Question

A monopoly serves two markets with demand functions of Q1(p) = X-2p and Q2(p) = 10X...

A monopoly serves two markets with demand functions of Q1(p) = X-2p

and Q2(p) = 10X + 50 - 2p, where X is 5. Determine the optimal

two-part tariff for each market if the marginal costs are 10?

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Homework Answers

Answer #1

Optimal two part tariff for each market--------

Market(1)=$6.25

Market (2)=$30

Explanation-------

The optimal( profit maximising )point for a monopolist occurs where MR=MC

FINDING TARIFF FOR MARKET 1------

- finding MR------

Q1(p)=X-2p

As X=5----

Q=5-2p

2p=5-Q

P=2.5-.5Q1

TR=PQ=2.5Q-.5Q2

MR= derivative of TR----

MR= 2.5-Q1

At equilibrium-----

2.5-Q1=10( where MC=$10)

Q1=$_7.5

Putting this value in demand equation-----

P=2.5-1/2(-7.5)=$6.25

FINDING TARIFF FOR MARKET 2-----

Q2(p)=10x+50-2p

50+50-2p(as X=50)

Q=100-2p

P=50-.5Q

TR=50Q-.5Q2

MR=50-Q

At EQUILIBRIUM------

50-Q=10

Q2=40

Putting this value in demand equation--------

P=50-1/2(40)

P=$30

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