Question

In a certain large city, hot dog vendors are perfectly competitive, and face a market price of \(\$ 1.00\) per hot dog. Each hot dog vendor has the following total cost schedule: $$\begin{array}{cc} \begin{array}{c} \text { Number of Hot } \\ \text { Dogs per Day } \end{array} & \text { Total cost } \\ \hline 0 & \$ 63 \\ 25 & 73 \\ 50 & 78 \\ 75 & 88 \\ 100 & 103 \\ 125 & 125 \\ 150 & 153 \\ 175 & 188 \\ 200 & 233 \end{array}$$ a. Add a marginal cost column to the right of the total cost column. (Hint: Don't forget to divide by the change in quantity when calculating \(M C .)\) b. What is the profit-maximizing quantity of hot dogs for the typical vendor, and what profit (loss) will he earn (suffer)? Give your answer to the nearest 25 hot dogs. One day, Zeke, a typical vendor, figures out that if he were the only seller in town, he would no longer have to sell his hot dogs at the market price of \(\$ 1.00\). Instead, he'd face the following demand schedule: $$\begin{array}{cc} \text { Price per Hot Dog } & \begin{array}{c} \text { Number of Hot } \\ \text { Dogs per Day } \end{array} \\ \hline>\$ 6.00 & 0 \\ 6.00 & 25 \\ 5.00 & 50 \\ 4.00 & 75 \\ 3.25 & 100 \\ 2.75 & 125 \\ 2.25 & 150 \\ 1.75 & 175 \\ 1.25 & 200 \end{array}$$ c. Add total revenue and marginal revenue columns to the table above. (Hint: Once again, don't forget to divide by the change in quantity when calculating MR.) d. As a monopolist with the cost schedule given in the first table, how many hot dogs would Zeke choose to sell each day? What price would he charge? e. A lobbyist has approached Zeke, proposing to form a new organization called "Citizens to Eliminate Chaos in Hot Dog Sales." The organization will lobby the city council to grant Zeke the only hot dog license in town, and it is guaranteed to succeed. The only problem is, the lobbyist is asking for a payment that amounts to \(\$ 200\) per business day as long as Zeke stays in business. On purely economic grounds, should Zeke go for it? (Hint: If you're stumped, re-read the section on rent-seeking activity.)

Short answer

The profit-maximizing amount for a typical vendor in competitive market is 75 hot dogs, with a profit of -\$13. If Zeke were a monopolist, he would sell 125 hot dogs at a price of \$2.75 per hot dog. And on purely economic grounds, whether Zeke should enter the monopolistic market depends on whether his profit as a monopolist (minus lobbying cost \$200) surpasses his current profit as a competitive vendor.

Step-by-step solution

Calculate the Marginal Cost

Marginal Cost is the extra cost of producing one more unit of a product. For this, we will have to find the difference between the total cost of current and previous quantities, which is then divided by the change in quantity. Remember to treat the product quantity at 0 as \(\$63\) divided by 25, resulting in MC=\(\$2.52\).

Determine the Profit-Maximizing Quantity

The profit maximizing quantity happens where price equals marginal cost (P=MC). Looking at our marginal cost calculations, the price for a hot dog (given as \$1) is closer to the marginal cost after producing 75 (\(\$1.33\)) and 100 hotdogs (\(\$1.5\)). In terms of quantity, the nearest 25 hotdogs refer to 75 hot dogs as the profit-maximizing quantity.

Calculate the Vendor's Profit

We calculate profit using the equation Profit = Total Revenue - Total Cost. In this case, Total Revenue is calculated by multiplying the quantity (75 hotdogs) by the price (\(\$1.00\)). Subtract the total cost (\(\$88\)) from the total revenue (\(\$75\)) to get the profit. If the result is a negative number, then there is a loss.

Calculate Total Revenue and Marginal Revenue

For the monopolist situation, total revenue (TR) is calculated by multiplying the price per hot dog by the quantity. Marginal Revenue (MR) is the additional revenue that is generated by increasing product sales by one unit. Once again, remember to treat the product quantity at 0 as the first price, \$6, divided by 25, resulting on the first MR=\(\$0.24\).

Determine Quantity as a Monopolist

As a monopolist, Zeke would choose to sell where Marginal Cost is equal to Marginal Revenue (MR = MC), which is the rule of profit maximization for monopolists. In this instance, MR = MC at 125 hot dogs.

Determine Price as a Monopolist

Using the demand table, we can find the price that Zeke would choose to charge per hot dog. He would charge the price corresponding to the quantity of 125 hotdogs, which yields a price of \(\$2.75\).

Analyzing the Economic Decision

Lastly, we must calculate if Zeke would profit from this rent-seeking activity. This is done by subtracting the daily lobbyist payment (\(\$200\)) from Zeke's daily profit as a monopolist, and comparing it to his current profit as a competitive vendor. If he would earn more as a monopolist, even after the lobbyist payment, he should go for it. If not, then he should remain under perfect competition.