Answer to Question #284462 in Microeconomics for beki

Question

Given the following demand function and total cost function as:

Q = 250-5P and TC = 0.5Q² + 5Q + 125 

Calculate the equilibrium price, Equilibrium Quantity and the total profit

A.        under perfectly competitive market structure.

B.         Under monopolistic competitive market. 

Answer 1

A. P=MC

$MC=TC' =( 0.5Q2 + 5Q + 125 )'=Q+5$

$P=\frac{250-Q}{5}$

$\frac{250-Q}{5}=Q+5$

250-Q=5Q+25

225=6Q

Q=37.5

$P=\frac{250-37.5}{5}=42.5$

$Profit=TR-TC=PQ-(0.5Q2 + 5Q + 125)=37.5\times42.5-(0.5(37.5)^2+5\times37.5+125)=578.125$

B.

MR=MC

MR-MC=0

MC=Q+5

$TR=\frac{250-Q}{5}\times Q=\frac{250Q-Q^2}{5}=$

$MR=TR'=(\frac{250Q-Q^2}{5})'=50-\frac{2Q}{5}$

$50-\frac{2Q}{5}=Q+5$

$45=Q+\frac{2Q}{5}$

225=5Q+2Q

225=7Q

Q=32.14

$P=\frac{250-Q}{5}=\frac{250-32.14}{5}=43.572$

$Profit=TR-TC=PQ-(0.5Q2 + 5Q + 125)=32.14\times43.572-(0.5(32.14)^2+5\times32.14+125)=598.2143$