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

To get Marginal cost function (MC), differentiate the above equation with respect to q

MC(q) = 1/4 + 1/4q

2. In a competitive market, price (P) is equal to MC. P = 4

4 = 1/4 + 1/4q

Hence, q = 15

3. At a firm level, the equilibrium is at the quantity at which P = MC

P = 1/4 + 1/4q

q = 4P - 1

Since, all firms are identical, Total industry quantity(Qs) is equal to 200q

200q = 800P - 200 { Multiplying the above equation by 200}

Qs = 800P - 200

The above equation is the industry supply equation.

4. Since, at equilibrium, market demand is equal to market supply

Qd = Qs

2500 - 100P = 800P - 200

P = 3

Hence, the market price is 3.