Exercise 4: AK Model One of the first models of endogenous growth was the AK model, which proposes to treat the workas if it were another type of capital. In this way, the model proposes the following production function: F(K) = AK. In this model, capital does not have diminishing marginal returns, but constant marginal returns. Prove each question mathematically a) Although the production function is different, suppose that the saving rate is still s, that the population grows at rate n and that capital depreciates at rate 8. Write down what is the growth rate of capital per capita in this economy, that is, in other words, obtain where k(t)=L(1) b) Calculate the growth rate of K. c) Imagine that the depreciation rate is 0.05, that the population growth rate is 0.04 and that A = 1. What is the steady state level of output per capita and capital per capita?

Exercise 4: AK Model One of the first models of endogenous growth was the AK model, which proposes to treat the workas if it were another type of capital. In this way, the model proposes the following production function: F(K) = AK. In this model, capital does not have diminishing marginal returns, but constant marginal returns. Prove each question mathematically a) Although the production function is different, suppose that the saving rate is still s, that the population grows at rate n and that capital depreciates at rate 8. Write down what is the growth rate of capital per capita in this economy, that is, in other words, obtain where k(t)=L(1) b) Calculate the growth rate of K. c) Imagine that the depreciation rate is 0.05, that the population growth rate is 0.04 and that A = 1. What is the steady state level of output per capita and capital per capita?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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