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A monopolist is faced with the inverse demand function P(Q) and has a constant average cost c per unit produced. There are no other costs.

(a) Write the profit function (Q) and derive the first-order condition for maximum profit at Q* > 0.

(b) Derive the second-order condition. Can you verify that the second-order condition for a maximum profit is satisfied?

(c) The monopolist's profit maximizing output Q* can be derived using the first-order condition. How do you expect its profit maximizing output to be affected by changes in average cost (i.e. Q*/c > 0, Q*/c < 0, or Q*/c = 0)? How do you expect its maximum profit to be affected by changes in average cost (i.e. (Q*)/c > 0, (Q*)/c < 0, or (Q*)/c = 0)?

(d) Suppose now that the inverse demand function is P(Q) = a - Q and that 0 < c < a. Find the profit maximizing output Q* and the associated maximum profit (Q*). How does the monopolist's profit is affected by changes in average cost?