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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.

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

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

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?

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.

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?

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?

Capital’s share of total income is about 10% in both Colombia and Costa Rica. The capital–labor ratio is $15.25 thousand per worker in Colombia and $23.12 thousand per worker in Costa Rica. Real GDP per worker is $12.18 thousand in Colombia and $13.31 thousand in Costa Rica. Predict what will happen to the capital stocks

How do increases in total factor productivity increase the standard of living? What factors cause total factor productivity to change? What is human capital? How does the acquisition of human capital improve the quality of labor? What are the two basic ways in which workers can acquire human capital?

What does it mean to say that an economy is “accumulating capital”? Why does the marginal product of capital decrease as capital is accumulated? What is the difference between a stock variable and a flow variable?