Question

Can you solve this activty for me please got stuck,

Each employer faces competitive weekly wages of $2,000 for whites and $1,400 for blacks.
Suppose employers under-value the efforts/skills of blacks in the production process. In
particular, every firm is associated with a discrimination coefficient, d where 0 ≤ d ≤ 1. In
particular, although a firm’s actual production function is Q = 10(EW + EB), the firm manager
acts as if its production function is Q = 10EW + 10(1 – d) EB. Every firm sells its output at a
constant price of $240 per unit up to a weekly total of 150 units of output. No firm can sell
more than 150 units of output without reducing its price to $0.
(a) What is the value of the marginal product of each white worker?
(b) What is the value of the marginal product of each black worker?
(c) Describe the employment decision made by firms for which d = 0.2 and d = 0.8
respectively.
(d) For what value(s) of d is a firm willing to hire blacks and whites?

Answer 1

a) VMPe for white workers = MPe * P = 10*240 = $2400

b) VMPe for black workers = MPe * P = $2400 again

c) Firm acting as though black workers are less productive.

White: VMPe*P>=Ww gives us $2400>=$2000

They want to hire 15 white workers to get Q=150, unless black workers change the picture.

Black: VMPe*P>=Wb gives us $2400(1-d)>=$1400

Solving for d: 1-d >= 14/24, meaning 1-(14/24)>=d, so hire black workers only if d<=.416666

For d=0.8, hire 15 white workers. For d=0.2, hire 18.75 black workers, call it 18.

d) Hire both if d=0.3

Step-by-step explanation:

a) Take the derivative of the production function w.r.t. Ew, multiply by P, simple

b) Take the derivative of the production function w.r.t. Eb, multiply by P, simple.

(I believe your Borjas textbook wants you to notice they are equally productive here)

c) New derivatives with perceived production functions.

White: still VMPe=$2400

Black: VMPe=10*(1-d)*$240=$2400(1-d)

Firm hires white if $2400 >= $2000, this occurs until 15, as the 16th worker produces above 150 where P goes to $0.

Firm hires black if $2400(1-d)>=$1400, this happens for d<=.41666

For d=0.8, only hires white workers ==> Ew=15

For d=0.2, only hires black workers ==> Eb = 15 or 18.75, depending on how you interpret the problem. They should hire 15, but the manager treats them as inferior inputs, so they will hire 18.75. Can't have .75 of a worker, so truncate to 18. This will produce more than 150 units, even though the manager incorrectly perceives production as lower.

d) The firm can save money by hiring black workers if their discrimination doesn't get in their way. However they discriminate, so I would set VMPe for black workers equal to the white wage, that is where the firm is indifferent.

So: $2400(1-d)=$2000, this occurs when d=0.3

I believe the previous respondent is incorrect in their solutions.

Answer 2

a. The marginal product of each white worker is 143%

b. The marginal product of each black worker is 70%

c. Since, adjusted wage of black labor with d=0.2 is less than the wage of white labor of $2,000, the profit maximizing firm would hire only black labor.

Since, adjusted wage of black labor with d=0.8 is greater than the wage of white labor of $2,000, the profit maximizing firm would hire only white labor.

d. Value of D coefficient that allows to employ black and white labor is 0.43

Step-by-step explanation:

According to the given data we have the following:

Weekly wage for white labor is $2,000

Weekly wage for black labor is $1,400

production function is Q = 10(EW + EB)

manager production function is Q = 10EW + 10(1 – d) EB

Price of the product is $240

Weekly output is 150 units

a. To calculate the value of the marginal product of each white worker we use the following formula:

marginal product of each white worker=Weekly wage for white labor/Weekly wage for black labor

marginal product of each white worker=$2,000/$1,400

marginal product of each white worker=1.43=143%

b. To calculate the value of the marginal product of each black worker we use the following formula:

marginal product of each black worker=Weekly wage for black labor/Weekly wage for white labor

marginal product of each black worker=$1,400/$2,000

marginal product of each black worker=0.7=70%

c. To describe the employment decision we have to calculate the adjusted wage of black labor with d=0.2 and d=0.8 as follows:

adjusted wage of black labor with d=0.2=Wage black(1+D coefficient)

=1,400(1+0.2)

=1400(1.2)

=1,680.

Since, adjusted wage of black labor with d=0.2 is less than the wage of white labor of $2,000, the profit maximizing firm would hire only black labor.

adjusted wage of black labor with d=0.2=Wage black(1+D coefficient)

=1,400(1+0.8)

=1,400(1.8)

=2,520

Since, adjusted wage of black labor with d=0.8 is greater than the wage of white labor of $2,000, the profit maximizing firm would hire only white labor.

d. To calculate for what value(s) of d is a firm willing to hire blacks and whites we would have to calculate the following formula:

Wage black(1+D coefficient)=Wage white

1,400(1+D coefficient)=2,000

(1+D coefficient)=2,000/1,4000

D coefficient=1.43-1

D coefficient=0.43

Value of D coefficient that allows to employ black and white labor is 0.43