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