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I demand is p a - bq then mr a - 2bq mc dtcdq c the

If demand is P = A - bQ, then MR = A - 2bQ. MC = dTC/dQ = c. The monopoly firm will profit-maximize by setting A - 2bQ = c, so the equilibrium quantity traded will be Q* = (A-c)/2b. The profit-maximizing price will be given by substituting this into the demand curve, so P* = A - b((A-c)/2b) = A - A/2 + c/2 = A/2 + c/2 = (A + c)/2.

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