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Calculate: Optimal Output, Price and Profit Levels

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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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This solution is comprised of a detailed, step by step response which outlines how to calculate the optimal output and profit in the given cases.

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If they successfully collude:

Their total output will be?
Q=105-P

On rearranging, we get:
P=105-Q

Total Revenue=TR=P*Q=(105-Q)*Q=105Q-Q^2
Marginal Revenue=MR=dTR/dQ=105-2Q

Both firms have the same cost structure, So, combined Total Cost function is given by
Total Cost=TC=5Q+0.5Q^2
Marginal Cost=MC=dTC/dQ=5+Q

Combined profit will be maximized if MR=MC i.e.
105-2Q=5+Q
3Q=100
Q=(100/3) i.e. 33.33 units

Their maximum joint profits will be ? ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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