Question

Assume a firm engaging in selling its product and promotional activities in monopolistic

competition face short run demand and cost functions as Q = 20-0.5P and TC= 4Q2

-8Q+15,

respectively. Having this information (5 marks)

a) Determine the optimal level of output and price in the short run.

b) Calculate the economic profit (loss) the firm will obtain (incur).

c) Show the economic profit (loss) of the firm in a graphic representation.

Answer 1

Given,

$TC=4Q^2-8Q+15 \\ Q=20-0.5P$

Average cost $AV=\dfrac{TC}{Q}=4Q-8+\dfrac{15}{Q}$

$AV( at\; Q=1)=4(1)-8+\dfrac{15}{1}=11$

(a) Differentiate TC w.r.t. Q-

$TC'=8Q-8$

Putting $TC'=0\Rightarrow 8Q-8=0\Rightarrow Q=1$

Putting Q=1, we get $0.5P=20-1=19\Rightarrow P=\dfrac{19}{0.5}=38$

Hence Optimal level of output and Price are 1 and 38.

(b) Economic profit $= ( Price- AC)\times Quantity$

$=(38-11)\times 1=27$

(c) Economic profit curve is-