5 Suppose a union has so much bargaining power over a firm that the union can set any wage it wants. In addition, suppose the union membership has collectively decided that their objective should be to maximize the wage differential times the number of employed union members at the firm.

(The wage differential is the difference between the union wage and the wage available to union members that quit the firm.) Assume that the wage union members can get if they quit the firm is $10 and that the firm’s (inverse) labor demand curve is given by:

where w is the wage received by each employed union member, and L is the total number of union members employed by the firm.