Question

Suppose an economy's production is defined by the following neoclassical production function: Y=50K ^1/3L ^2/3. Suppose further that the economy wide supply of capital and labor are given as 125 and 64. What happens to output per worker if there is a war that destroys half the capital in the economy?

		Output per capital falls to half the initial level
		Output per capita falls to less than half the initial level
		Output per capita falls to more than half the initial level
		Output per capita doubles

Answer 1

Answer: It is given that an economy's production is defined by the following neoclassical production function: Y=50K ^1/3L ^2/3. Further, there is a war that destroys half the capital in the economy.

Initially, total output is:

Y = 50 * 125^1/3 * 64^2/3 = 4000 units.

Output per worker initially is (Y/L): 62.5 units

When war destroys half the capital; total capital falls to 62.5 units. Thus, total output falls to:

Y = 50 * 62.5^1/3 * 64^2/3 = 3174.80 units.

Output per worker now is (Y/L): 49.61

Hence, Output per capita falls to more than half the initial level