Hi, if anyone can explain the parts of this to me that would be great. If you do

Question

Hi, if anyone can explain the parts of this to me that would be great. If you don't have that kind of time, i may be able to grasp some of it from the answers. Thanks.

Daniel Dynamite runs a high end car wash called "Daniel's Car Wash". The car wash market is very table, Daniel hired an e 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. a. Find the equations that describe Daniels: i. Average Total Cost (ATC) AVC . Average Variable Cost (AVc). If the market price of a car wash is $15, what is the profit maximizing number of that Daniel should be washingeach day? b. cars c. How much profit can Daniel make if he maximizes profit?

Explanation / Answer

Don't worry, I'll explain all answers.

TC = 6 + 3Q + Q2

MC = dTC / dQ = 3 + 2Q

The TC has 2 parts: Fixed and Variable cost. The Fixed cost (FC) does not vary with output and so, is the part of TC independent of Q (FC = 6). Variable cost (VC) is that component which varies with output, and so, VC = 3Q + Q2 .

(a)

(i) ATC = TC / Q = (6 / Q) + 3 + Q

(ii) AVC = VC / Q = 3 + Q

(b)

In a competitive industry, an individual firm is a price taker who maximizes profits by equating Price with MC.

P = 15 = 3 + 2Q*

2Q* = 15 - 3 = 12

Q* = 12 / 2 = 6

(c)

Profit = Q* x (P - ATC)

When Q* = 6, ATC = (6 / Q) + 3 + Q = (6 / 6) + 3 + 6 = 1 + 3 + 6 = 10

So,

Profit = 6 x $(15 - 10) = 6 x $5 = $30

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