Consider a cost function of producing an outputqof the formc(q) =q²+ 2q+ 16.

As a calculus refresher, if you have y = f(q) = a +bq + bq² + cq³, the partial derivative of f with respect to q is b + 2bq + 3cq² (see the pattern?).

Determine the following:

a. Marginal cost

b. Average total cost

c.Average variable cost (which part of c(q) =q²+ 2q+ 16 is fixed? That is the fixed cost; the remainder is the variable cost)

d. Graph the long-run supply curve, assuming the cost function is for a single plant and can be replicated without change.