20.10 In Example 20.5 we showed that the Nash equilibrium in this first-price, sealed bid auction was for each participant to adopt a bidding strategy of b(v)
[(n 1)/n]v. The total revenue a seller might expect to receive from such an auction will obviously be [(n 1)/n]v*—

where v* is the expected value of the highest valuation among the n auction participants.

a. Show that if valuations are uniformly distributed over the interval [0, 1], the expected value for v* is n/(n 1). Hence expected revenue from the auction is (n 1)/(n 1).

Hint: The expected value of the highest bid is given by E(v*)


1 0

vf(v)dv 21.1 Suppose demand for labor is given by L
50w  450 and supply is given by L
100w, where L represents the number of people employed and w is the real wage rate per hour.

a. What will be the equilibrium levels for w and L in this market?

b. Suppose the government wishes to raise the equilibrium wage to $4 per hour by offering a subsidy to employers for each person hired. How much will this subsidy have to be?
What will the new equilibrium level of employment be? How much total subsidy will be paid?

c. Suppose instead that the government declared a minimum wage of $4 per hour. How much labor would be demanded at this price? How much unemployment would there be?

d. Graph your results.