Question

A firm is operating in the perfectly competitive market for gummy bears. It faces the following conditions:

TC(q)=4+ (q²/16 )

MC(q)=q/8

Market Demand: D(P)=1008-200P

Please answer the following questions.

Suppose market price is currently at $2.

a) What is the profit maximizing quantity for the firm to produce at?

b) What is the profit for the firm at the profit maximizing quantity?

c) If all firms are identical to this firm, how many firms must there be in the market?

Consider the long run in this market. Continue to assume all firms are identical.

d) What is the long run price for this market? How much do individual firms produce?

e) How many firms do we expect in the long run?

Answer 1

A) A profit maximizing perfectly competitive firm produces at the point where Market price = MC.

Therefore, setting (q/8) = 2

Or, q = 16

It means profit maximizing quantity is 16 units.

B) When q = 16, TC = 4 +[ (16)² /16] = $20

And Total revenue = price * quantitity = $(2 * 16) = $32

Profit = TR - TC = $(32 - 20) = $12

C) At price = $2, from the market demand equation we get, Market quantitity = 1008 - (200*2) = 608.

Therefore, there should be (608/16) = 38 firms in the market.

D) in long run, market price should be equal to the minimum ATC so that each firm in the market earns zero economic profit in the long run.

ATC = TC/q = (4/q) + (q/16)

When ATC is minimized, then d(ATC)/dq = 0

Or, -(4/q^{​​​​​​2}​​​​​) + (1/16) = 0

Or, 4/q² = (1/16)

Or, q² = 64

Or, q = 8

At q = 8, ATC = (4/8) + (8/16) = $1

Therefore LR price in this market should be $1 and each firm will produce 8 units.

E) At long run price, Market demand = 1008 - 200 = 808. Therefore, there should be (808/8) = 101 firms in the market.