# 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?

https://brainmass.com/economics/pricing-output-decisions/calculate-optimal-output-price-and-profit-levels-460771

#### Solution Preview

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 Summary

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.