Answer to Question #272094 in Microeconomics for Michael

Question #272094

Assume a firm is a small business and act as a price-taker in the market, the market price of the firm’s product is 20. The firm’s cost function is:

C(q) = 0.5q2+5q+100.

1. What is the firm’s optimal output level?

2. What’s the firm’s highest profit?


1
Expert's answer
2021-11-29T19:25:45-0500

1. Optimal output level

Firm’s cost function is:

"C(q) = 0.5q^2+5q+100"

Under perfect competition, a firm is a price taker of its good since none of the firms can individually influence the price of the good.

To calculate the optimal level of output at which its;

Marginal Cost (MC) = Market Price (P)

"MC=\\frac{d(TC)}{dQ}"


"MC=\\frac{d(0.5q^2+5q+100)}{dQ}=q+5"

"MC=P"

"q+5=20"

"q=15"


2. Firm's profit

"Profit = Revenue - TC"

"Revenue =PQ=20\\times15=300"

"TC=0.5\\times(15)^2 +(5\\times15)+100=287.5"

"Profit = 300-287.5=12.5"



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS