Question

The short-run cost curve for each firm's long run equilibrium output is C=y^2-20y+400. Calculate the short-run average and marginal cost curves. At what output level does short-run average cost reach a minimum? I already know the MC and the SRA is TC/Q. I got the minimum as 10. Is that right?

b) Calculate the short-run supply curve for each firm and the industry short-run supply curve? Total market demand is y=2500-20p. Each firm has an identical cost structure such that long-run avg. cost is minimized at an output of 20. The minimum avg. cost is $30.

Answer 1

the short-run average cost is
TAC=y^2/y-20y/y+400/y
=y-20+400/y
The marginal cost curve is the first derivative of the cost curve.
so,mc=2y-20
short run average cost reaches it's minimum when smc=sAc or the derivative of SAC=0
SO,2y-20=y-20+400/y