Question

A certain production process requires only two types of inputs — capital and labor. In 2006, 100 units of labor and 50 units of capital were employed, and 100 units of output were produced. In 2013, 112 units of labor and 56 units of capital were employed. If the production process displays constant returns to scale, then how many units of output were produced in 2013?a. 100 b. 112 c. 124 d. 144

Answer 1

Answer:

Option (b)=112 units of output was produced in 2013

Explanation:

Returns of scale refers to how much output changes given a proportional change in input, where the input changes by a constant factor.

This can be represented by the equation;

Input 2=Constant×Input 1

where;

Input 1=100 units of Labor+50 units of capital=100l+50c

Constant=k

Input 2=112 units of Labor+56 units of capital=112l+56c

Replacing;

112l+56c=k×(100l+50c)

Since k is a common factor which when multiplied by the input 1 labor and capital equals input 2 labor and capital, it can be calculated as;

k=(Input 2 labor units/input 1 labor units)=(Input 2 capital units)/Input 1 capital units)

k=(112l/100l)=(56c/50c)=1.12

To calculate the output for input 2;

Output 2=k×Output 1

where;

Output 1=the output produced by input 1=100 units

k=constant returns=1.12

Output 2=the output produced by input 2=x

Replacing;

x=100×1.12

x=112 units

Output 2=112 units

112 units of output was produced in 2013