Question

Your family recently began operating a car wash at a beach resort. There are many other car washes at this beach resort. You have observed that the customers care only about finding the cheapest price for car washes; they do not care which company they use. In other words, the market for car wash is perfectly competitive.

Your family took out a small business loan. The cost of the loan comes to $15 per day for the next 3 years. The business must hire labor and purchase cleaning solutions, car wax, etc. to operate the car wash. After some research, you have figured out that the cost for labor and supplies is as follows:

Number of car washes sold per day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Daily cost for labor and supplies (variable cost) $10.67 $12.67 $16.00 $20.67 $26.67 $34.00 $42.67 $52.67 $64.00 $76.67 $90.67 $106.00 $122.67 $140.67 $160.00 $180.67 $202.67 $226.00 $250.67 $276.67

When the beach resort is in-season, you have observed that you can charge a price of $14.00 per car wash. When the resort is off-season, the demand for car washes is much lower. You are only able to charge a price of $4.67 per car wash. Right now, the resort is in-season. Currently, you are selling 17 car washes per day.

Your family wants your advice.

a) To maximize profit, should they keep selling 17 car washes per day in-season? Use your knowledge of the golden rule of profit maximization to form a cohesive argument. Do not forget to include the fixed cost while you calculate the total cost/average total cost for this business. Show your work.

Answer 1

To maximize profits in a perfectly competitive market, your family should equate marginal revenue with marginal cost. Without specific cost data, exact profit-maximizing quantity cannot be determined, but adjustments should be made based on marginal costs in relation to market price.

Step-by-step explanation:

To determine if your family should keep selling 17 car washes per day to maximize profit in a perfectly competitive market, we need to apply the golden rule of profit maximization. This rule states that to maximize profit, a firm should produce at the quantity where marginal revenue (MR) equals marginal cost (MC).

Since it is given that customers are only looking for the cheapest price, we can assume the price is equal to marginal revenue. Without specific cost information for the car wash, we cannot calculate the exact profit-maximizing quantity. However, if the marginal cost of washing an additional car is less than the price, it would make sense to wash more cars. Conversely, if the marginal cost of additional car washes exceeds the market price, washing less would be the profit-maximizing choice.

You must also consider fixed costs in your calculation of total costs. Even though fixed costs do not change with the quantity produced, they still affect the average total cost (ATC). If the price covers the ATC, then your family's business is making a profit. To maximize profit, you should continue to adjust the number of car washes provided until MC just equals MR.