Answer to Question #280956 in Microeconomics for abeni

Question

A monopolist’s demand and Average total has cost functions are given by

Q=250-5P

ATC =10 +40/Q

A. What will be the profit maximizing level of price and output?

B. What will be the firm’s total profit if it exercises first degree price discrimination?

C. Assume the monopoly can sell his product in two separated markets with

the following demand functions

Q1 =110-P1

Q2=140-4P2

A. Determine the profit maximizing level output in each market

B. What price should the monopoly sell each unit of output in each market?

C. In which market is the price high? Why?

Answer 1

A)

TC= ACT*Q

=(10+40/Q)Q

=10Q+40

Q=250-5P

5P=250-Q

P=50-0.2Q

TR= P*Q

=(50-0.2Q)Q

=50-0.2Q²

MR= 50-0.4Q

MC=10

For profit maximization,

MR=MC

50-0.4Q=10

0.4Q=40

Q= 100

p=50-0.2(100)

= 30

B) Firms total profit

$\Pi$ =TR-TC

TR=50(100)-0.2(100²)

=3000

TC=10(100)+40

=1040

$\Pi$=3000-1040

=1960

C)( a) profit Maximizing in each market

Q₁=110-P₁

P₁=110-Q₁

Q₂=140-4P₂

4P₂=140-Q₂

P₂=35-0.25Q₂

For profit Maximization in each marlket,

MR₁₌MC

MR₂=MC

TR₁=P₁Q₁

=(110-Q₁)Q₁₌110Q1-Q₁²

110Q₁-Q₁²

MR₁=110-2Q₁

110-2Q₁=10

2Q₁=100

Q₁=50

MR₂=MC

TR₂=P₁Q₁

=(35-0.25Q₂)Q₂

=35Q₂-0.25Q₂²

MR₂₌35-0.5Q₂

35-0.5Q₂=10

0.5Q₂=25

Q₂=50

B) What price the monopoly should charge in each market

P₁=110-Q₁

=110-50= 60

P₂= 35-0.25Q₂

=35-0.25(50)

= 22.5

C) The price is higher in market 1 because it is price inelastic