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EXERCISES

1. By comparing two different rows in the preceding table, show that the marginal product of labor is positive. Make sure you keep all other inputs the same. In other words, find two rows that show that an increase in labor, keeping all other inputs the same, leads to an increase in output.

2. By comparing two different rows in the preceding table, show that the marginal product of human capital is positive. Again, make sure you keep all other inputs the same.

3. By comparing two different rows in the preceding table, show that the marginal product of technology is positive.

4. Does the production function exhibit diminishing marginal product of physical capital? [Hint: if more and more extra capital is needed to generate the same increase in output, then there is diminishing marginal product.]

5. Does the production function exhibit diminishing marginal product of labor?

6. (Difficult) Can you guess what mathematical function we used for the production function?

7. Why are electricians not paid the same amount in Topeka, Kansas, and New York City? Why are electricians not paid the same amount in North Korea and South Korea? Is the explanation the same in both cases?

8. Think about the production function for the university or college where you are studying. What are some of the different inputs that go into it? Classify these inputs as physical capital, human capital, labor, knowledge, natural resources, and social infrastructure. Try to come up with at least one example of each.

9. Suppose government spending is 30, government income from taxes (including transfers) is 50, private saving is 30, and lending to foreign countries is 20. What is national savings? What is investment?

10. Explain how it is possible for investment to be positive yet for the capital stock to fall from one year to the next.

11. Is a fireworks display nonrival? Nonexcludable?

12. Suppose that a country’s capital stock growth rate is 8 percent, the labor hours growth rate is 4 percent, the human capital growth rate is 2 percent, and the technology growth rate is 3 percent. The parameter a is 0.25. What is the output growth rate?

13. Suppose that a country’s capital stock growth rate is 4 percent, the labor hours growth rate is 3 percent, the human capital growth rate is 1 percent, and the output growth rate is 5 percent. The parameter a is 0.5. What is the technology growth rate?

14. Explain why a decrease in a country’s competitiveness can be a sign that the country is becoming more prosperous.

15. Firms are sometimes willing to pay for training courses for their workers. Other things being equal, do you think a firm would prefer to pay for one of its employees to do a general management course or a course that trains the employee in the use of software designed specifically for the firm? Explain.