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 MC of single firm=.07+.18q

2.At equilibrium P=MC

4=.07+.18q

q=21.84

3.When Price=P

P=.07+.18q

This is the supply curve of each vendor because in a competitive market price is equal to marginal cost.

4.Q=2500-10P

P=250-(1/10)Q

At equilibrium:P=MC

250-(1/10)Q=14+36Q

Here we are taking market supply because the market equilibrium has to found out.

236=(361/10)Q

Q=6.54

P=250-(1/10)*6.54

P=249.364

TR=P*Q

TR=249.364*6.54=1630.84

TC=14(6.54)+18(6.54)^2

TC=861.45

Since TR>TC the firm is making profits.Thus attracted by positive profits new firm will enter the market in the long run.