Answered: List all the equilibrium conditions of…

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. List all the equilibrium conditions of this model and Using the equilibrium conditions listed, write down an expression that describes the evolution of the aggregate capital stock, K_t over time. Briefly explain why this expression is not particularly convenient for our analysis of the model?

b.Using your answer to the above question, derive the equation that describes the evo- lution of the the capital stock per effective unit of worker, k_t. ' Why is the analysis in terms of the variables per effective unit of worker more useful than the one with the aggregate capital stock?

c. Assume that a E (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. Find the expressions for the steady state variables k*, y*, and c* in terms of the parameters of the model. , 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.

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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