Question

Short-run Equilibrium: Bumper sticker firms produce bumper stickers in a perfectly competitive market. Each identical firm has a short-run total cost function equal to: STC (Q) = 3 + 2q + 2Q2. Suppose that there are 100 firms, and the market demand is D(P) = 100 - 5P where D(P) is the quantity consumed in the market when the market price is P. 1. What is the short-run equilibrium price? 2. How much does each firm produce? 3. Are they making profits, losses, or zero economic profit? (Show the comparison you made to get your answer).

Answer 1

1)

STC(Q)=3+2Q+2Q^2

Marginal Cost=SMC=dSTC/dQ=2+4Q

Set MC=P for profit maximization

2+4Q=P

Q=-0.5+0.25P

There are 100 similar firms. So, Market supply is given by

S(P)=100*Q=100*(-0.5+0.25Q)=-50+25P

Set S(P)=D(P) for market equilibrium

-50+25P=100-5P

30P=150

P=$5 (Short run equilibrium price)

2.

Each firm will produce such that MC=P

2+4Q=5

4Q=3

Q=0.75 (Optimal output of a firm)

3.

Total Revenue of firm=TR=P*Q=5*0.75=$3.75

Total Cost=TC=3+2Q+2Q^2=3+2*0.75+2*0.75^2=$5.625

Total variable cost=TVC=2Q+2Q^2=2*0.75+2*0.75^2=$2.625

AVC=TVC/Q=2.625/0.75=$3.50

ATC=TC/Q=5.625/0.75=$7.50

We can observe that P<ATC. So, the firm will make a loss in the short run.

We can also see that P>AVC. So, the firm will continue to produce in the short run.