Need some major help and explanations for this type of probelm. Suppose the prod

Question

Need some major help and explanations for this type of probelm.

Suppose the production function of our sports gaming franchise is given by:

q = 10 * ( LW + LNW )1/2

Where q is measured in matches, and LW and LNW represent white players (labor) and non-white players (labor), respectively.

We can then show that, indeed, white and non-white players are perfect substitutes in the production of matches, as evidenced by the fact that for either type, the marginal product of labor is represented by:

MPL = 5 / ( LW + LNW )1/2

[Note: As expected, the MPL decreases in both LW and LNW .]

Suppose the market wage for non-white players is $10 / player, while the market wage for white players is $20 / player. The value of output to the franchise (again measured in broadcasting rights fees) is $100 / match .

Assume at first that the franchise does NOT discriminate and seeks to maximize profit.

In this case, the franchise would hire ________ players, ________ of whom are white.

a. 100 ; all
b. 100 ; none c. 625 ; all
d. 2500 ; None

In this case, the franchise would produce (air) _________ matches and earn profits of ________.

100 ; $10,000

100 ; $0

250 ; $12,500

500 ; $25,000

Now, assume the franchise develops a taste for discrimination and has a discrimination coefficient ( di ) of 0.25 .

With this discrimination coefficient, the franchise maximizes profit by hiring ________ players, ________ of whom are white.

625 ; all

1600 ; none

625 ; none

1600 ; all

With this discrimination coefficient, the franchise would produce (air) _________ matches and earn profits of ________.

100 ; $10,000

100 ; $0

400 ; $24,000

500 ; $25,000

c. Finally, suppose that over time, the franchise’s taste for discrimination intensifies, raising its discrimination coefficient to 1.25 .

With this higher discrimination coefficient, the franchise maximizes profit by hiring ________ players, ________ of whom are white.

100 ; all

100 ; half

625 ; all

2500 ; None

With this higher discrimination coefficient, the franchise would produce (air) _________ matches and earn profits of ________.

100 ; $10,000

100 ; $0

250 ; $12,500

500 ; $25,000

This franchise suffers a profit loss from having a taste for discrimination because the value of the marginal products of white players and non- white players are in fact ________, but they act as if the costs of hiring white players and non-white players are __________.

Equal ; equal

Equal ; unequal

Unequal ; equal

Unequal ; unequal

Explanation / Answer

Solution: We are given production function as : Q = 10(LW + LNW)1/2

MP for both types of workers : MP = 5 (LW + LNW)-1/2

1) We can see from the question that whites and non-whites are perfect substitutes and wage rate for non-white players is less than the wage rate of white players, 10< 20. So, in case of no discrimination, firm will rather hire all of non-white players.

Then, it will hire till W = MRPL ,or wage equals marginal revenue product of labour.

MRPL = MP*MR. Also, we know MR = P

Value of output = P*Q

Then, value of output per unit (or per match in our case) = P. So, P=$100

MRPL = 100*5*(LNW)-1/2. Since, we have seen LW=0

So, W = MRPL implies 10 = 100*5*(LNW)-1/2

On solving, LNW = 2500 workers. So, correct answer is d).

2) Then from part 1), Q = 10 *(2500)1/2 = 500 matches

Profit = P*Q - W*L ,here L = LNW

Profit = 100*500 - 10*2500

= 50000 - 25000 = $25,000. So correct answer is d).

3) With discrimination coefficient, di = 0.25, now percieved wage rate to a non-white worker = W(1+di)

= 10(1+0.25) = $12.5

Note that this wage rate is still less than the one set for white workers, i.e, $20, and the two types are perfect substitutes, so again firm will hire all non-white workers and none white workers.

Again, like part 1), W = MRPL = 500*(LNW)-1/2

12.5 = 500 (LNW)-1/2. On solving this, we get, LNW = 1600 workers. So correct answer is b).

4) Q = 10(LNW)1/2 = 10*(1600)1/2 = 400 matches

Profit = P*Q - W*LNW

Profit = 100*400 - 10*1600 = $24,000 (we put W=$10, because due to discrimination, firm perceived wage for non whites as $12.5 but actual market wage is $10). So, correct answer isc).

5) Now, perceived wage rate for non-whites = 10(1 + 1.25) = $22.5 > $20, so hire all whites

W = MRPL

20 = 500*(LW)-1/2

On solving, we get LW = 625 workers. So, correct answer is c).

6) Q = 10*(LW)1/2 = 10*(625)1/2 = 250 matches

Profit = P*Q - W*LW

Profit = 100*250 - 20*625 = $12,500. So, the correct answer is c).

7) We have seen that the two types are perfect substitutes and thus have same marginal products, as seen in the question itself. But due to taste of discrimination, the firm perceives as if it has to pay higher to the non-white worker than the actual wage rate in the market. Thus, they hire less of them, or in case of high discrimination coefficient, none of them, and instead end up incurring higher costs. So, even if the cost of hiring the two workers is unequal (lower for non-whites), firms assumes it be same. So, correct answer is a) Equal, Equal

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.