Evaluate the sign of the derivative at these three points -

Question

The quadratic network:-

In the quadratic network, p(n, n) = An - an2. At a point n, the consumer and producer surpluses are

(a) Show that the social surplus is

(b) Show that the derivative of the social surplus with respect to n is

(c) Evaluate the sign of the derivative at these three points:

I. At the marginal cost solution n₀.

II. At the maximum point n_max = A/a.

III. At n = 0. Accounting for the fact that SS'(n) is quadratic, determine the value of n that maximizes social surplus.