Question

Suppose that an economy has a Production Function given by the following: Y=A⋅Kᵃ⋅L⁽¹⁻ᵃ⁾

Where A is a Total Factor Productivity (TFP) parameter, Y is Real GDP, L is the total labour in the economy, and K is the economy's total capital stock. Suppose that foer this economy, that:
A=234
K=29
L=41
a=0.44
​What is the Long-Run Potential GDP (Y∗) in this economy? Note: Please round your answers to two decimal places.

Answer 1

The Long-Run Potential GDP (Y*) in this economy is calculated using the provided production function with the given values for TFP, capital stock, labor, and elasticity. By plugging in the values into the function and computing the result, the Long-Run Potential GDP is found to be approximately $18,329.82.

Step-by-step explanation:

The question refers to calculating the Long-Run Potential GDP (Y*) for an economy using the given production function Y = A ⋅ Kᵃ ⋅ L⁴ᵃ⁴). Given the values:

• Total Factor Productivity (TFP), A = 234
• Capital Stock, K = 29
• Labor, L = 41
• Elasticity of output with respect to capital, a = 0.44

The Long-Run Potential GDP can be calculated by substituting these values into the production function

Y* = 234 ⋅ 29⁰⁴⁴ ⋅ 41¹⁰⁴⁶

Calculating this yields:

Y* = 234 ⋅ (29^0.44) ⋅ (41^(1-0.44))

Y* = 234 ⋅ (29^0.44) ⋅ (41^0.56)

Y* = 234 ⋅ (7.77) ⋅ (10.07)

Y* = 234 ⋅ 78.33

Y* = 18329.82

Therefore, the Long-Run Potential GDP (Y*) in this economy is approximately $18,329.82.