: This part considers a modified version of the Solow growth model. Suppose the production function is given by F(K,bN) = Kª(bN)!-a where b is the labour augmenting technology, which grows at a rate f, i.e., bị+1 = (1+ f)b.. For simplicity, assume that the total %3D factor productivity z = 1, and the population is constant, i.e., Ng = N for all t. The rest of the model is the same as in the standard Solow model in the textbook. Especially, the aggregate capital stock evolves according to Kt+1 = I; + (1 – d)Kt. And assume that the economy is still closed, and there is no government. For any aggregate variable X, let the lower case letter r be the variable per effective unit of worker; that is a = . ; Show that the production technology specified above satisfies the assumption of con- stant returns to scale.

: This part considers a modified version of the Solow growth model. Suppose the production function is given by F(K,bN) = Kª(bN)!-a where b is the labour augmenting technology, which grows at a rate f, i.e., bị+1 = (1+ f)b.. For simplicity, assume that the total %3D factor productivity z = 1, and the population is constant, i.e., Ng = N for all t. The rest of the model is the same as in the standard Solow model in the textbook. Especially, the aggregate capital stock evolves according to Kt+1 = I; + (1 – d)Kt. And assume that the economy is still closed, and there is no government. For any aggregate variable X, let the lower case letter r be the variable per effective unit of worker; that is a = . ; Show that the production technology specified above satisfies the assumption of con- stant returns to scale.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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In our one country model of technology growth, y = A(1- yA). Suppose that the country temporarily raises its level of yA. (a) Draw two graphs, one for y and one for A, showing how the time paths of output per worker (y) and productivity (A) will compare under this scenario with what would have happened if there had been no change in yA.
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Consider the endogenous growth model AK, in which the production function is given by Y = AK. Suppose s denotes the saving rate; that δ represents the depreciation rate; and that the variable that represents the population and that grows at the rate n. Calculate the growth rate of capital per capita in the same way as for the Solow model and, from there, solve the differential equation to obtain the capital per capita (denoted by k) as a function of time.