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Analyzing monopolist's cost and demand functions

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A monopolist produces a single homogeneous good, which she sells in two distinct markets
between which price discrimination is possible. Her total cost function is:
TC = 1/3 Q3 - 7.5Q2 + 370Q + 100
The demand curves in the two markets are given by:
q1 = 80 - 0.2p1 and q2= Ap2-5
The monopolist achieves a profit-maximizing equilibrium at which her total output (Q = q1 + q2) is 10 and she charges a price of $360 in market 1.

(a)What is the profit-maximizing output in markets 1 and 2?
(b)Calculate marginal revenue in either market.
(c)What is the cost of producing an extra unit at the profit maximizing output?
(d)What price is charged in market 2?

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Solution Summary

Solution describes the steps for finding monopolist's profit maximizing output in two different markets where price discrimination is possible. It also calculate marginal revenue in either market.

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Solution:

(a) What is the profit-maximizing output in markets 1 and 2?
We are given that profit maximizing total output is 10
q1+q2=10
i.e. q2=10-q1 -----------------(1)
p1=360

demand in market 1 is given by
q1=80-0.2p1
demand at ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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