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# Determining Profit Maximizing Price and Output Level

In a pure monopoly the company faces an inverse demand (price) for their product.

p = 20-0.04q1

marginal revenue is r= 20- 0.08q1

and marginal cost is mc1= 0.1+ 0.5q1

total costs is TC1= 5 + 0.1q + 0.25q1(squared)

what is profit maximising level for
a) price
b) quantity
c) monopoly profit

If the company wants to produce some of the same product offshore with cheaper labour costs how much production should be undertaken in each factory to maximise total firm profit. Assume transport costs are the same.

and for another factory is m2= 0.1 + 0.3q2

Total costs for another factory are TC1=2 + 0.1q2 + 0.15q2(squared)

#### Solution Preview

Part 1

P = 20-0.04q1
Marginal revenue is MR1= 20- 0.08q1

and Marginal cost is MC1= 0.1+ 0.5q1

Total costs is TC1= 5 + 0.1q + 0.25q1^2

A monopolist sets its output such that MR=MC to maximize its profit.
Put MC=MR
0.1+0.5q1=20-0.08q1
0.5q1+0.08q1=20-0.1
0.58q1=19.9
q1=19.9/0.58 =34.31 units

Price P=20-0.04*34.31=18.63

TC1=5+0.1*34.31+0.25*34.31^2=302.725
TR=P*q1=18.63*34.31=639.1953
Profit=TR-TC1=639.1953-302.725=336.4703

Part 2

If the company wants to produce some of the same product ...

#### Solution Summary

Solution describes the steps to determine profit maximizing level of price, quantity and profit for a monopolist. It also calculates the profit maximizing level of price, quantity and profit if monopolist produces in two factories.

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