Consider a city that has a number of hot dog stands operating throughout the downtown area. Suppose that each vendor has a marginal cost of $1.50 per hot dog sold and no fixed cost. Suppose the maximum number of hot dogs that any one vendor can sell is 100 per day.(a) If the price of a hot dog is $2, how many hot dogs does each vendor want to sell?(b) If the industry is perfectly competitive, will the price remain at $2 for a hot dog in the long run? If not, what will the price be?(c) At the price in part (b), if each vendor sells exactly 100 hot dogs a day and the demand for hot dogs from vendors in the city is Q = 4400 – 1200P, how many vendors are there?(d) Suppose the city decides to regulate hot dog vendors by issuing permits. If the city issues only 20 permits and if each vendor continues to sell 100 hot dogs a day, what price will a hot dog sell for?(e) Suppose the city decides to sell the permits. What is the highest price that a vendor would pay for a permit?

(a) Since the marginal cost is constant at $1.50 and not increasing, the amount of hot dogs suppliers would want to supply is infinite as $1.50 will always be less than $2 and the more they supply, the more they earn.

(b) No, it would not remain at $2 for a long time. In a perfectly competitive industry, firms can easily enter or leave the industry, therefore, any supernormal profits will attract new firms to enter the industry and increase the overall supply of hot dogs, bringing the price back down to $1.50, where P = MC.

(c) When P = 1.50, Quantity demanded = 4400 - 1200(1.50) = 2600.

Number of firms = 2600/100 = 26 firms.

(d) Quantity supplied = 20(100) = 2000

When demand = supply, 2000 = 4400 - 1200P

P = 2

(e) Supernormal profits per day = (2-1.50)(100) = $50

Therefore, firms will pay a maximum of $50 a day, which is equals to the amount of supernormal profits earned.