## PROBLEMS AND APPLICATIONS

1. When you or one of your friends is looking for a part-time job, how many weeks does it typically take? After you find a job, how many weeks does it typically last?

2. From your estimates, calculate (in a rate per week) your rate of job finding f and your rate of job separation s. (Hint: If f is the rate of job finding, then the average spell of unemployment is 1/f.)

3. What is the natural rate of unemployment for the population you represent?

2. In this chapter we saw that the steady-state rate of unemployment is U/L = s/(s + f). Suppose that the unemployment rate does not begin at this level. Show that unemployment will evolve over time and reach this steady state. (Hint: Express the change in the number of unemployed as a function of s, f, and U. Then show that if unemployment is above the natural rate, unemployment falls, and if unemployment is below the natural rate, unemployment rises.)

3. The residents of a certain dormitory have collected the following data: People who live in the dorm can be classified as either involved in a relationship or uninvolved. Among involved people, 10 percent experience a breakup of their relationship every month. Among uninvolved people, 5 percent will enter into a relationship every month. What is the steady-state fraction of residents who are uninvolved?

4. Suppose that the government passes legislation making it more difficult for firms to fire workers. (An example is a law requiring severance pay for fired workers.) If this legislation reduces the rate of job separation without affecting the rate of job finding, how would the natural rate of unemployment change? Do you think that it is plausible that the legislation would not affect the rate of job finding? Why or why not?

5. Consider an economy with the following Cobb–Douglas production function:

Y = K1/3L2/3.

The economy has 1,000 units of capital and a labour force of 1,000 workers.

1. Derive the equation describing labour demand in this economy as a function of the real wage and the capital stock. (Hint: Review Chapter 3.)

2. If the real wage can adjust to equilibrate labour supply and labour demand, what is the real wage? In this equilibrium, what are employment, output, and the total amount earned by workers?

3. Now suppose that the government, concerned about the welfare of the working class, passes a law requiring firms to pay workers a real wage of 1 unit of output. How does this wage compare to the equilibrium wage?

4. The government cannot dictate how many workers firms hire at the mandated wage. Given this fact, what are the effects of this law? Specifically, what happens to employment, output, and the total amount earned by workers?

5. Will the government succeed in its goal of helping the working class? Explain.

6. Do you think that this analysis provides a good way of thinking about a minimum-wage law? Why or why not?

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6. Suppose that a country experiences a reduction in productivity—that is, an adverse shock to the production function.

1. What happens to the labour demand curve?

2. How would this change in productivity affect the labour market—that is, employment, unemployment, and real wages—if the labour market were always in equilibrium?

3. How would this change in productivity affect the labour market if unions prevented real wages from falling?

7. When workers’ wages rise, their decision on how much time to spend working is affected in two conflicting ways, as you may have learned in courses in microeconomics. The income effect is the impulse to work less, because greater incomes mean workers can afford to consume more leisure. The substitution effect is the impulse to work more, because the reward to working an additional hour has risen (equivalently, the opportunity cost of leisure has gone up). Apply these concepts to Blanchard’s hypothesis about American and European tastes for leisure. On which side of the Atlantic do income effects appear larger than substitution effects? On which side do the two effects approximately cancel? Do you think it is a reasonable hypothesis that tastes for leisure vary by geography? Why or why not?

8. In any city at any time, some of the stock of usable office space is vacant. This vacant office space is unemployed capital. How would you explain this phenomenon? Is it a social problem?