# Determination of optimal price and output for two firms

Two firms face a demand equation given by P=200,000 -6(Q1 + Q2) where Q1 and Q2 are the outputs of the two firms. The total cost equations for the two firms are given by: TC1 = 8000Q1 and TC2 = 8000Q2.

If each firm sets its own output rate for profit maximization, and the other firm holds constant, what is the optimal output of each firm, as well as the optimal price for each firm.

Please show the work and/or formulas to derive the solution.

© BrainMass Inc. brainmass.com October 9, 2019, 10:13 pm ad1c9bdddfhttps://brainmass.com/economics/output-and-costs/determination-optimal-price-output-two-firms-212442

#### Solution Preview

Solution is also attatched in MS word file.

Solution:

Q1= output of one firm

Q2 = output of other firm

Total Revenue of one firm = P*Q1

= {200,000-6(Q1+Q2)}*Q1

= 200000Q1-6Q1^2-6Q1Q2

Profit for firm 1 (Pi-1) = Total Revenue - ...

#### Solution Summary

The solution describes the steps for determining optimal output and price for given two firms.