Answer to Question #165579 in Microeconomics for Aksheeta

Question

Each of 100 firms in a perfectly competitive industry has an AVC function AVC=2Q where Q represents the output produced. If the price of the product is ₹100 find the total quantity supplied in the market when a) TFC= ₹10000 b) TFC= ₹20000

Answer 1

It is well known that marginal cost per unit (denoted by MC) represents supply curve.

Let's write a total cost function

$TC=AVC\times Q+TFC$ ,

where Q is quantity produced by one firm.

The MC can be calculated as the first derivative of TC with respect to Q

$MC= \frac{dTC}{dq}=Q \frac{dAVC}{dq}+AVC+\frac{dTFC}{dq}=Q \frac{dAVC}{dq}+AVC$

(it is well known that $\frac{dTFC}{dq}=0$ )

Hence,

$MC =Q\times2+2Q=4Q$

Hence, the one-firm inverse supply function is the following

$Ps(Q)=MC(Q) =4Q$

The one-firm supply function is the following

$Qs=\frac{P}{4}$

The total quantity supplied in the market (denoted by MQs) can be calculated by means of following equation:

$MQs=100\times Qs=100\times P / 4=25\times P$

When the price is equal to 100, the total quantity supplied in the market is equal to 2,500. This quantity does not depend on TFC.

ANSWERS:

a) 2,500

b) 2,500