Question

In a monopolistic market, given the demand function Q=120-5P, and the cost function is C=14Q. Find the monopolistic price, quantity and profit. (10 points)

Here MC=14, MR=24-2/5Q.

Answer 1

Price function should be set first.

Given the demand function,

Q = 120 – 5P

Now by rearranging,

5P = 120 – Q

Or, P = 120/5 – Q/5

Or, P = 24 – Q/5 ……………… [Price function]

Profit-maximizing stage,

MR = MC

24 – 2Q/5 = 14

Or, 24 – 14 = 2Q/5

Or, 10 = 2Q/5

Or, 10 × 5 = 2Q

Or, 50 = 2Q

Or, 50/2 = Q

Or, Q = 25

Answer: quantity is 25 units.

Now this is to be placed in the price function.

Or, P = 24 – Q/5 ……………… [Price function]

Or, P = 24 – 25/5

Or, P = 24 – 5

Or, P = 19

  

Answer: price is 19.

Profit = TR – C

            = (Q × P) – (14 × Q)

            = (25 × 19) – (14 × 25)

            = 475 – 350

            = 125 (Answer)