Suppose in an economy the production function is defined by the following equation: Y(t) = 20K(t)04L(t)0.6 where Y(t) stands for production level at time t, 20 `is the technological level that will affect positively all inputs, K(t) is the physical capital, and L(t) is the used labor force. 1- Deduce the productivity function. 2- Suppose that K(t) and L(t) increase by the same rate 0% . Find the growth rate of production and productivity. Interpret your result. 3- Suppose that the physical capital starts at 120 and the labor force at 60, find the new production level in terms of 0 after inputs' growth of 0%. 4- What is the growth rate of production using result from 3? Link this to the concept of constant returns to scale. 5- The marginal productivity of capital is given by the first derivative of productivity with respect to capital. Economically, this function captures the returns of an extra unit of capital. a. For L = 243, find the marginal productivity of capital for the 80th unit and the 120th unit of physical capital. b. Compare the marginal productivities found in (a) and explain.

Suppose in an economy the production function is defined by the following equation: Y(t) = 20K(t)04L(t)0.6 where Y(t) stands for production level at time t, 20 `is the technological level that will affect positively all inputs, K(t) is the physical capital, and L(t) is the used labor force. 1- Deduce the productivity function. 2- Suppose that K(t) and L(t) increase by the same rate 0% . Find the growth rate of production and productivity. Interpret your result. 3- Suppose that the physical capital starts at 120 and the labor force at 60, find the new production level in terms of 0 after inputs' growth of 0%. 4- What is the growth rate of production using result from 3? Link this to the concept of constant returns to scale. 5- The marginal productivity of capital is given by the first derivative of productivity with respect to capital. Economically, this function captures the returns of an extra unit of capital. a. For L = 243, find the marginal productivity of capital for the 80th unit and the 120th unit of physical capital. b. Compare the marginal productivities found in (a) and explain.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.2P

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