Help me with brief elaboration of the answers
Qua nt'rtatiye questions ch. 3' of Mankiw: Problem ?.1: Country A and B has the production function: x = Fix, L}: x\"- L\"2 A. Does this production function haye constant returns to scale? B. What is the per-worker production function. WL=f{K.fL) C. Assume that neither country experiences population growth or technological progress and that 5 percent of capital depreciates each year. Assume further that country A sayes 1D percent of output each year, and country B sayes 2|] percent of output each year. Find the steady state level of capital per worker, the steady-state Ieyel of income per worker and consumption per worker. D. Suppose that both countries start off with a capital stock per worker of 2. What are the levels of income per worker and consumption per worker? Remembering that the change in the capital stock is gross investment minus depreciation, calculate capital stock per worker, income per worker, and consumption per worker overtime. How many years will it be before consumption per worker in Country B is higher than the leyel of consumption per worker in country A. Problem 12: In the discussion of German and Japanese postwar growth, the text describes what happens when part of the capital stock is destroyed in a war. By contrast, suppose that a war does not affect the capital stock, but that casualties reduce the labor force. A. What is the immediate impact on total output and on output per person? B. Assuming that the saving rate is unchanged and that the economy was in a steady state before the war, what happens subsequently to output per worker in the postwar economy? Is the growth rate of output per worker after the war smaller or greater than normal? Problem 13: Consider an economy described by the production function: x = Fix, L}: k?\"- L\" A. What is the per-worker production function? E. Assuming no population growth or technological progress, nd the steady- state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate. C. Assume that the depreciation rate is it] percent per year. Make a table showing steady-state capital per worker, output per worker, and consumption per worker for saying rates of i] percent, 'I percent, 2D percent, and Si] percent and so on. What saving rate maximizes output per worker? What saving rate maximizes consumption per worker? D. Use calculus to find the marginal product of capital. Add to your table the marginal product of capital net of depreciation for each of the saying rates. urn-r-r-ur-upageBreakur-u-u-ur-uur-ru-r-uu-r-ru-r-ur-u-run-r-r-II-r-r-u-r-ur-u-r-un-r-u Problem 1d. "Devoting a larger share of national output to investment would help restore rapid productivity growth and rising living standards". Do you agree with this claim? Explain. Problem 15: (somewhat hard) ne view of the consumption function is that workers have high propensities to consume and capitalists have low propensities to consume. To explore the implications of this view, suppose that an economy consumes all wage income and saves all capital income. Show that if the factors of production earn their marginal product, this economy reaches the Golden rule level of capital. (Hint: Begin with the identity that saving equals investment. Then use the steady- state condition that investment is just enough to keep up with depreciation and population growth. and the fact that saving equals capital income in this economy.) Problem 1s: Many demographers predict that the US will have zero population growth in the 21Er century. in contrast to an average population growth of about 1 percent per year in the 20\"\" century. Use the Solow model to forecast the effect of this slowdown in population growth on the growth of total output and the growth of output per person. Consider the effects both in the steady state and in the transition between steady states. Problem 19: Empirically. as an indicator of the saving rate is investmenUGDP. In a closed economy, saving equals investment. And in an open economy saving may be close to investment. No question here. Problem 11D: Assume the Solow growth model with population growth and with no technological progress: Derive steady-state expressions for capital per worker, output per worker. the real wage and the real return to capital. x: FULL}: A-K\"-.i_1_" As functions of the exogenous variables: What happens to the real wage and the real return to capital if the saving rate increases? These questions are optional as the Solow model with on-going technological progress is optional. 3. More questions of economic growth: The model with technological progress. The questions are from the second chapter on economic growth in the textbook of lvlankiw. When doing problems, assume that 'r'rjr} = K (l'}-'5"(.r-'I(r}-JL(r}}\"_m 2; j} = k\Combining the intertemporal choice model with endogenous labor supply In this model. the individual chooses labor supplyr in two time periods and consumption in 2 time periods. Assume that 1'1 and 1'2 are not exogenous from the point of view of the individual. Assume that Y1=W1*L1. where L1 =1-R1. where L1 is hours worked in period 1. and R1 is hours of leisure in period 'I. 1=L1+R1 equals time endowment {total number of hours available) in period 1 that is normalized to 1. That is. we assume that the time endowment is not 24 hours but equals 1. Assume also that i1"2=W21"L2. where L2=1-R2. where L2 is hours worked in period 2. and R2 is hours of leisure in period 2 of life. 1=L2+R2 equals total number of hours available in period 2 that are normalized to 1. We also assume that W1 (=nominal wage in period 1} and W2 [=nominal wage in period 2] are exogenous from the point of view of the individual. Assume that the price of current consumption equals 1: P1 =1. Assume: U = 1\".CEA.R1A_R21mxs Where the preference parameters. a. ,5 435*. 1 a (a. all are assumed to be between zero and 1. a] Write up the intertemporal budget constraint of the individual. b] Derive the optimal levels of C1. C2. R1. R2. L1. L2. and saving as functions of the exogenous variables. c} What happens to the optimal levels of (31.122. R1. R2. L1. L2. {and Saving) if W2 increases? d] What happens if r increases? e} What happens if the pension in period 2 increases? [Here you have to assume that the individual may receive non-labor income In the second period.)
