How much Despero Inc. should produce if it chooses to produce?

If the firm chooses to produce, it will choose its optimal quantity at the point where P = MC.

From the total cost function:

• TC=250+40q+20qTC=250+40q+20q

The marginal cost is equal to:

• MC=ΔTCΔq=−40q2+20MC=ΔTCΔq=−40q2+20

The marks price is given as P = $10. Equating the MC to the market price and solving for q:

• −40q2+20=10−40q2+20=10

• 40q2=1040q2=10

• q2=4q2=4

• q∗=√4=2q∗=4=2 units.

 

Question B:

 

Should Despero remain in the market in the long term at that price? What about the short term?

In the short run, the firm should remain in the market if P = $10 is greater than the average variable cost at q* = 2.

From the total cost function, the variable cost is:

• VC=40q+20qVC=40q+20q

And the average variable cost is equal to:

• AVC=VCq=40q2+20AVC=VCq=40q2+20

At q = 2, the AVC is equal to:

• AVC=4022+20=$30AVC=4022+20=$30

Thus, firm should leave the market in the short run since the market price is less than the average variable cost.

 

In the long run., the firm should continue producing if P = $10 is greater than the average total cost at q* = 2.

From the total cost function, the average cost is equal to:

• AC=250q+40q3+20AC=250q+40q3+20

At q = 2, the average total cost is equal to:

• AC=2502+4023+20=$135AC=2502+4023+20=$135

Since the average cost is greater than the P = $10, the firm should exit the market in the long run.