The demand a monopoly faces is p 100-a+A.5 where Q is the quantity, p is the pri

Question

The demand a monopoly faces is p 100-a+A.5 where Q is the quantity, p is the price, and A is the level of advertising. Marginal cost is a constant $10 per unit, the cost per unit of advertising is $1, and there are no foxed costs. Solve for the firm's profit-maximizing price, quantity. and level of advertising. Hint: the profit function must be maximized with respect to two choice variabies (O and A) The profit-maximizing quantity isunits. (round your answer to two decimal places) The profit-maximizing level of advertising is units. (round your answer to two decimai places) The profit-maximizing price is (round your answer to two decimai places)

Explanation / Answer

The profit function is as follows:

p = (100 – Q + A1/2 )Q – 10Q – A

After differentiating the profit function with respect to Q and A the following first-order conditions will be obtained:

p/A = (0.5Q)A-0.5 – 1 = 0

p/Q = 100 – 2Q + A0.5 – 10 = 0

Solve the above equations to get the following values of A, p, and Q:

A = 900
p = 70

Q = 60

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