Suppose the production function in an economy is Y = K0.5L0.5, where K is the amount of capital and L is the amount of labor. The economy begins with 64 units of capital and 16 units of labor. Use a calculator and equations in the chapter to find a numerical answer to each of the following questions. If a sudden immigration quadruples the size of the population, while the capital stock is unchanged, what is the new level of output?

What is the new wage and rental price of capital?

What share of output does labor receive now?

Therefore new level of output = (64x0.5) * (64.0.5) = 1,024

Explanation:

Suppose the production function in an economy is Y = K0.5L0.5,

where K is the amount of capital and

L is the amount of labor.

The economy begins with 64 units of capital and 16 units of labor.

If a sudden immigration quadruples the size of the population, while the capital stock is unchanged, what is the new level of output?

K remains 64 and L = 16 x 4 = 64

Therefore new level of output = (64x0.5) * (64.0.5) = 1,024

What is the new wage and rental price of capital?

The rental price for capital is expected to remain unchanged because there is no change in the quantity of capital But the wage level is expected to drop because of excess supply due to the immigration boom.

What share of output does labor receive now?

The function remains unchanged in proportion which is 0.5 but in absolute figures it will receive 0.5*1,024 = 512