We will consider a model of discrimination in the labor market. There are two groups: Earth- lings and Martians, who are applying for jobs on Earth. Each employee has some ability a, and an employer who hires an employee will make profit a - w, where w is the wage that the employer pays the employee. The ability of Earthlings is distributed N (HEarthling,02), and the ability of Martians is distributed N (uMartian, 02). For notation, we will use r to denote whether the employee is from Earth or Mars. Each employee receives offers from two employers, and accepts the job that offers a higher wage (if both offers are the same, then the employee randomly picks one of the offers). Neither employer knows what the other employer offered. (b) Let us define the conditional wage gap as E [wi W; | ri = Earthling, r; = Martian, a; = a;], which is the average gap in wages between a Martian and an Earthling of the same abil- ity. Assume that abilities are observable. What is the conditional wage gap in this case? i. Positive ii. Negative iii. Zero Let's now think about a case with statistical discrimination. Now, instead of observ- ing ability directly, the employer observes a noisy signal, 2, of ability. Both employers observe the same = (you can think of as being the resume). Let = a + 5, where EN (0, s2). The employer also observes whether the employee is an Earthling or Martian. In equilibrium, both employers will offer w=Ear,r). Why is this the case? i. Because employers are maximizing expected profit and have the same information ii. Because employers are maximizing expected profit and do not consider the signal they receive iii. Because employers are minimizing wages, but do not have the same information iv. Because employers are minimizing wages and do not consider the signal they receive v. Other What will the wage gap be between an Earthling and a Martian who both have the same resume r. To do this, it will be useful to note that E[a | 2,r] = is a convenient property of normal distributions). +9-2 + (this = Consider the conditional wage gap. (Hint: You can use the fact that w = E[a 1,r] = 0-247**, and take expectations.). If yEarthling