# 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?

https://brainmass.com/economics/pricing-output-decisions/analyzing-monopolist-s-cost-and-demand-functions-215507

#### Solution Preview

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.