Answer to Question #220024 in Microeconomics for Allan

Question

The monopolistic competitor faces a demand curve given by Q (p) = 50−5p. Its cost function is C(y) = 4y. What is its optimal level of output and price?

Answer 1

The quantity demanded function can be written as:

Q(p) = 50 - 5p

Y = 50- 5p

5p = 50 - Y

$p = 10 - y/5$

P = 10- Y/ 5 is the inverse function.

The cost function: C(y) = 4y 

The profit = Total revenue - Total expenditure (cost).

The profit function becomes: (10 - y/5) Y- 4Y.

By differentiating the profit function, the Y is (6 x 5) / 2 = 15

Optimal output level becomes is 15.

The Y, which is 15 can be replaced in the inversed quantity demanded function and obtain:

P = 10 - y/ 5

P = 10 - 15 /5

P = 10- 3

Price is 15