Your family operates a car wash. There are many other car washes around. You have observed that the customers care only about finding the cheapest price for car washes; they do not care which company they use. To purchased the equipment and the building for the car wash, your have to take out a small business loan. The cost of the loan comes to $10 per day for the next 40 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 VC(Q)=Q2, where Q is the number of car wash.

You have observed that you can charge a price of $10.00 per car wash. How many car wash should you sell to maximize the profit?

Hint1: How did you derive the supply curve of a perfectly competitive firm?

Hint2: If your total cost is TC(Q)=A+BQ+CQ2, where A,B,and C are constant, the marginal cost at Q is MC(Q)=B+2CQ. You should remember this formula. It sure will be on the exam.(Example: If TC(Q)=2+3Q+5Q2, then MC(Q)=3+10Q.)

You have observed that you can charge a price of $6.00 per car wash. How many car wash should you sell to maximize the profit?

You have observed that you can charge a price of $2.00 per car wash. How many car wash should you sell to maximize the profit?

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