capital per worker for some time, and a higher level of capital per effective worker in the steady state, but not a higher rate of growth of output per worker in the balance growth path. True. The increase of saving rate will lead to an increase of growth rate for some time, but in the new ss, the output per effective labor is still constant. 2. Question 2 of Chapter 10 in the textbook. a. $2*200+$3*3000=$13,000 b. 10*800+30*300=17,000 pesos c. (10*800+30*300)/10=$1700 d. $2*800+$3*300=$2500 e. Mexican standard of living relative to the U.S. exchange rate method: 1700/13000 =0.13; PPP method: 2500/13000=0.19 3. Question 7 of Chapter 11 in the textbook. a. Yes. b. Yes. c. Yes. d. Y/N = (K/N) 1/3 e. In steady state, sy//n = δk/n, which, given the production function in part (d), implies K/N=(s/δ) 3/2 f. Y/N =(s/δ) 1/2 g. Y/N = 2 h. Y/N = 2 1/2 4. Question 8 of Chapter 11 in the textbook. a. Substituting from problem 7 part (e) implies K/N=1. b. Substituting from problem 7 part (f), Y/N=1. c. K/N=0.35; Y/N=0.71 d. K/N Y/N t 1.00 1.00 t+1 0.90 0.965 t+2 0.817 0.935 t+3 0.747 0.907 5. Analyze using a diagram (similar to Figure 12-3) the short run and long run effect of an increase in on the level of K/AN, Y/AN, and the growth g A 2
rate of K/N, Y/N, K and Y. Draw the time paths of K/AN, Y/AN, K/N, Y/N, K and Y before and after the change of. g A 3
4
5
6. Question 3 of Chapter 12 in the textbook. a. Most technological progress seems to come from R&D activities. See discussion on fertility and appropriability. b. This proposal would probably lead to lower growth in poorer countries, but higher growth in rich countries. c. This proposal would lead to an increase in R&D spending. If fertility did not fall, there would be an increase in the rates of technological progress and output growth. d. Presumably, this proposal would lead to a (small) decrease in the fertility of applied research and therefore to a (small) decrease in growth. e. This proposal would reduce in the appropriability of drug research. Presumably, there would be a reduction in the development of new drugs, a reduction in the rate of technological progress, and a reduction in the growth rate. Q7 will be in AS2. 8. a)-c): Question 7 of Chapter 12 in the textbook. d) Find the golden rule level of saving rate that maximizes the steady state consumption per effective worker, C/AN. a. i. K/(AN) = (s/(δ+g A +g N )) 2 = 1 ii. Y/(AN)= (K/AN) 1/2 =1 iii. g Y/(AN) = 0 iv. g Y/N = g A =4% v. g Y = g A +g N =6% b. i. K/(AN) = (s/(δ+g A +g N )) 2 = 0.64 ii. Y/(AN)= (K/AN) 1/2 =0.8 iii. g Y/(AN) = 0 iv. g Y/N = g A =8% v. g Y = g A +g N =10% An increase in the rate of technological progress reduces the steady-state levels of capital and output per effective worker, but increases the rate of growth of output per worker. c. i. K/(AN) = (s/(δ+g A +g N )) 2 = 0.64 ii. Y/(AN)= (K/AN) 1/2 =0.8 iii. g Y/(AN) = 0 iv. g Y/N = g A =4% v. g Y = g A +g N =10% 6
(K/(AN)) = (4/5) 2 ; (Y/(AN)) = (4/5); g Y/(AN) = 0; g Y/N = 4%; g Y = 10% People are better off in case a. Given any set of initial values, the level of technology is the same in cases (a) and (c), but the level of capital per effective worker is higher at every point in time in case (a). Thus, since Y/N=AY/(AN)=A(K/(AN)) 1/2 =A 1/2 (K/N) 1/2, output per worker is always higher in case (a). d. Golden Rule level of saving rate: C Y C s C = ( 1 s) Y = (1 s) = (1 s) AN AN AN δ + g A + g N d C d s 1 d ( ) = ((1 s) ) = s(1 s) ds AN ds δ + g A + g N δ + g A + g N ds d C ( ) = 0 1 2s = 0 s = 0.5 ds AN 7