Answer to Question #272676 in Microeconomics for Fidan

Question

There is monopolistic competition in the shampoo market. One of monopolistic firms

- DG. Company offers a special shampoo. Over a long period of time, G's total costs

(CK) of this special shampoo production (hi) are expressed by the following function

TC=3q3 - 27q? +100q. DG's total revenues (CZK) are given by the following quadratic

function TR = 63.25q - 6q?.

a) What amount of shampoo will DG produce?

b) What price will DG charge?

c) What profit will DG generate?

d) Present all results in an appropriate microeconomic model of G's behaviour.

Answer 1

Solution:

a.). In monopolistic competition, the quantity produced will be where: MC = MR

Derive MC:

TC = 3q3 - 27q² + 100q

MC = $\frac{\partial TC} {\partial Q}$= 9q² – 54q + 100

MC = 9q² – 54 + 100

 

Derive MR:

TR = 63.25q – 6q²

MR = $\frac{\partial TR} {\partial Q}$ = 63.25 – 12q

 

MC = MR

9q² – 54q + 100 = 63.25 – 12q

9q² – 54q + 12q + 100 – 63.25 = 0

Q = 3.5

DG will produce 3.5 shampoos

 

b.). TR = P $\times$ Q

63.25q – 6q² = PQ

P = 63.25q – $\frac{6^{2} }{q}$ = 63.25 – 6q

P = 63.25 – 6q = 63.25 – 6(3.5) = 63.25 – 21 = 42.25

Price = 42.25

DG will charge a price of 42.25

 

c.). Profit = TR – TC

Profit = (42.25 $\times$ 3.5) – 3(3.5³) – 27(3.5²) + 100(3.5)

Profit = 147.875 – (128.625 – 330.75 + 350)

Profit = 147.875 – 147.875 = 0

DG will generate a profit of 0.