Question: Suppose a firm has a labor demand curve given by w = 20 - 0.01E. Furthermore, suppose that the union representing workers in the firm derives utility from the wage rate and the level of employment according to the utility function U = w · E where the marginal utility of an increase in the wage is MUw = E and the marginal utility of an increase in employment is MUE = w.
a) Graphically represent the union's utility-maximization problem, as well as its optimal wage-employment choice.
b) Algebraically solve for the union's optimal wage-employment choice.
c) Intuitively, explain why this outcome might not be "pairwise efficient".