Question

1. This chapter considers only the competitive equilibrium.

(a) For a general inverse demand function, p(y), and a general cost function, c(x, y), write down the monopoly’s optimization problem in the two-period setting. (b) Under the assumption that the monopoly exhausts the resource and sells a positive amount in both periods, write down the equilibrium condition for the monopoly.

(c) Interpret this equilibrium condition.

Answer 1

(a) Monopolist will always strive to make large profits.But if Monopolist is rational unlike the competitive firms monopolists will only only sell according to the demand of consumers.Thus in a two period setting
py-C(y)
Now if demand of product is D(p) units at price p.The optimisation problem of monopolists is
Max py -C(Y)
Sub to y greater than or equal to D(p) or max pD(p)-C(D(p))

(b) if there is inverse and direct demand
D(p)=a-bp
y=a-by
P(y)=a/b -1/by=A-By

(C) optimal or equilibrium condition
Maxp(y) to c(y)
P'(y) +p(y) -c'y=0
P'y+p(y)=c'y