Question

3. Jamie Co. has a patented disinfectant to clean the kitchen of restaurants. The market demand for her patented disinfectant is Q = 1,000 – 0.2P. Jamie Co. has a total cost function of C = 100,000 + 2,000Q + 10Q2 . What is the profit-maximizing price and output level of Jamie Co.? Show your workings.

Answer #1

Because Jamie Co. has a patent, so it functions as a monopolist.

Q = 1000 - 0.2P

or 0.2P = 1000 - Q

or P = 5000 - 5Q

MR = 5000 - 10Q

Total Cost = 100,000 + 2,000Q + 10Q^2

MC = 2000 + 20Q

At profit maximizing condition,

MR = MC

or 5000 - 10Q = 2000 + 20Q

or 30 Q = 3000

or Q = 100

P = 5000 - 5Q = 5000 - 5*100 = 4500

So the profit maximizing price is 4500 and the profir maximizing output is 100.

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