4 Mathematical Malthusian Model This question is about determining if the Malthusian trap still exists when the production function has increasing returns to scale. Consider a slightly different production function from the one we had in the Malthusian model in class. Y₁ = F (AX, L₁) = (AX)ª (L₁)³ where A> 0 is the technological level, X> 0 is the amount of land, a > 0 and 1 > > 0. (In the slides' model, 3= 1-a. In this question, we only impose that 1 >8>0 and a > 0.) 3. With this production function, the evolution of income per capita in the Malthusian model B-1 would be given by yt+1 = w(y₁) = (2) ³ (3₁)³. Draw the function w(y) together with a 45-degree line. Show graphically that there is a unique stable steady-state where income per capita is constant. hint: remember that 3 < 1. 4. Based on this question, are increasing returns to scale enough to escape the Malthusian trap and enter a state in which income per capita keeps growing?

4 Mathematical Malthusian Model This question is about determining if the Malthusian trap still exists when the production function has increasing returns to scale. Consider a slightly different production function from the one we had in the Malthusian model in class. Y₁ = F (AX, L₁) = (AX)ª (L₁)³ where A> 0 is the technological level, X> 0 is the amount of land, a > 0 and 1 > > 0. (In the slides' model, 3= 1-a. In this question, we only impose that 1 >8>0 and a > 0.) 3. With this production function, the evolution of income per capita in the Malthusian model B-1 would be given by yt+1 = w(y₁) = (2) ³ (3₁)³. Draw the function w(y) together with a 45-degree line. Show graphically that there is a unique stable steady-state where income per capita is constant. hint: remember that 3 < 1. 4. Based on this question, are increasing returns to scale enough to escape the Malthusian trap and enter a state in which income per capita keeps growing?

Principles of Economics (MindTap Course List)

8th Edition

ISBN:9781305585126

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter18: The Markets For The Factor Of Production

Section: Chapter Questions

Problem 9PA

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