An economy's total labor income is $2 trillion,and total capital income is $1 trillion.In the Cobb-Douglas production function,the exponent on capital is ________.
A)two-thirds
B)one-half
C)one-third
D)0.3
E)none of the above

Question

Quizplus · Accepted Answer

In the Cobb-Douglas production function, the share of capital income is given by the exponent on capital, which is denoted by α. The share of labor income is then given by (1-α). Since the total labor income is twice the total capital income, we have:

2 trillion = (1-α)Y
1 trillion = αY

where Y is the total output of the economy. Dividing the second equation by the first one, we get:

α/(1-α) = 1/2

Solving for α, we obtain:

α = 1/3

Therefore, the exponent on capital in the Cobb-Douglas production function is one-third.

An Economy's Total Labor Income Is $2 Trillion,and Total Capital