Problem 3 - Monopolistic Competition and Advertising Consider a firm with monopo

Question

Problem 3 - Monopolistic Competition and Advertising Consider a firm with monopoly power due to some patented technology (like a new type of ice cream!) faces the inverse demand of p(y) = 2500-2y and has a cost of production of: e(y) 100,000+-y2 2 where 100,000 is the fixed cost all firms face when entering the market (oncea firm is in the market, the fixed cost is sunk) Find the monopolist's profit maximizing price and quantity. How much profit does it make? Suppose this firm faces entrants to the industry after the patent expires. The industry becomes monopolistically competitive due to the established brand names of the products, though there is free entry of firms. The monopolist now faces a demand of p(y) = -Zy Find the long-run equilibrium output (y) and value of . (Hint First find the profit maximizing output in terms of . How much profit does the monopolistically competitive firm make in the long run? This will determine a.) Desperate after seeing their profits go to zero, the CEO of the firm considers embarking on an aggressive advertising campaign to boost the brand value. This will raise the firm's demand froin p(y)--2p to p(y) = 1500-2p The campaign will cost $200.00(). Should the firm embark on this advertising campaign?

Explanation / Answer

c(y) = 100,000 + 1/2y2

A monopolist maximizes profit where MR = MC

Total Revenue (TR) = p(y).y

                                   = 2500y – 2y2

Marginal Revenue (MR) = 2500 – 4y

Marginal Cost = y

Therefore, 2500 – 4y= y

                                  y =500 which is the profit maximizing output

p(y) = 2500 – 2y

        = 1500 which is the profit maximizing price.

Profit = Total Revenue – Total cost

           = 2500y – 2y2 – 100,000 – 1/2 y2

           = 2500y – 100,000 – 5/2 y2

           = 525,000

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