Suppose inverse market demand is given by

p(y) =Ay^1/

where <0.

(a) Show that the price elasticity of demand is constant.

(b) Suppose=1. Show that the total revenue for this demand function is a

constant as well. Plot this demand curve forA= 1. What happens to the graph asAincreases?

(c) What is marginal revenue for=1? What will a profit maximizing monopolist do when faced with this demand curve? Think intuitively: suppose its producing some output level y - Could it maximize profits by reducing or increasing output from this level?

(d) Suppose=2. Find the profit maximizing price and quantity for a monopolist with

C(y) =y²+y