Question

Suppose the total cost of a representative perfectly competitive apple producer is given as

tc = 12 + 6q + q^2$. All apple producers in the market are assumed to be identical. Suppose

further that the demand for apples is estimated as qd= 18,000 − 500p and market supply is

qs = 2,000 + 500p

a. (2 points) Find the equilibrium market price and total supply of apples in the market.

b. (4 points) What is the profit maximizing quantity of apples each company would

produce? Find the total revenue, total cost and profits associated with the profit

maximizing quantity.

c. (4 points) Comment on whether this is an equilibrium in the short-run or in the long-run.

Which assumption of perfectly competitive markets do you base your response on?

d. (3 points) What is the short-run supply function of this apple producer?

e. (2 points) What is the number of companies in the market in the short-run?

f. (5 points) Using the assumptions of the perfectly competitive model, comment on what

will happen in the market in the long-run. What will be the new equilibrium price?

What will be the number of companies? Assume input prices will remain the same, no

matter what, regardless of the number of apple producers in the market.

Answer 1

a)

Set Qd=Qs for equilibrium

18000-500p=2000+500p

1000p=16000

p=$16 (equilibrium price)

Qd=18000-500p=18000-500*16=10000

Qs=2000+500p=2000+500*16=10000

Equilibrium quantity=Qd=Qs=10000

b)

TC=12+6q+q^2

Marginal Cost=MC=dTC/dq=6+2q

Set MC=Price for profit maximization

6+2q=16

2q=10

q=5 (Profit maximizing output of a firm)

Total Cost=TC=12+6q+q^2=12+6*5+5^2=$67

Total Revenue=TR=P*q=16*5=$80

Profit=TR-TC=80-67=$13

c)

Firm is making positive economic profit. It means firm is in short run equilibrium.

Above answer is based upon the assumption that a perfectly competitive firm makes zero economic profit in long run.

d)

TC=12+6q+q^2

TVC=6q+q^2

AVC=TVC/q=6+q

We can see that minimum AVC is 6. So, a competitive firm will produce in short run if price is higher than $6.

Firm's marginal cost curve represent the short run supply curve. So, a competitive firm's supply is given as

p=6+2q

or

2q=-6+p

q=-3+0.5p for p6

e)

Number of firms in short run=Equilibrium quantity/output of a firm=10000/5=2000

f)

Firms are making positive economic profit in short run. This positive economic profit will attract other firms to enter the market. Supply will increase and price will come down. Profit will also start declining.

In long run price will be equal to minimum ATC and economic profit of each firm will be zero.

ATC=TC/q=(12+6q+q^2)/q=(12/q)+6+q

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

(12/q)+6+q=6+2q

12/q=q

q^2=12

q=3.4641

Minimum ATC=(12/q)+6+q=(12/3.4641)+6+3.4641=$12.9282

Long run price=Minimum ATC=$12.9282

Qd=18000-500p=18000-12.9282*500=11535.90

Number of firms in long run=Qd/q=11535.90/3.4641=3330.13 or say 3330