.Solve these problems.
2. Suppose that you are given the aggregate production function for Canada: Y = AKON 1-a The assumptions of the Solow Growth Model hold. The parameter values are: a = 0.5 s = 0.45 6 = 0.1 n = 0.05 A = 2 a) What is the per capita production function? Hint: Divide the aggregate production function by N and express it in terms of k = KN . b) Recall that S = sY in the model. What is the per capita law of motion for capital? Hint: I am asking for k 0 as a function of k. Also, S = I in equilibrium. c) What is the steady state capital stock, output and consumption? d) Use the key growth model diagram to depict the steady state. Suppose that k starts below k ss. Show using arrows how it will grow over time towards the steady state. e) Show the effects on your diagram the effects of a decrease in productivity. What effect will this have on consumption, capital and output per capita? You do not have to re-solve the model. Just discuss the effects. f) Suppose that Canada and South Korea each have the same productivity: ^ACanada = ^ASouth Korea As well, the per capita capital stock is bigger in Canada: ^kCanada > ^kSouth Korea Which country to you expect to grow quicker in per capita terms? Discuss why. g) Suppose that Sierra Leone has a lower producitivity than Canada. Which country to you expect to have a higher per capita capital stock? Explain whyConsider how unemployment would affect the Solow growth model. Suppose that output is produced according to the production function Y = K\" [(1 ulLll'\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.Covid 19 and Economic Growth An economy is characterized by the following production function: f(K, N) = K1/4N3/4. The savings rate in the economy is s=0.3 and the depreciation rate is 6=0.15. 1. a) Derive the per-capita production function. 2. b) Derive the steady state level of capital per worker. How does the capital stock evolve over time if it is at this level? Find the steady state value of output and consumption per worker. 3. c) Read the article "The toll on growth". The author talks about the effect of Covid 19 on economic growth in Africa and mentions, among other things, education. Explain why lower education could lead to lower output and lower economic growth. In the Solow model covered in parts a) - b), would the effect on economic growth be temporary or permanent? 4. d) Assume that educational deficits affect the production function. It is now f(K, N) = 0.8K1/4/3/4. Calculate the new steady state level of output per capita. 5. e) Show graphically the effect of lower education in the Solow model. 6. f) Another channel that the text mentions is government spending. Explain why lower government spending can have a negative effect on economic growth and output. (There is no government in the model, but you can assume that government spending is a type of investment.) Describe how you would model the change in the Solow model. If it helps you, you can draw a Solow diagram.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
