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Calculating optimal output and profit levels

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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

(A) If each of the firms sets its own output rate to maximize its profits, assuming that the other firm holds its rate of output constant, solve for the optimal output of each firm (q1* and q2*), the optimal price (P*), and the profit of each firm.

(B) If the firms collude, what will be the monopoly price (optimal price P*), total output of the two firms (Q= q1 + q2), and the total profits of the two firms?

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Solution Preview

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

(A) If each of the firms sets its own output rate to maximize its profits, assuming that the other firm holds its rate of output constant, solve for the optimal output of each firm (q1* and q2*), the optimal price (P*), and the profit of each firm.

Let
q1= output of one firm
q2 = output of other firm

Total Revenue of one firm = P*q1
= {200,000-6(q1+q2)}*q1
...

Solution Summary

Solution depicts the methodology to find optimal output and profit levels in the given cases.

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Calculate: Optimal Output, Price and Profit Levels

Two local ready-mix cement manufacturers, Here and There, have combined demand given by Q = 105 - P. Their total costs are given by TCHere = 5QHere + 0.5Q2Here and TCThere = 5QThere + 0.5Q2Here.

If they successfully collude:

Their total output will be?
Their maximum joint profits will be ?

If they cannot successfully collude and instead produce where the market price equals marginal cost

Their total output will be?
Each firm's profits will be?

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