7 An economy is characterized by the following relations:Y = F(K,AL) = Kª(AL)1-a : Production functionf (k) = F(k, 1) : Functional transformation with capital per capita with labor-augmentingtechnology.f'(k) : Marginal productivity of capital.K+1 = K; + I - SK; : Capital accumulationY = C +I → I = Y – C = S = sY : Equilibrium and S=I relation%3DY: output, K: capital, L: labor, a: share of capital income, 8: depreciation rate, s: saving rate:x is a variable such as y, k, c, i considering the labor-augmenting technology.x =ALKYEx: k =etc..y 3DALALAxtdlnxt%3D: Growth rate of a variabledtXtALt=n,AAt= g : Exogenously determined growth rate of labor and technology.AtLt(a) Derive the Solow model equation: Ak, = sf (k,) - (n +g+ 8)k;(b) Illustrate the Solow model graphically. How does this economy arrive at the steady state?Answer with this case: ko < k* (ko: initial kk*: k in the steady state)(c) Graphically show the effect of increase in saving rate (s → s', s< s')(d) Show time paths of output per capita, consumption per capita, and investment per capita.ỹ =, č = , i = the technology term is extracted out.L(e) Summarize what the Solow model tells us. Comment at least two limitations of the model.

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An economy is characterized by the following relations: Y = F(K,AL) = Kª(AL)1-a : Production function f(k) = F(k, 1) : Functional transformation with capital per capita with labor-augmenting technology. f'(k) : Marginal productivity of capital. K+1 = K, + I - 8K : Capital accumulation Y = C +I → I = Y – C = S = sY : Equilibrium and S=I relation %3D %3D -

An economy is characterized by the following relations: Y = F(K,AL) = Kª(AL)1-a : Production function f(k) = F(k, 1) : Functional transformation with capital per capita with labor-augmenting technology. f'(k) : Marginal productivity of capital. K+1 = K, + I - 8K : Capital accumulation Y = C +I → I = Y – C = S = sY : Equilibrium and S=I relation %3D %3D -

Microeconomics

13th Edition

ISBN:9781337617406

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter2: Production Possibilities Frontier Framework

Section: Chapter Questions

Problem 11QP

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