4 Mathematical Malthusian ModelThis question is about determining if the Malthusian trap still exists when the production functionhas increasing returns to scale.Consider a slightly different production function from the one we had in the Malthusian modelin class.Y₁ = F (AX, L₁) = (AX)ª (L₁)³where A> 0 is the technological level, X> 0 is the amount of land, a > 0 and 1 > > 0. (In theslides' model, 3=1-a. In this question, we only impose that 1>3> 0 and a > 0.)1. For what values of 3 does the production function have decreasing, constant, and increasingreturns to scale? (your answer can be a function of any other parameter A, X, a if needed)2. For what values of 3 does the production have decreasing, constant, and increasing marginalproduct of labor? (your answer can be a function of any other parameter A, X, a if needed)3. With this production function, the evolution of income per capita in the Malthusian modelB-1would be given by yt+1 = w(y₁) = (2)³ (3₁)³. Draw the function w(y) together with a45-degree line. Show graphically that there is a unique stable steady-state where income percapita is constant. hint: remember that ß < 1.4. Based on this question, are increasing returns to scale enough to escape the Malthusian trapand enter a state in which income per capita keeps growing?

Here due to multible question, only 1st question is answered.So, here we are going to analyse the…

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)" (L₁)³ where A> 0 is the technological level, X>0 is the amount of land, a > 0 and 1>3 > 0. (In the slides' model, 3 = 1-a. In this question, we only impose that 1>3> 0 and a > 0.) 1. For what values of 3 does the production function have decreasing, constant, and increasing returns to scale? (your answer can be a function of any other parameter A, X, a if needed)

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)" (L₁)³ where A> 0 is the technological level, X>0 is the amount of land, a > 0 and 1>3 > 0. (In the slides' model, 3 = 1-a. In this question, we only impose that 1>3> 0 and a > 0.) 1. For what values of 3 does the production function have decreasing, constant, and increasing returns to scale? (your answer can be a function of any other parameter A, X, a if needed)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.2P

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2. Which of the following statements is the best articulation of Malthusian dynamics?(A) “Technology will endeavour to make us increasingly less reliant upon fixed resources, since said resources can be stretched out in an exponential manner.”(B) “It is not possible that we can sustain ourselves indefinitely with fixed resources.”(C) “Since population grows exponentially, and farmland only grows linearly, human beings are cursed, in the long-term, to live in subsistence.”(D) “The wealthiest nations have the lowest population growth levels, but have also destroyed their environment with careless pollution that impedes on their ability to cultivate food.”
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