Question

Countries 1 and 2 have the production function: Yt = AiKαt L1−α

t , where country 1 has
Total Factor Productivity (TFP) of A1 = 25, country 2 has TFP A2 = 100, and α = 0.35
for both. In the two countries population is constant and there is no technological progress.
Every year capital depreciates by 6% in both countries. Country 1 saves 40% of output, and
country 2 saves 20%.
a) Write down the function of production per unit of labor. Suppose the two countries
start with an initial capital stock (per unit of labor) of 500, what are the initial income and
consumption per unit of labor in both countries?

Answer 1

The production function per unit of labor for countries 1 and 2 is given by Yt = AiKαt L1−αt. Country 1 has an initial income per unit of labor of approximately 609,350 and an initial consumption per unit of labor of approximately 365,610. Country 2 has an initial income per unit of labor of approximately 2,437,400 and an initial consumption per unit of labor of approximately 1,949,920.

Step-by-step explanation:

The production function per unit of labor for countries 1 and 2 is given by Yt = AiKαt L1−αt. To calculate the initial income per unit of labor, we substitute the given values into the production function. For country 1, with A1 = 25, α = 0.35, initial capital stock (per unit of labor) of 500, and depreciation rate of 6%, the equation becomes:

Y1 = 25 * (500^0.35) * (500^0.65) = 25 * (164.92) * (147.49) ≈ 609,350

Similarly, for country 2, with A2 = 100, α = 0.35, initial capital stock (per unit of labor) of 500, and depreciation rate of 6%, the equation becomes:

Y2 = 100 * (500^0.35) * (500^0.65) = 100 * (164.92) * (147.49) ≈ 2,437,400

The initial consumption per unit of labor in both countries can be calculated by subtracting the savings rate from the initial income per unit of labor. For country 1, with a savings rate of 40%, the initial consumption per unit of labor is:

C1 = (1 - 0.40) * 609,350 ≈ 365,610

For country 2, with a savings rate of 20%, the initial consumption per unit of labor is:

C2 = (1 - 0.20) * 2,437,400 ≈ 1,949,920