12. Consider an economy without technological progress and population growth. The production function is given as Y = K²/3N/3_ _ Both the saving rate and the capital depreciation rate are assumed to be 0.1. Which of the following saving rate delivers the highest consumption per worker in the steady-state: (а) 1/3 (b) 1/2 (c) 2/3
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- Parameters Equations s =0,20 marginal propensity to save Y=WKr.L1-r Production Function u=0,02 Population growth rate K.=s.f(k)−aK Capital Accumulation b=0,04 Technological growth rate L./L= ? Population Growth a=0,05 Depreciation rate W./W=b Technological Progress S=s.f(k) Savings a. Find steady-state level of capital per effective labor: k* b. Draw a graph and show output function, actual investment and breakeven investment lines. c. Assume that in this economy, people start spending more and therefore marginal propensity to save decline permanently. What will happen to variables in the model (steady-state level capital per effective labor; output growth etc.). d. Instead of reduction in saving assume this time that we face lower fertility rate in the country. What will happen to variables in…Given a saving rate of 5%, a depreciation rate of 1%, and a production function in which y = k0.5where y is output per worker and k is capital per worker, calculate the steady state values fori. capital per worker, ii. output per worker, iii. consumption per workerQuestion 2Assume production function is given by:Y= K(1/2) L(1/2)a. Write the production function in per worker terms (y=f(k))b. Assume that the per worker level of capital in the steady state is 4, the depreciation rate is 5% per year, and population growth is 5% per year. Does this economy have “too much” or “too little” capital? How do you know? [Show your work].
- Please no written by hand Yt = 3Kt saving rate= 0.24 depreciation ratre=0.03 but savings rate, depreciation rate, and population remain the same.(d) What is the per-worker production function, yt = f(kt)? Define yt = YtLt.(e) Find the equation for the evolution of capital per worker in terms of ktand kt+12. An economy has a production function:Yt = 3(squaredKt)(squaredLt). The economy has a saving rate of 24 percent, a depreciation rate of 3 percent,and Lt = 1 for all period (no population growth). There is no technologicalprogress. (a) What is the per-worker production function, yt = f(kt)? Define yt =YtLtand kt =KtLt.(b) Find the equation for the evolution of capital per worker in terms of ktand kt+1. (c) Find the long-run growth rate of output per worker. Now the economy has the following production function:Yt = 3Kt but savings rate, depreciation rate, and population remain the same. (d) What is the per-worker production function, yt = f(kt)? Define yt =Yt/Lt (e) Find the equation for the evolution of capital per worker in terms of ktand kt+1. (f) Find the long-run growth rate of output per worker. (g) Explain why the economy with production function (2) explain persistent growth without the assumption of exogenous technologicalprogress. How does this differ from the economy…Consider the Production Function: Y=0.5√K√N a) Derive the steady-state levels of output per worker and capital per worker in terms of the saving rate (s) and the depreciation rate.b) Derive the equation for steady-state output per worker and steady-state consumption per worker in terms of the saving rate (s) and the depreciation rate.c) Suppose depreciation is 5% and savings rate is 10%. Calculate the steady-state output per worker.d) Now suppose the savings rate increases to 20%. What is the new steady-state output per worker?
- Suppose that the production function for an economy is given by Y = K1/4L3/4. The depreciation rate is 4%, the saving rate is 12%, Find the steady-state capital-labor ratio, real GDP per worker, investment per worker and consumption per worker for this economy.Consider the Production Function: Y=√K√N a) Derive the steady-state levels of output per worker and capital per worker in terms of the saving rate (s) and the depreciation rate.b) Derive the equation for steady-state output per worker and steady-state consumption per worker in terms of the saving rate (s) and the depreciation rate.c) Suppose depreciation is 5% and savings rate is 10%. Calculate the steady-state output per worker.d) Now suppose the savings rate increases to 20%. What is the new steady-state output per worker?Suppose that the production function for an economy is given by Y = K1/4L3/4. The depreciation rate is 4%, the saving rate is 12%, Suppose that now there is labor augmenting technology, the rate of labor-augmenting technological is 2 percent. At what rate does total output, output per worker, and output per effective worker grow?
- (Long Run) The country of Prosperous has: Production function: Y = 2 K1/2 (AN)1/2, where Y=output;K=capital; A=technology; and N=labor Saving rate (s): 20% per year Depreciation rate (d): 10% per year Labor growth rate (n): 2% per year Rate of technological change (g): 8% per year d. If the country of Prosperous aims to achieve the optimal level of steady state consumption, what would you advise the government of the Prosperous to do regarding the country saving rate? Explain!Let’s suppose economy is operating at steady state level of capital, explain graphically infollowing situations. a. If depreciation rate increasesb. If saving rate decreasesConsider an economy’s production function is Y=K^1/3 N^2/3 and that both the saving rate and the depreciation rate are equal to 0.15. A. What is the steady-state level of capital per worker? B. What is the steady-state level of output per worker? Now suppose that the economy has reached its steady-state in period t, and then, in period t+1, the saving rate doubles to 0.30. The depreciation rate remains constant at 0.15. C. Solve for the new steady-state levels of capital per worker and output per worker. D. Calculate the path of capital per worker and output per worker over the first three periods after the change in the saving rate.