Answer to Question #284465 in Economics of Enterprise for beki

Question

Given the demand function for the two markets and total cost function that:

Q₁ = 55 – P₁; Q₂ = 70 – 2P₂ and TC=5Q + 20 where Q = Q₁ + Q₂

A.   Calculate the equilibrium price, equilibrium quantity in each market with price discrimination.

B.    Calculate the maximum profit using equilibrium price and quantity with price discrimination.

C.    Calculate the price elasticity of demand in each market using MR=P(1+1/Ɛ_p).

D.   Calculate the equilibrium price and quantity without price discrimination.

E.    Calculate the maximum profit without price discrimination.

F.     Is the Monopolist better off with or without price discrimination.

Answer 1

A. MR1=MR2=MC

MC=TC'

$MC'=TC'=(5Q + 20)'=5$

$TR1=(55-Q1)Q1=55Q1-Q1^2$

MR1=TR1'=55-2Q1

55-2Q1=5

Q1=25

P1=25

$P2=\frac{70-Q2}{2}$

$TR2=\frac{70-Q2}{2}\times Q2=\frac{70Q2-Q2^2}{2}$

MR2=TR2'=35-Q2

35-Q2=5

Q2=30

$P2=\frac{70-30}{2}=20$

B.

$Profit1=TR-TC=25\times25-(5\times25+20)=480$

$Profit1=TR-TC=30\times20-(5\times30+20)=430$

C.$MR=P(1+\frac{1}{Ɛp})$

Let's Ep1=2, Ep2=4

$MR1=25(1+\frac{1}{2})=37.5$

$MR2=20(1+\frac{1}{4})=25$

D.

Q=125-3P

MC=5

MR=MC

$TR=\frac{125-Q}{3}\times Q=\frac{125Q-Q^2}{3}$

$MR=TR'=\frac{125-2Q}{3}$

$\frac{125-2Q}{3}=5$

125-2Q=15

110=2Q

Q=55

$P=\frac{125-55}{3}=23.33$

E.

$Profit=TR-TC=55\times23.33-(5\times55+20)=988.15$

F. The Monopolist is better without price discrimination.