Daniel Dynamite runs a high end car wash called “Daniel’s Car Wash” … he’s not v

Question

Daniel Dynamite runs a high end car wash called “Daniel’s Car Wash” … he’s not very creative. The car wash market is very competitive and Daniel has no control over the prices that he can charge. Concerned that he is leaving money on the table, Daniel hired an economist to help him maximize profits. The economist, Elana Marketa, estimated that Danial’s total cost of production could be modeled by the total cost function TC=6+3Q+Q2 and that his marginal costs could be described as MC=3+2Q, where Q is the number of cars washed.

Find the equations that describe Daniel’s:

- Average Total Cost (ATC).

- Average Variable Cost (AVC).

-If the market price of a car wash is $15, what is the profit maximizing number of cars that Daniel should be washing each day?

-How much profit can Daniel make if he maximizes profit?

Explanation / Answer

1. ATC= TC/Q

= (6+3Q+Q2)/Q

= 6/Q+3+Q

2. AVC = TVC/Q

= (3Q+Q2)/Q

= 3+Q

3. If market price is $15, then Total revenue will be

TR = P*Q = 15Q

Then, Marginal Revenue(MR) = 15

Therefore, profit will be maximum when MR=MC

3+2Q = 15

2Q = 15-3 = 12

So, Q =12/2 = 6 units

Therefore, 6 is the profit maximizing number of cars that Daniel should be washing each day.

4. So, profit = TR-TC

if we will put the values of P and Q in TR & TC function, we will get the following

= (15*6) - ( 6 + 3*6 + 62 )

= 90 - 60

= $30

So, Daniel can make a profit of $ 30.

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.