a.Assume that α(0, 1). Draw a diagram that describes the evolution of kt, and show that there exists a unique steady state, k* > 0. Label properly. also Find the expressions for the steady state variables k*, y*, and c* in terms of the parameters of the model. ,b.Now, assume that α = 1. Draw a diagram that describes the evolution of kt, and show that income per worker can grow indefinitely in this case. Label properly.c.Discuss the key difference(s) between the scenario in a and b as much as you want. This part considers a modified version of the Solow growth model. Supposethe production function is given by F(K,bN) = K°(bN)1-a where b is the labour augmentingtechnology, which grows at a rate f, i.e., b+1 = (1+f)b. For simplicity, assume that the totalfactor productivity z = 1, and the population is constant, i.e., N = N for all t. The rest of themodel is the same as in the standard Solow model in the textbook. Especially, the aggregatecapital stock evolves according to Kt+1 = 4 + (1– d)Kt. And assume that the economy is stillclosed, and there is no government.For any aggregate variable X, let the lower case letter z be the variable per effective unitof worker; that is a =

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Answered: :This part considers a modified version…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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a.Assume that α(0, 1). Draw a diagram that describes the evolution of k_t, and show that there exists a unique steady state, k* > 0. Label properly. also Find the expressions for the steady state variables k*, y*, and c* in terms of the parameters of the model. ,

b.Now, assume that α = 1. Draw a diagram that describes the evolution of k_t, and show that income per worker can grow indefinitely in this case. Label properly.

c.Discuss the key difference(s) between the scenario in a and b as much as you want.

This part considers a modified version of the Solow growth model. Suppose
the production function is given by F(K,bN) = K°(bN)1-a where b is the labour augmenting
technology, which grows at a rate f, i.e., b+1 = (1+f)b. For simplicity, assume that the total
factor productivity z = 1, and the population is constant, i.e., N = 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 = 4 + (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 z be the variable per effective unit
of worker; that is a =

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