Question

Consider a competitive firm whose cost is given by

                 C = 60 + 2Q + 4Q² .

The product sells at $26 per unit.

(1) Find the optimal quantity of output in the short run.

(2) Evaluate the profitability of the optimal quantity of output that you found in (1). If it is a loss, make a decision whether or not the firm should shut-down.   Provide a reason for your decision.  

(3) What long-run adjustments should you expect? Explain.

Answer 1

1)

C=60+2Q+4Q^2

Marginal Cost can be determined by differentiating C with respect to Q

MC=dC/dQ=2+8Q

A competitive firm sets its output such that MC=Price to maximize profit. So,

MC=P

2+8Q=26

8Q=24

Q=3 (optimal output of competitive firm)

b)

Total Revenue=TR=P*Q=26*3=$78

Total Cost=TC=60+2Q+4Q^2=60+2*3+4*3^2=$102

Profit=TR-TC=78-102=-$24

Firm is making a loss in the short run.

In this case, fixed cost is $60, since loss amount is lower than the fixed cost. firm should continue to operate to minimize losses.

c)

Since firm is making a loss in short run, some of the firms will exiting the market. It will decrease the quantity. A leftward shift in supply will push the price up. So, profitability of firm will start increasing. In long run, Price will be equal to minimum ATC.

Let us calculate the minimum ATC in this case.

Given

C=60+2Q+4Q^2

ATC=C/Q=(60/Q)+2+4Q

Set ATC=MC to determine the output where ATC is minimized

(60/Q)+2+4Q=2+8Q

4Q^2=60

Q=15^0.5=3.87

Minimum ATC=(60/3.87)+2+4*3.87=$32.98

So, in long run price of product will be around $32.98 and economic profit of each firm will be zero.