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4. Consider the employer prejudice model of labor market discrimination with exactly two types of employers: a fraction 6 that are prejudiced against workers from \"group B\" and have a common \"discrimination coefcient\" of d,- = d > 0, and the complementary fraction 1 6 that are unprejudiced and have a common \"discrimination coefcient\" of d; = 0. There are two groups of workers in the labor market \"group A\" and \"group B\" which each supply labor perfectly inelastically and which comprise positive shares 1 7t and rt, respectively, of the labor force. There are N workers and M employers in the labor market, where both N and M are large. The value marginal product curve for each employer is VMP = f'(EA + E3) = a b(EA + EB), where a > b > 0, and El- is the quantity of labor employed from group 1'. Note that the VMP curve implies that the two labor types are equally productive perfect substitutes and that the output price has been normalized to 1. Finally, the labor market is competitive, with each agent taking as given the market wage of each labor type, WA and W3. a. Find an unprejudiced employer's labor demand rnctions for group A labor and group B labor. b. Find a prejudiced employer's labor demand functions for group A labor and group B labor. c. Find the overall market labor demand functions for group A labor and group B labor. d. Find the conditions that dene the equilibrium values of WA and W3. What bounds can be placed on the between-group wage gap, WA wB, that exists in equilibrium? Explain briey. f. If there are no integrated rms in equilibrium (and if all rms strictly prefer this), what bounds can be placed on the between-group wage gap, WA wB, that exists in equilibrium? Explain briey. g. Suppose that the initial market equilibrium is completely segregated, as in (1). How would a small increase in either 9 or it alter the equilibrium wages? Explain briey. Would your answer change if there were some integrated rms in the initial market equilibrium? Explain briey. 9