# maximum profits

A monopolist with two plants operates with a marginal revenue of 500-4Q and marginal costs of 4Q for plant 1 and 2Q for plant 2.

What are outputs at each plant to maximize profits?

What price maximizes profits?

What are maximum profits?

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#### Solution Preview

part a)

Let plant 1 produces q1 and plant 2 produces q2

Q=q1+q2

For profit maximization MC=MR or MR=MC1=MC2

MR=500-4Q=500-4q1-4q2

MC1=4q1

Equating MR=MC1, we get 500-4q1-4q2=4q1 or we can say 2q1+q2=125 eq--1

MC2=2q2

Equating MR=MC2, we get 500-4q1-4q2=2q2 or we can say ...

#### Solution Summary

This solution determines maximum profits.

$2.19