Question

National Income: Where It Comes From and Where It Goes - End of Chapter Problem

Suppose that an economy's production function is Cobb-Douglas with parameter a = 0.3.
a. Capital and labor receive shares of income of _______ and ______ respectively.
b. Suppose immigration increases the labor force by 10 percent.
(i) Total output will increase by _____

Answer 1

In a Cobb-Douglas production function with parameter a = 0.3, capital and labor receive shares of income of 0.7 and 0.3 respectively. An increase in the labor force by 10 percent would theoretically increase total output by 3 percent, considering labor's share in income.

Step-by-step explanation:

The question deals with a Cobb-Douglas production function, which is frequently used in economics. This production function posits that the total output of an economy is a function of two inputs: capital and labor. In a Cobb-Douglas production function with a parameter 'a' representing the output elasticity of labor, the complement (1-a) represents the output elasticity of capital. Here, given a = 0.3, it implies that:

• Capital receives a share of income of 0.7 (1 - 0.3)
• Labor receives a share of income of 0.3

For part (b), an increase in the labor force by 10 percent does not proportionately increase total output by 10 percent because the parameter 'a' of the production function denotes the percentage increase in output resulting from a 1% increase in labor, holding capital constant. If labor contributes to 30% of output (a = 0.3), a 10% increase in labor would increase total output by 3%.