December 2020

Briefly explain whether the following Cobb-Douglas production function exhibits constant returns to scale: Y = AK1/2L3/4. What determines the shares of labor and capital in total income? How are these shares related to the production function?

Draw a graph of the aggregate production function with capital, K, on the horizontal axis. a. Why does the graph have the shape that you have drawn? b. Indicate on the graph the effect of an increase in the capital stock. c. Indicate on the graph the effect of an increase in the productivity of labor.

Assume that the labor force is 140 million workers, the capital stock is $50,000 billion, and real GDP is $6,500 billion to answer the following questions: a. If the production function is Y = AK1>2L1>2, what is total factor productivity? b. If the production function is Y = AK1>4L3>4, what is total factor productivity?

Suppose that the production function is Y = AK1>4L3>4. Assume that A = 1,000, the current level of the capital stock is $16,000 billion, and the labor force is 200 million workers. a. Find the marginal product of labor. b. Graph the marginal product of labor. c. Graph the production function, putting labor on the horizontal axis and assuming

Suppose that the production function is given by Y = AK1>5L4>5. a. If A = 2,000, K = $10,000 billion, and L = 50 million workers, what is real GDP? b. Find the real wage. c. Find the real rental cost of capital. d. Graph the relationship between the production function and the labor and capital markets.

Consider the economy described in problem 2.7. Briefly explain the likely changes in real GDP, the real wage, and the real rental cost of capital under each of the following scenarios. Include a graph with your answers: a. There are breakthroughs in technology that improve the productivity of all factors of production, causing A to increase to

What is the per worker production function? What is the equation for the per worker production function? Which two factors determine labor productivity? Which of the two is more important? Briefly explain.

Suppose that y = Ak1>4, the capital-labor ratio is $20,000 per worker, the level of total factor productivity is 500, 60% of the population works, and there are 60 million workers. What are real GDP per worker and real GDP per capita?

Assume that total factor productivity is constant. a. Use the per worker production function to show the effect of a decrease in the capital– labor ratio. What happens to the marginal product of labor? Briefly explain. b. What happens to real GDP per capita? c. What happens to the marginal product of capital?

Assume that the capital–labor ratio is constant. a. Use the per worker production function to show the effect of an increase in total factor productivity. What happens to the marginal product of labor? Briefly explain. b. What happens to real GDP per capita? c. What happens to the marginal product of capital?