Chapter 7, Problem 9E

a

To determine

To find:Labor, fuel, capital input production elasticities.

Answer to Problem 9E

Labor production elasticity = 0.45

Capital production elasticity= 0.30

Fuel production elasticity= 0.20

Explanation of Solution

Given Information:

  $\begin{array}{l}\alpha =0.0012\\ {\beta }_1=0.45\\ {\beta }_2=0.20\\ {\beta }_3=0.30\end{array}$

The production function is given as:

  $Q=\alpha L{\beta }_{1}F{\beta }_{2}K{\beta }_3$

Taking log both the sides:

  $InQ=In\alpha +{\beta }_{1}InL+{\beta }_{2}InF+{\beta }_{3}InK\mathrm{.......}$

  $\begin{array}{l}\alpha =0.0012\\ {\beta }_1=0.45\\ {\beta }_2=0.20\\ {\beta }_3=0.30\end{array}$

  $\text{According to the situation, labor production elasticity = }\frac{d(InQ)}{d(InL)}$

  $\text{Labor production elasticity = }{\beta }_1=0.45$

  $\text{Fuel production elasticity}=\frac{d(InQ)}{d(InF)}$

  $={\beta }_2$

  $=0.20$

  $\text{Capital production elasticity}=\frac{d(InQ)}{d(InK)}$

  $={\beta }_3$

  $=0.30$

Economics Concept Introduction

Introduction:

Labor input production elasticity is a measurement of percentage change in output due to percentage change in labor. It shows productivity of labor.

Fuel input production elasticity is a measurement of percentage change in output due to percentage change in fuel. It shows productivity of fuel.

Capital input production elasticity is a measurement of percentage change in output due to percentage change in capital. It shows productivity of capital.

b)

To determine

To ascertain:Percentage change in output due to change in labor input.

Answer to Problem 9E

Percentage change in output due to change in labor input is 0.90.

Explanation of Solution

Given Information:

Increase in labor input = 2%

Percentage change in $Q=0.20(\text{Percentage change in L)}$

It is given that percentage change in labor is 2 percentage. Hence,

  $\text{Percentage change in Q = 0}\text{.45(2)}$

  $=0.90\text{ percentage}$

Economics Concept Introduction

Introduction:

Labor input production elasticity is a measurement of percentage change in output due to percentage change in labor. It shows productivity of labor.

c)

To determine

To find:Percentage change in output due to change in capital input.

Answer to Problem 9E

Percentage change in output due to change in capital input is -0.90.

Explanation of Solution

Given Information:

Decrease in capital = 3%

Percentage Change in $Q=0.30(\text{Percentage change in K)}$

It is given that percentage change in capital is -3 percentage. Hence,

  $\text{Percentage change in Q = 0}\text{.30(-3)}$

  $=-0.90\text{ percentage}$

Economics Concept Introduction

Introduction:

Capital input production elasticity is a measurement of percentage change in output due to percentage change in capital. It shows productivity of capital.

d)

To determine

To know:Types of returns to scale.

Answer to Problem 9E

It is decreasing returns to scale.

Explanation of Solution

Given Information:

  $\begin{array}{l}\alpha =0.0012\\ {\beta }_1=0.45\\ {\beta }_2=0.20\\ {\beta }_3=0.30\end{array}$

  $\text{Returns to Scale = }{\beta }_1+{\beta }_2+{\beta }_3$

  $=0.45+0.20+0.30$

  $=0.90$

  ${\beta }_1+{\beta }_2+{\beta }_3<1$

This represents decreasing returns to scale.

There are decreasing returns to scale.

Economics Concept Introduction

Introduction:

Returns to scale is the output growth due to input change. It measures change in output due to change in all factor inputs. It is a long run phenomenon.

e)

To determine

To ascertain:Problems due to time series data for estimating parameters of model.

Explanation of Solution

Certain problems due to time series data are:

• Variables are interdependent on each other which leads to incomplete analysis of single variable.
• Time series data are not used for prolonged time duration. Analysis fails after a certain period of time.
• Labor, capital or fuel input may be efficient at certain time period but may become inefficient after certain period after an optimal usage of any of the inputs.