Harrod-Domar Growth Model. Given the following equations: Y = F(K) S = sY I = AK %3D %3D c = K/y C = S = I a. Assuming that the marginal product of capital is constant and that the production function exhibits constant returns to scale (CRTS), show mathematically how the net savings rate and the capital-output ratio affect the GDP growth rate as predicted by the model. b. Based on your answer in (a), what should a country do in order to achieve economic growth? Explain. c. Given a net savings rate equal to 5% and a capital-output ratio equal to 2, calculate the predicted GDP growth rate.

Harrod-Domar Growth Model. Given the following equations: Y = F(K) S = sY I = AK %3D %3D c = K/y C = S = I a. Assuming that the marginal product of capital is constant and that the production function exhibits constant returns to scale (CRTS), show mathematically how the net savings rate and the capital-output ratio affect the GDP growth rate as predicted by the model. b. Based on your answer in (a), what should a country do in order to achieve economic growth? Explain. c. Given a net savings rate equal to 5% and a capital-output ratio equal to 2, calculate the predicted GDP growth rate.

Macroeconomics

13th Edition

ISBN:9781337617390

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter17: Economic Growth: Resources, Technology, Ideas And Institutions

Section: Chapter Questions

Problem 3WNG

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Consider an economy that has access to a production technology Y = AKαL1−α where Y is output, A is the level of technology, K is capital and L is the amount of labor in the economy. Capital evolves according to K˙ = sY (thus, the depreciation rate δ = 0). The x˙ population growth rate is n. (Throughout, gx = x , where x can be any of the variables in the model.) (a) Assume that technology is determined by A = BKφ What sort of endogenous growth model is this? Find K/K in terms of the K, L, and other parameters of the model.
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Consider the simple innovation model. In this model, the society allocates a fraction "gamma" of workforce to innovation and the remaining fraction to production. Suppose that, for simplicity, total workforce is normalized to unity: L = 1. If the productivity growth rate is defined by d A_t / d t = "theta" * "gamma" * A_t and real GDP per worker by y_t = A_t * ( 1 - "gamma" ), what is the long-run growth rate of y_t ?
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