Practice Questions on the production function, growth facts, and growth accounting

"The lecture notes that I made up for this course are a stock. The number of lectures that I give per week are a flow." Comment.

Suppose that the production function for mowing laws is

Y/L = 16K - 2L

where Y is output, L is labor input, and K is capital input. If capital costs $50 an hour to rent and labor costs $10 an hour, what is the lowest-cost combination of labor and capital that can produce 25 units of output? Assume that labor has to be an integer (1, 2, 3, etc.) but that capital can be any positive rational number, including fractions.

Suppose that from now on, India's per capita GDP grows at a 5 percent annual rate, and in the United States per capita GDP grows at a 1.5 percent annual rate. Which economy will have a higher GDP per capita in 20 years? in 50 years? in 100 years?

Suppose that the production function for an economy is

(Y/L) = (K/L)

^{0.25}E^{0.75}where Y/L is labor productivity, K/L is the capital-output ratio, and E is the efficiency of labor.

- If the capital-output ratio rises from 3.0 to 3.3, what will be the approximate percentage increase in labor productivity?
- If the efficiency of labor falls from $10,000 to $9500, what will be the approximate percentage decrease in labor productivity?