Consider a simple variant of the Solow Growth model. The main difference from the standard model is in the aggregate production function. All other aspects are the same as in the Solow framework (and the steps in the solution of the model are the same). The aggregate production function is as follows: Y = aK, + BN where Y, stands for output, K, for the aggregate capital stock, N, for the size of the labor force (there is no unemployment), and a and 8 are two positive numbers. Notice that the aggregate production function is linear in the inputs (i.e., if you were to graph their marginal products, they would be constant and not decreasing as in the standard Solow case). The labor force grows at rate n, capital depreciates at rate d, and the households save a constant fraction s of their income. (a) Manipulate the aggregate production function to express output per worker y, as a function of the capital-labor ratio kt. (b) Write the condition for a steady-state and find the expression for the steady-state capital-labor ratio k, assuming that sa

Consider a simple variant of the Solow Growth model. The main difference from the standard model is in the aggregate production function. All other aspects are the same as in the Solow framework (and the steps in the solution of the model are the same). The aggregate production function is as follows: Y = aK, + BN where Y, stands for output, K, for the aggregate capital stock, N, for the size of the labor force (there is no unemployment), and a and 8 are two positive numbers. Notice that the aggregate production function is linear in the inputs (i.e., if you were to graph their marginal products, they would be constant and not decreasing as in the standard Solow case). The labor force grows at rate n, capital depreciates at rate d, and the households save a constant fraction s of their income. (a) Manipulate the aggregate production function to express output per worker y, as a function of the capital-labor ratio kt. (b) Write the condition for a steady-state and find the expression for the steady-state capital-labor ratio k, assuming that sa

Essentials of Economics (MindTap Course List)

8th Edition

ISBN:9781337091992

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter17: Production And Growth

Section17.1: Economic Growth Around The World

Problem 1QQ

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Consider a simple variant of the Solow Growth model. The main difference from the standard model is
in the aggregate production function. All other aspects are the same as in the Solow framework (and the
steps in the solution of the model are the same). The aggregate production function is as follows:
Y; = aK; + BN,
where Y, stands for output, K, for the aggregate capital stock, N, for the size of the labor force (there is
no unemployment), and a and B are two positive numbers. Notice that the aggregate production function
is linear in the inputs (i.e., if you were to graph their marginal products, they would be constant and not
decreasing as in the standard Solow case). The labor force grows at rate n, capital depreciates at rate d,
and the households save a constant fraction s of their income.
(a) Manipulate the aggregate production function to express output per worker y as a function of the
capital-labor ratio kt.
(b) Write the condition for a steady-state and find the expression for the steady-state capital-labor ratio
k*, assuming that sa < d+n. Draw a graph representing the steady-state.
(c) How much are the steady-state values of output per worker, consumption per worker and investment
per worker?
(d) Represent graphically the effect of a small increase in a (i.e., in the marginal productivity of capital).
Is there any effect on the steady state of the economy? Describe how the economy adjusts after the change
in a and if the economy is going to have long run growth in the output per worker y

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