Suppose, in our efficiency wage model, we have q=2/3; E, the cost of working hard, is 2; the MPL is constant, equal to 30, and the labor force is 100.
a) Find the equilibrium unemployment rate.
b) Find the return to shirking and the return to non-shirking in this equilibrium. Verify that they are identical.
c) Find the effect on u* of more effective monitoring that raises q from 2/3 to 8/10.
d) In general the MPL will be downward-sloping. See if you can show that. If so, an increase in the labor force must raise the natural rate unemployment. (Hint: If the labor force doubles, say, it must be the case that the value of the of the No-shrinking wage that used to be associated with L=X will now be associated with L=2X. For example, if the no-shirking wage associatd with L=80 when the labor force is 100 was 30, the NSW of 30 will be associated with E=160 when the labor force increases to 200. That's because the NSW depends on u [and q and c, which are unchanged] and u= .8 both when E=80 and L=100 and when E=160 and L=200).