Answer to Question #284322 in Economics 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. The equilibrium price, equilibrium quantity in each market with price discrimination are:

MC = 5,

MR1 = TR1'(Q1) = 55 - 2Q1,

MR1 = MC,

55 - 2Q1 = 5,

Q1 = 25 units,

P1 = 55 - 25 = 30.

MR2 = TR2'(Q2) = 35 - Q2,

MR2 = MC,

35 - Q2 = 5,

Q2 = 30 units,

P2 = 35 - 0.5×30 = 20.

B. The maximum profit using equilibrium price and quantity with price discrimination is:

TP = (30×25 + 20×30) - (5×(25 + 30) + 20) = 1055.

C. The price elasticity of demand in each market using MR = P(1+1/Ɛp) or Ep = 1/(MR/P - 1) is:

Ep1 = 1/(5/30 - 1) = -1.2, so the demand is elastic;

Ep2 = 1/(5/20 - 1) = -1.33, so the demand is elastic.

D. The equilibrium price will be higher and quantity will be lower without price discrimination.

E. The maximum profit without price discrimination will be lower.

F. The Monopolist is better off with price discrimination.