Question

Two suppliers have been contracted by a government agency to train agency employees learning to use a new computer system. The marginal cost curve of firm 1 is MC1=160+2Q1, while the marginal cost curve for Firm 2 is MC2=100+Q2, where Q is hours of training per week. Originally, each firm provides 60 hours of training services each week.

What is the total cost to firm 1 of providing 60 hours of training each week?

What is the total cost to firm 2 of providing 60 hours of training each week?

An economically-literate manager suggests it would be better to state a price that the government is willing to pay for an hour of training, and let each firm provide the number of hours they are willing to at this price.

What price should the government set to cost-effectively distribute the number of hours between the two firms while maintaining the total training provided at 120 hours per week?

How many hours of training will firm 1 provide at this price?

What is firm 1’s total cost?

How many hours will firm 2 provide at this price?

What is firm 2’s total cost?

How large is the cost savings resulting from the price rationed system relative to the original allocation of 60 training hours for each firm?

Answer 1

A.Total cost is the integration of marginal cost of a firm.

Total cost of firm 1= =

At Q1= 60

TC1= 160*60+60²= 9,600+3,600= 13,200

B. Total cost of firm2= =

With Q2= 60

TC2= 100*60+60²/2= 6,000+3600/2= 6,000+1800= 7,800

C. For efficiency, the marginal costs between the firm's should be equalized (equimarginal principle) and the sum of total hours of training should be 120.

Thus, condition 1 is , MC1=MC2

160+2Q1= 100+Q2=> 2Q1-Q2= 100-160=> 2Q1-Q2= -60

CONDITION 2 is Q1+Q2= 120

Rearranging this, we get Q1=120-Q2

Put this in condition 1,

2(120-Q2)-Q2= -60

240-2Q2-Q2= -60

240+60=3Q2

Q2= 300/3= 100

And Q1= 120-100=20

Thus, quantity should be 20 for firm 1.

The price the government should set shoudl be equal to the marginal cost. Since Marginal costs are equalized,the price should be 160+2Q1= 160+2*20=160+40=200 100+Q1=100+100=200

Thus, if government sets price equal to 200, the firm's marginal costs will be equalized and the quantities would sum up to 120 in total.

D. Firm1 total cost at quantity=20

TC at Q1=20, TC= 160Q1+Q1²= 160*20+20²= 3200+400=3600

E. At calculated, firm 2 will provide 100 hours of training.

Total cost at Q2=100,

TC= 100Q2+Q2²/2= 100*100+100²/2= 10000+10000/2=10,000+5,000= 15,000

F. Total cost of both the firms with 60 hours each was sum of TC1 and TC2 from part a and b, i.e., 13,200+7800 =21,000

With new allocation, total cost from part d and e is 3600+15000=18,600

Thus, total savings =21000-18,600=2,400