A monopolist's demand curve is given by:
p = 100 + A1/2 – Q
where Q is the quantity of output and A is the quantity of advertising. Suppose the cost of advertising and output is given by:
C(Q,A) = 10Q + A
Determine the profit maximizing quantity of output and advertising.
The monopolist maximizes profit
Profit = (100 + A1/2 – Q)Q – 10Q + A
The first order conditions are:
dProfit/dQ = 100 – 2Q – 10 = 0
dProfit/dA = .5A-1/2Q – 1 = 0
Solve the first condition to find Q*= 45. Use this to solve the second conditions for A* = 506.
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