Question

The market demand is D=1900-20p, and the market supply is S=1000+10p.

1. A firm has cost function C = q2+100. How many outputs the firm should produce? What is the firm’s profit?(Hint: Setting supply equals to demand, we can get the market price)

2. If the market price is $10, how many outputs the firm should produce? What is the firm’s profit?

3. If the market price is $10, should the firm shut down in the short run?(Hint, comparing the profit vs the profit with 0 outputs.)

Answer 1

1) market price,

Qd=Qs

1900-20p=1000+10p

P=900/30=30

C=q^2+100

MC=2Q

A perfect competition firm produces at ,p=MC

30=2Q

Q=15

So firm will produce 15 units.

TC=15*15+100=325

TR=30*15=450

Profit=450-325=125

2)P=10

Firm Produces at P=MC

10=2Q

Q=5

TC=5*5+100=125

TR=10*5=50

Profit=50-125=-75( loss of 75)

3)The loss of firm is lower than Fixed cost.

So if firm shut down it willhave to bear a loss Equal to fixed cost =100 ,while operating it has to bear only loss of 75 .so to minimize loss ,firm will operate .