Question

Problem. Suppose that, in a large city, 200 identical street vendors compete
in a competitive market for hot dogs.
1. The vendors total costs to produce q hot dogs is, C(q) = 1/4q + 1/8q². What is
the marginal cost function of each firm?

2. Given your answer from above, how many hot dogs will each vendor produce
if offered a price of $4 per hot dog?

3. Using your answer from part 1 of this problem, what is the competitive
supply curve for this market? (That is, how much will a vendor produce if
the market price is P?)

4. Let market demand for hot dogs be Q = 2500−100P, where P is the market
price and Q is the market output. What is the short run equilibrium price?
What is the total quantity of hot dogs sold in equilibrium?

5. In the long run, would you expect this industry to experience entry or exit?
Explain your answer.

Answer 1

1)

C(q) = 1/4q + 1/8q²

Marginal cost=MC=dC(q)/dq=1/4 + 1/4q

2)

In perfect competition each firm sets its output level such that MC=Market price

So,

1/4 + 1/4q=4

1+q=16

q=16-1=15

Each vendor will produce 15 hotdogs at a market price of $4 per hotdog

3)

We know that each firm sets its output level such that MC=Market price in short run. So,

MC=1/4 + 1/4q

Set MC=P

P=1/4+ 1/4q

4P=1+q

q=-1+4P

There are 200 identical vendors. So,

Market supply, Qs=200*q=200*(-1+4P)=-200+800P

Qs=-200+800P

4)

In equilibrium, Qd=Qs

2500-100P=-200+800P

2700=900P

P=3

Equilibrium price=$3 per hotdog

Qs=-200+800*3=2200

Qd=2500-100*3=2200

Equilibrium quantity=2200 hotdogs

5) Output of each vendor=q=Equilibrium quantity/200=2200/200=11

Total revenue of each vendor=TR=P*q=3*11=33

Total cost of each vendor=TC=C(q) = 1/4q + 1/8q² =(1/4)*11+(1/8)*11²=17.875

Profit=TR-TC=33-17.875=$15.125

Each vendor is making economic profit. So, more vendors will be attracted in long run. This will increase the supply. In long run, vendors will work at minimum ATC and economic profit will be zero.