Part 1: Taste-Based Discrimina6on from Employers

Consider a market with 10 employers (firms f=1, 2, …, 10), who each want to hire 20 workers.

These workers can be male or female. The prevailing wage for male workers is wm = 50, and this is paid to all male workers at all firms.

Each employer has a certain level of taste-based discrimina2on (animus) against employing women. The amount of animus varies across employers and takes on these values, in monetary terms: d1=0; d2=5; d3=10; d4=15; d5=20; d6=25; d7=30; d8=35; d9=40; d10=45.

1)   What is the general rule for how many female workers each firm wants to hire, as a

func2on of the female wage, wf, and of the firm’s level of discrimina2on, dj? (Hint: This not a smooth func2on. It will jump from one value to another at a key threshold.)

2)   What is the market level demand curve (summed across firms) for female labor.

3)   Assume that the supply of female workers is inelas2c (does not depend on wages) and

takes the form. LSF = 95. Depict the market demand curve from ques2on 2 and this supply curve on the same graph and indicate the equilibrium quan2ty of female workers hired and their equilibrium wage rate. Solve for the value of d* (the discrimina2on level  of the marginal firm that is just indifferent between hiring female workers or not) and the equilibrium gender pay gap.

4)   Which firms (j = 1, 2, … 10) will hire female workers in this equilibrium? Which firms will hire male workers in this equilibrium?

5)   Assume that male and female workers are equally produc2ve, and they each have a

marginal revenue product of labor (MRPL) equal to 50. What is the profit (marginal revenue minus wage) that the employer earns from hiring a male worker? What is the marginal profit from hiring a female worker? Given the employment choices that each firm makes, what profits are earned by each of the 10 firms?

6)   Solve for the new equilibrium ader two new firms enter the market. These firms (j = 11,

12) have values of d11  = d12 = 0. Graph the equilibrium in a new picture and indicate the levels of female employment and wages.

7)   What is the new gender pay gap ader the entry of the two addi2onal firms? What is new the level of d*?

8)   Using this new equilibrium, solve for the marginal profits from hiring male and female

workers. Do the two new firms that entered the market (j = 11, 12) earn posi2ve, zero or nega2ve profits?

9)   Now consider another firm with d=0 (j = 13, d13=0) that is considering entering the market. If they enter, will they earn posi2ve, zero or nega2ve profits?

10) What will happen to the gender pay gap if firm j=13 enters the market?

11) In your own words, explain how this example illustrates the key predic2on from Becker’s model of taste-based discrimina2on from employers regarding the long-run level of discrimina2on (d*) and pay gaps in perfectly compe22ve markets. (State the predic2on and then relate it to the example you solved.)

12) Staying with the situa2on in problem 5, with 10 firms in the market, what would happen to the gender pay gap and to d* if the level of discrimina2on of each employer df was cut in half (to d1=0; d2=2.5; d3=5; d4=7.5; etc.)? What does this imply about the rela2onship between discriminatory tastes and gender pay gaps? Does this predic2on match the empirical finding that geographic areas with higher sexism measures in surveys tend to have larger gender pay gaps?

13) Now, consider again the market in problems 9 and 10, with 13 firms in the market, and evaluate what happens to the gender pay gap and to d* if female labor supply increases to LSF = 135? What does this imply about the expected rela2onship between the supply of female workers and gender pay gaps? Does this predic2on match the empirical finding that areas with higher rates of female labor force par2cipa2on tend to have lower gender pay gaps?

Part 2: Sta6s6cal Discrimina6on

Consider a world in which all workers can have one of three produc2vity levels: low (MRPL = 100), medium (MRPL = 200), or high (MRPL = 300). The level of produc2vity for an individual worker is not observed by firms. Instead, firms need to make employment and wage decisions based on their expecta2ons (best guesses) about produc2vity.

In this world there are two types of workers that can be iden2fied by employers: male and female. Male workers are equally divided between medium and low produc2vity levels and  female workers are equally divided between medium and high produc2vity levels. There are equal numbers of male and female workers.

14) What is the expected MRPL for male workers? What is the expected MRPL for female workers? [Reminder: the mean value of A and B is = (A+B)/2.]

15) If firms are allowed to engage sta2s2cal discrimina2on, what wages will they be willing to pay to male workers? What wages will they be willing to pay to female workers?

16) Imagine if all firms in the market pay different male and female wages, and a new entrant is thinking of paying equal wages (not discrimina2ng). What will that wage level be? Which workers will want to work for the new firm, instead of working for a different firm that pays prevailing male and female wages? Will this firm have higher or lower profits than firms that discriminate?

17) What impact does the entry of a non-discrimina2ng firm have on the profits of discrimina2ng firms? What does this imply about the long-run equilibrium with sta2s2cal discrimina2on from employers? Does ra2onal sta2s2cal discrimina2on from employers have the same long-run compe22ve equilibrium predic2on as the Becker model predic2on for taste-based discrimina2on from employers?

18) If no firms are allowed to pay workers different amounts based on their gender, what is the wage the firms will be willing to pay to all workers?

19) What if firms are not able to discriminate based on gender, but they instead devised a test that allows them to perfectly observe worker produc2vity before they make wage offers. What average wages will firms pay to male workers and to female workers? Compare the gender pay gaps and firm profits in this scenario to the ones that emerged in problem 15, with no tes2ng and sta2s2cal discrimina2on, and in problem 18, with no tes2ng or sta2s2cal discrimina2on.

20) Finally, let’s consider a different problem for employers. In this case, each employer is considering what worker to hire for an open posi2on that pays a wage of 150 with the same rela2onship between worker ability and MRPL described above. Assume that each employer receives applica2ons from the full distribu2on of gender and ability and is only going to hire one worker. Under each of the three scenarios examined above (tes2ng to observe produc2vity, no tes2ng and sta2s2cal discrimina2on, no tes2ng and no sta2s2cal discrimina2on), what will be the share of female and male workers of each type that are hired? What are expected firm profits in each scenario?