Question

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? If not, what will the price be?

c. If each vendor sells exactly 100 hot dogs a day and the demand for hot dogs from vendors in the city isQ= 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?

Short answer

1. Each vendor will want to sell 100 hot dogs.

2. The price will not remain at $2. It will shift to a price level of $1.50

3. There are 26 vendors.

4. The new price would be $2 for each hot dog.

5. The highest price that a vendor would pay for the permit is $0.50.

Step-by-step solution

Determining the quantity of hot dogs which every vendor wants to sell

The marginal cost on each hot dog is $1.50, and there is no fixed cost. The total cost of production of one hot dog will be $1.50. The price is $2. The vendors are earning a profit of $0.50 on each unit sold. Since the profit on each unit sold is constant, their profit increases with each unit sold.

Thus, they will try to sell as many hot dogs as possible in the market. But the maximum they can sell is 100 hot dogs, so each vendor will try to sell 100 units of hot dogs.

Change in price level and its determination

The vendors can earn positive profits on each unit sold. This will invite other vendors to enter the hot dog business. Their entry will increase the supplied quantity of hot dogs, which will decrease the price in the market.

The firms will continue to enter, and the price will fall until it reaches a price where the economic profit is zero.Because of zero economic profit, no new firm will enter the market, and the existing firm will not leave it because there is no incentive to enter or exit the market.

The new price level will be the total cost of each unit of hot dogs sold. Since there is no fixed cost, the marginal cost would be the price level. Thus, the new price level would be $1.50.

Calculation of the number of vendors in the market

Suppose there are ‘n’ numbers of vendors selling hot dogs in the market. The demand function for hot dogs in the city isQ= 4400 – 1200P. Since each vendor sells exactly 100 units of hot dogs, the supply function for hot dogs in the market will be 100n.

The value of n is calculated by equating the demand with supply because the market is perfectively competitive.

Q_D = Q_S

4400 - 1200P = 100n

4400 - 1200 (1.50) = 100n

n = 26

There are 26 vendors in the market.

Calculating the new price of hotdogs after the implementation of the permit policy

The number of permits issued by the city is 20. It means that the number of vendors in the city allowed to sell hotdogs is 20. Since each vendor is selling 100 hotdogs, the supplied quantity of hotdogs is 2000.

The price at which the market demand is equal to the market supply is the equilibrium price.The equilibrium price is calculated below by equating demand with supply:

Q_D = 20 x 100

4400 - 1200P = 2000

1200P = 2400

P = $2

The equilibrium price after the implementation of the permit policy is $2.

Calculating the highest price that a vendor would pay for the permit

In the absence of a permit system, the lowest price the vendor is willing to sell each hot dog unit is $1.50. The permit increases the price of hot dogs to $2.Thus, the highest price a vendor would be willing to pay for the permit will be the difference between ‘price after permit system (P2)’ and ‘price in the absence of permit system (P1)’.

The highest price which a vendor would be willing to pay is calculated below:

Highest price offered by a vendor for permit = P2 - P1

=$2 - $1.50

=$0.50