## Quantitative Problems

 1. In the simple competitive supply and demand framework, unemployment arises if the real wage exceeds its market clearing value. Given this, why is it unsatisfactory to seek to explain unemployment by simply assuming that the wage exceeds this value? 2. What factors might account for the apparent observed downward rigidity of nominal wages? 3. Consider the shirking variant of the efficiency wage model.(a) What happens if the government raises the level of unemployment benefits b?(b) Suppose, instead, that it becomes easier to monitor workers, so q rises. What happens now?(c) Some observers have noted that the introduction of the Internet—with the resulting emergence of a host of job-search websites—has made it much easier for unemployed workers to find work. Show that this (somewhat paradoxically) may increase the equilibrium level of unemployment. 4. In the context of the shirking model presented on page 771, suppose that the facts are as follows:v = \$8 and b = \$2G = \$2.5 and q = 0.5s(u) = a constant = 0.5The marginal revenue product of labor (MRP) is MRP = 100 − 100 · e, where e is the employment rate.(a) Temporarily assume that q = 1, so there is perfect monitoring. What is the equilibrium employment rate, e*c ? Is any unemployment that arises involuntary?(b) Now assume that the detection probability is q = 0.5. What is the no-shirking wage? Determine the equilibrium employment (e*1) and unemployment (u*1) rates. Is this unemployment involuntary? (c) Suppose that the government increases the value of unemployment benefits to b = \$7. What happens to the equilibrium unemployment rate? (Hint: Use the no-shirking condition (NSC), Equation 22.3.) 5. A pension is nonvested if the employee has not completed the required years of employment to earn the right to receive benefits from it. (By contrast, with a vested pension the worker does have these rights.) How might nonvested pensions be used to overcome the shirking problems discussed in the text? Does the use of such a scheme create other potential difficulties? 6. Suppose that after painstaking research, it is just discovered that those workers who switch from industry A to B experience a 10% wage gain, and of those who switch from B to A a 10% wage decline. What, if anything, might we conclude from these observations?