Question

A perfectly competitive firm has cost given by C = 10,000 + q2. How many units of output will this firm produce in the long run?

A)

1,000

B)

250

C)

100

D)

600

Answer 1

C.100

Explanation :

First we need to calculate ATC.

ATC =TC /Q

=10,000+q^2/q

=10,000/q+q

=10,000q^-1+q

Now we will take derivative of ATC and will set result equals to zero.

Minimum ATC =dATC/dq

=-10,000q^-2+1

Now,

-10,000q^-2+1=0

-10,000q^-2=1

-10,000/q^2 =1

-10000=q^2 *1

-10,000=q^2

100=q.

In long run perfectly competitive firm earns zero economic profit. Thus they produce where ATC is minimum. Here at quantity 100, ATC is minimum thus that will be quantity.