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 is \(Q=4400-1200 P\), 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

a. Each vendor wants to sell 100 hot dogs. b. The price will decrease to $1.50 in a perfectly competitive market. c. The number of vendors is 26. d. The price will rise to $2 per hot dog under a permit system. e. The highest price a vendor would pay for a permit is $50.

Step-by-step solution

Determine the number of hotdogs sold at $2

With a marginal cost of $1.50 per hot dog and a selling price of $2, each vendor gets a profit of $0.50 per hot dog. Because the maximum number of hot dogs that any one vendor can sell is 100 per day, each vendor would want to sell the maximum number to maximize their profits.

Determine if the price of hotdogs would remain at $2 in a perfectly competitive market

In a perfectly competitive market, the price is determined by the intersection of supply and demand. In the long run, firms in a perfectly competitive market make zero economic profit. Thus, the price would have to equal marginal cost. In this case, the price would decrease to $1.50 per hot dog as the vendors would still be able to cover the cost of making a hot dog.

Determine the total number of vendors

The demand for hot dogs from vendors in the city is given by the function \(Q=4400-1200 P\). If each vendor sells 100 hot dogs at a price of $1.50, substituting this price into the demand function, we get \(Q = 4400 - 1200*1.5 = 2600\). Therefore, the number of vendors would be the total quantity divided by the quantity each vendor sells, i.e., \(2600/100 = 26\) vendors.

Determine the new price of hotdogs with 20 permit system

If the city issues 20 permits, then only 20 vendors are allowed to sell hot dogs, with each of them selling 100 hotdogs a day. This means that the total quantity of hot dogs sold in the city decreases to 2000. Re-arrange the demand function to find the new price: \(P = (4400 - Q)/1200\). Substitute Q=2000 to find the new price; \(P = (4400 - 2000)/1200 = \$2\). So, the new price will rise to $2 per hot dog.

Calculate the maximum price a vendor would pay for permit

The permit allows a vendor to sell hot dogs and generate extra profit. The maximum price a vendor would be willing to pay for the permit is the extra profit they make from having a permit. This is found by taking the difference in profits between the quantity sold (100 hot dogs) at the new price ($2) and the old price ($1.50). The extra profit is calculated as: profit = (new price- marginal cost)*quantity = (2 - 1.5) * 100 = $50. A vendor would not pay more than $50 for the permit.

Key concepts

Marginal Cost

Marginal cost is a crucial concept in the study of economics. It refers to the additional cost incurred by producing or selling one more unit of a product. In the context of our exercise, each hot dog vendor has a marginal cost of $1.50 per hot dog. This means every extra hot dog sold costs $1.50 to produce. Understanding marginal cost helps businesses determine the optimal level of production.
If the price at which a product is sold is higher than the marginal cost, producers make a profit on each unit sold. Conversely, if the price equals the marginal cost, businesses cover their costs exactly but earn no profit. In our hot dog example, each vendor initially sells at $2 per hot dog, making $0.50 profit per dog at first. However, in a perfectly competitive market, the tendency is for prices to adjust to match marginal costs, leading to zero economic profit in the long run.

Supply and Demand

Supply and demand are fundamental principles of economics that determine the market price of goods. Demand reflects how much consumers want to buy at various prices, while supply indicates how much producers are willing to sell. Together, these forces establish the market equilibrium, where the quantity supplied equals the quantity demanded.
In our hot dog stand scenario, the demand is modeled by the equation \(Q = 4400 - 1200P\), where \(Q\) is the quantity demanded and \(P\) the price per hot dog. When vendors sell 100 hot dogs each at a price matching the marginal cost ($1.50), the total demand calculates to 2600 hot dogs. Given 26 vendors sell 100 hot dogs each, the market stays balanced. This equation shows how any increase in price will reduce demand, pushing prices down again in the long run.

Economic Profit

Economic profit is the difference between total revenue and total costs, including both explicit and implicit costs. In a perfectly competitive market, firms tend to make zero economic profit in the long run. This situation arises as new firms enter the market when profits are high, increasing supply until prices fall to equal marginal costs.
For our hot dog vendors, economic profit initially exists when they sell at $2, as they make $0.50 per hot dog. But because the market is perfectly competitive, the price tends to drop to the marginal cost of $1.50 over time. This adjustment results in no economic profit, leaving vendors just covering costs but still motivated to stay in business.

Market Regulation

Market regulation often involves government-imposed controls that can influence supply and demand. In our hot dog example, the city introducing a permit system is a form of regulation. This limits competition by controlling the number of vendors allowed to sell hot dogs.
When the city issues only 20 permits, supply decreases to 2000 hot dogs, raising the price back up to $2. This regulated market reshapes the dynamics seen in a perfectly competitive marketplace. Despite rising costs ($2 per dog), the restriction on new entrants keeps the price elevated, allowing those with a permit to generate a profit.

• Regulation can help achieve specific policy objectives, like reducing congestion.
• It can affect market competition, sometimes leading to higher consumer prices.
• Understanding regulation's impacts helps businesses strategize within new frameworks.