Consider a firm that faces a constant per unit price of $1,200 for its output. The firm hires workers, E, from a union at a daily wage of w, to produce output, q, where
q = 2E½.
Given the production function, the marginal product of labor is 1/E½. There are 225 workers in the union. Any union worker who does not work for the firm can find a non-union job paying $96 per day.
(a) What is the firm's labor demand function?
(b) If the firm is allowed to specify w and the union is then allowed to provide as many workers as it wants (up to 225) at the daily wage of w, what wage will the firm set? How many workers will the union provide? How much output will be produced? How much profit will the firm earn? What is the total income of the 225 union workers?