2. An economy has a production function: Y 3KtLt. (1) The economy has a saving rate of 24 percent, a depreciation rate of 3 percent, 1 for all period (no population growth). and Lt Yt Lt (a) What is the per-worker production function, yt f(kt)? Define yt Ки Lt and kt (b) Find the equation for the evolution of capital per worker in terms of kt and kt+1 (c) Find the long-run growth rate of output per worker. Now the economy has the following production function: Y 3Kt (2) but savings rate, depreciation rate, and population remain the same Yt Lt f (kt)? Define yt (d) What is the per-worker production function, yt (e) Find the equation for the evolution of capital per worker in terms of kt and kt+1 (f) Find the long-run growth rate of output per worker. (g) Explain why the economy with production function (2) explain per- sistent growth without the assumption of exogenous technological progress. How does this differ from the economy with production func- tion (1)?

2. An economy has a production function: Y 3KtLt. (1) The economy has a saving rate of 24 percent, a depreciation rate of 3 percent, 1 for all period (no population growth). and Lt Yt Lt (a) What is the per-worker production function, yt f(kt)? Define yt Ки Lt and kt (b) Find the equation for the evolution of capital per worker in terms of kt and kt+1 (c) Find the long-run growth rate of output per worker. Now the economy has the following production function: Y 3Kt (2) but savings rate, depreciation rate, and population remain the same Yt Lt f (kt)? Define yt (d) What is the per-worker production function, yt (e) Find the equation for the evolution of capital per worker in terms of kt and kt+1 (f) Find the long-run growth rate of output per worker. (g) Explain why the economy with production function (2) explain per- sistent growth without the assumption of exogenous technological progress. How does this differ from the economy with production func- tion (1)?

Principles of Economics 2e

2nd Edition

ISBN:9781947172364

Author:Steven A. Greenlaw; David Shapiro

Publisher:Steven A. Greenlaw; David Shapiro

Chapter20: Economic Growth

Section: Chapter Questions

Problem 12SCQ: Why dues productivity growth in high-income economies not slow down as it runs into diminishing...

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What do the growth accounting studies conclude are the determinants of growth? Which is more important, the determinants or how they am combined?
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2. 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…
Let’s suppose economy is operating at steady state level of capital, explain graphically infollowing situations. a. If depreciation rate increasesb. If saving rate decreases
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+1
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(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 a. Transform the production function into the relation between output per effective worker (Y/AN) and capital per effective worker (K/AN). Does the function exhibit diminishing return?
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(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!
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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…