3. A firms production function is given by Q = 10 x (EM + EF)1/2, where EM and E

Question

3. A firms production function is given by Q = 10 x (EM + EF)1/2, where EM and EF

are the quantities or male and female employees. Males and females are perfect

substitutes. Please note that the marginal product of labor is given by the

equation MPE = 5/(EM + EF)1/2. The firm sells its output for $50. The market

wage for males is $25 and the market wage for females is $15.

a. How many male workers would the firm hire if the employer did not

discriminate? How many female workers would be hired? What are the

firm’s profits?

4. Suppose that everything is the same as reported in Question 3 except that the firm

discriminates against females with a discrimination coefficient of 1.7. How many

male workers will be hired? How many female workers will be hired? What are

the firm’s profits?

Explanation / Answer

3)

a)

since wage of females is less than males...profit maximizing firm willonly hire females

No of male workers = 0

it will hire female workers untill their wage is equalto marginal product

femaleworkers wage = p* MPE = 50 * 5/sqrt(EF) = 15

EF = 278 workers

Q= 10 * sqrt(278) = 167 units

profit = 50 * 167 - 278 * 15 = 4180

4)

new wage of females = 15 * (1+1.7) =40.5

hence the firm willonly hire male workers

male workers wage = 25 = 50 * 5/sqrt(EM)

no of male workers = 100

no of female workers = 0

Q= 10 * sqrt(100) = 100

profit = 50 * 100 - 100 * 25 =2500

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