3 Statistical Discrimination Assume a competitive labor market where there are two types of workers: skilled and unskill

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3 Statistical Discrimination Assume A Competitive Labor Market Where There Are Two Types Of Workers Skilled And Unskill 1 (171.23 KiB) Viewed 33 times

3 Statistical Discrimination Assume a competitive labor market where there are two types of workers: skilled and unskilled. A skilled worker produces 10 units of output, an unskilled worker produces 0 3 units. Firms sell output produces at $1 per unit. Firms cannot tell if a worker is skilled or not, but they see that there are two groups of workers: A and B. Firms believe that 50% of type A workers are skilled while only 25% of type B workers are skilled. Firms pay a testing cost of $2 to find out if workers are skilled or not, which is accurate 90% of the time. Firms never hire workers who test as unskilled. Firms will pay two wages, wA and WB to workers from different groups. Question 3.1 Following our notation from class, what are the values of parameters Ps: Pu, TA, TB, d, r? Question 3.2 Write down the expression for firms' profit from interviewing a worker from group A. Write down the expression for firms' profit from interviewing a worker from group B. Question 3.3 Argue that in a competitive equilibrium, firms must earn zero profit inter- viewing each type of worker. Question 3.4 Find the wage for wA and wg and explain why WA > WB. ■ Question 3.5 What is the expected wage of a a) skilled worker from group A, b) unskilled worker from group A, c) unskilled worker from group B, d) unskilled worker from group B? HINT: Consider a skilled worker from group A. He passes the test with probability 0.9, is hired and gets the wage wA. He fails the test with probability 0.1, is not hired and gets wage of 0: w = 0.9 x WA +0.1 x 0 = 0.9 × 5 = 4.5 Do the analogous reasoning for other 3 cases. Question 3.6 Consider now an unskilled worker who has an opportunity to go to a special training program to become a skilled worker but the training costs 2. Assume that firms do not observe whether a worker went to that training program or not. Is it worth for an unskilled worker to go to that training program? To answer, compare the expected wages of skilled and unskilled workers. Assume that workers have discount factor 0 so that only current wage matters for the present discounted value.