Question

Suppose that GDP production function of the United States has the form Y = K∝ L∝⁻¹where K is capital, L is labor and Y is GDP. The parameter α has a value of 0.7.

Suppose that immigration to the US increases the labor force (L) by 5% percent. What happens to total output (GDP)? Express in percentage changes compared to the situation before immigration takes place.

a. Goes up by about 1.47%

b. Goes down by 2%

c. Goes up by 2%

d. None of the above

Answer 1

When the labor force (L) increases by 5% in the GDP production function Y = Kα Lα⁻¹ with α = 0.7, the total output (GDP) is expected to increase by 1.5%, which is approximately the option (a) 1.47%.

Step-by-step explanation:

To understand the economic consequences of a 5% increase in labor due to immigration on the United States' GDP production function, represented by Y = Kα Lα⁻¹, where α = 0.7, we apply the concept of elasticity. The percentage change in output is the elasticity of output with respect to labor multiplied by the percentage change in labor.

Therefore, the percentage change in GDP can be calculated as follows: (1 - α) × (% change in L) = (1 - 0.7) × 5% = 0.3 × 5% = 1.5%. Even when rounding, the 1.5% increase does not precisely match any of the choices provided in the question, but the closest approximate option is that total output (GDP) goes up by about 1.47% (option a). These calculations illustrate that while the overall gains to the U.S. economy from immigration are real, they are relatively small, as consistent with general economic observations.