Answer:
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
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
