Suppose the long-run total cost function for any firm in an industry is given by the cubic equation
TC=a+bq+cq^2+dq^3
a) Show (using calculus) that this total cost function is consistent with a U-shaped average cost curve for at least some values of a, b, c and d.
Please answer the rest of the question using the values of and you found in (a).
b) What is individual firm short-run supply curve?
(c) Suppose it is a constant cost industry and it is perfectly competitive. What is the long-run supply curve? How many units of output will each firm supply in the long-run?