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Analyzing monopolist's cost and demand functions

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:

(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 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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