.Answer the following questions.

Exercise 1 (Solow growth model, 20 points). Suppose that the production function is Y = zKIN and that 8% of capital wears out every year. Assume that the rate of growth of the population is 2% and the saving rate is 20%. I (a) If z = 2, what is the steady-state capital per worker, k.., the steady-state output per worker, yes, the steady-state consumption per worker, c.s, and the steady-state investment per worker, (b) What is the steady-state growth rate of the capital per worker, k.s, and the steady-state growth rate of the output per worker, y.,? And what is the steady-state growth rate of the capital stock, Ass, and the steady-state growth rate of the aggregate output, Y,,? Show your work. (c) What is the golden rule level of capital, k*, and the savings rate associated with the golden rule level of capital, s*? Can the country increase the consumption per-capita by changing the saving rate? (d) Now assume that there is no population growth, i.e. n =0, and that the saving rate is given by some other value called s'. Suppose that this economy is in a steady state where the marginal product of capital is less than the depreciation rate. By changing the saving rate is it possible to increase the steady state consumption per-capita? Explain how would you change the saving rate.Consider the Solow growth model. Recall that upper-case variables denote aggregate variables and lower-case variables denote per worker (or per capita) variables. Capital is assumed to evolve according to the following equation: K= I+ (1-d)K. (1) where K' denoffes aggregate capital in the future period and A is capital in the current period. There is a closed-economy model without a government, so in a competitive equilibrium the income-expenditure identity is Y = C + 1. (a) Use the income-expenditure identity and equation (1) to find an expression for the evolution of per- worker capital. In other words, show that equation (1) can be re-written as follows: K_ saf(k) (1 - d)k (2) 1+n 1+n (b) Denote the steady-state level of capital per worker as ". Show that in the steady state, equation (2) implies the following equilibrium equation: sef ( k' ) = (n+ d)k. (3) For the rest of this question, suppose there are two countries with an aggregate production function Y = =KNOT. Further suppose the following values for the model's parameters: s = 0.25, d = 0.1 and n = 0.02 in both countries. (c) Suppose =4 = 1 in Country A. Use equation (3) and the given values for the model's parameters and production function to calculate the steady-state level of income per capita, y', and the steady-state level of capital per worker, ka, in Country A. (d) Suppose ag = 2 in Country B, but otherwise the countries are equivalent. Because 28 > 24, Country B will have a higher standard of living (i.e., per capital income) in the initial period. In the long run, will Country A ever converge with Country B in terms of per capita income? Explain your answer. (e) How is the Solow model inconsistent with the growth fact that there is no correlation between the level of output per capita in 1960 and the average growth rate in output per capita since that time?Question 2. In this problem, we will consider how the rental price of capital R, and the wage rate 10, are determined under the assumptions of the Solow growth model. Suppose there exists a representative rm in this economy with Cobb-Douglas production flmction given by Y, = K313i\1. Country A and country B both have the production function 1' = F(K,L)= 41:71.. (5 Points) Does this production function have constant returns to scale? Explain. (5 Points) What is the per-worker production function, y = fat)? (10 Points) Assume that neither country experiences population growth or technological progress and that 5 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 20 percent of output each year. Using your answer from part (b) and the steady-state condition that investment equals depreciation, nd the steady-state level of capital per worker for each country. Then nd the steady-state levels of income per worker and consumption per worker. (15 Points) What saving rate maximizes output per worker for each country? What saving rate maximizes consumption per worker for each country? And nd the Golden Rule level of consumption, output, investment per worker for each country. (15 Points) 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 investment less depreciation, use a calculator or a computer spreadsheet to show how the capital stock per worker will evolve over time in both countries. For each year, calculate income per worker and consumption per worker. How many years will it be before the consumption in country B is higher than the consumption in country A? Country A and country B both have the production function Y=F(K, L)=K3\"L \"r\". (a) Does this production function have constant rettu'us to scale? Explahi. {h} What is the per-worker production function, y = f (k)? (c) Assume that neither country experiences population growth or technological progress and that 3 percent of capital depreciatcs each year. Assume further that country A saves 25 percent of output each year and country B saves 30 percent of output each year. Using your answer from part {b} and the steady-state condition that investment equals depreciation, nd the steady-state love] of capital per worker for each country. Then nd the steady-state levels of income per worker and consumption per worker. {{1} Suppose that both countries start off with a capital stock per worker of 3. What are the levels of income per worker and consumption per worker?I Remembering that the change in the capital stock is investment less depreciation. use a calculator or a computer spreadsheet to show how the capital stock per worker will evolve over time in both countries. For each year, calculate income per worker and consumption per worker. How many years will it be before the consumption in country B is higher than the consumption in country A? (c) Find the golden rule level of capital per worker in each country and the saving rate that supports it respectively