Question

A firm has total cost of TC(y)=y²+1 and marginal cost of MC(y)=2y. At what level of output does the firm's average total cost achieve its minimum?

Answer 1

firm's average total cost achieve its minimum

we have Marginal cost=2y

Total cost=y^2+1

when average total cost is equal to marginal cost

TC=y^2+1

Average total cost is equal to

ATC=TC/y

ATC=y^2+1/y

So equalizing ATC with marginal cost

y^2+1/y=2y

=2y^2=y^2+1

=2y^2-y^2-1=0

=y^2=1

=y=1/2

y=0.5

0.5 unit level of output is when firm's average total cost achieve its minimum