ANALYTICAL PROBLEMS

1. a. A technological breakthrough raises a country's

total factor productivity A by 10%. Show how this change affects the graphs of both the production function relating output to capital and the produc­tion function relating output to labor.

b. Show that a 10% increase in A also increases the MPK and the MPN by 10% at any level of capital and labor. (Hint: What happens to ∆ Y for any increase in capital, ∆ K, or for any increase in labor, ∆ N?)

c. Can a beneficial supply shock leave the MPK and MPN unaffected? Show your answer graphically.

2. How would each of the following affect the current level of full-employment output? Explain.

a. A large number of immigrants enter the country.

b. Energy supplies become depleted.

c. New teaching techniques improve the educational performance of high school seniors.

d. A new law mandates the shutdown of some unsafe forms of capital.

3. During the 1980s and 1990s the average rate of unemployment in Europe was high. Some econo­mists claimed that this rate was in part the result of “real-wage rigidity," a situation in which unions kept real wages above their market-clearing levels.

a. Accepting for the sake of argument that real wages were too high in Europe in the 1980s and 1990s, show how this situation would lead to unemploy­ment (a situation where people who would like to work at the going wage cannot find jobs).

b. What is the effect of real-wage rigidity on the output actually supplied by firms, relative to the output they would supply if there were no real-wage rigidity?

4. How would each of the following affect Helena Handbasket's supply of labor?

a. The value of Helena's home triples in an unex­pectedly hot real estate market.

b. Originally an unskilled worker, Helena acquires skills that give her access to a higher-paying job.

c. A temporary income tax surcharge raises the per­centage of her income that she must pay in taxes, for the current year only. (Taxes are proportional to income in Helena's country.)

5. Suppose that under a new law all businesses must pay a tax equal to 6% of their sales revenue. Assume that this tax is not passed on to consumers. Instead, consumers pay the same prices after the tax is imposed as they did before. What is the effect of this tax on labor demand? If the labor supply curve is unchanged, what will be the effect of the tax on employment and the real wage?

6. Can the unemployment rate and the employment ratio rise during the same month? Can the participation rate fall at the same time that the employment ratio rises? Explain.

7. Self-employed workers in the United States must pay Social Security taxes equal to 12.4% of any income up to $147,000 in 2022. This income level of $147,000 is known as the “cap." Income in excess of the cap is not subject to Social Security tax, so self-employed workers with incomes exceeding $147,000 pay $147,000 ? 0.124 = $18,228. Now consider two proposals designed to increase Social Security tax rev­enue. Proposal A increases the cap to $177,822.60 so that Social Security taxes equal 12.4% of income up to $177,822.60. Proposal B increases the Social Security tax rate to 15%, but leaves the cap unchanged at $147,000. For people with income that always exceeds the cap, the amount of Social Security tax is the same under Proposal A ($177,822.60 ? 0.124 = $22,050) as under Proposal B ($147,000 ? 0.15 = $22,050). There are no planned changes in future Social Security benefits anticipated by current workers.

a. Sally is self-employed and earns $200,000 per year. What are the effects of Proposal A and Proposal B on Sally's labor supply? Under which proposal would she supply a greater amount of labor? Explain your answers using the concepts of income effect and substitution effect.

b. Fred is self-employed and earns $50,000 per year. What are the effects of Proposal A and Proposal B on Fred's labor supply? Under which proposal would he supply a greater amount of labor? Explain your answers using the concepts of income effect and substitution effect.

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