Let A’s demand function be D(x) = 15 - 1.3 x , B’s supply function be S(x) = 2 x ^ 1/3 . [Definitions: consumer surplus = 0 Q D(x)dx - QP & producer surplus = QP - 0 Q S(x)dx, where Q = units of the product, P = price per unit ]
a) Find equilibrium point when Q = 27.
b) Schetch the graph of both demand and supply function and identify the regions of both consumer & producer surpluses.
c) Find the consumer surplus at the equilibrium point
d) Find the producer surplus at the equilibrium point