Amanufacturer of sunglasses currently sells one type for $15/pair. the price p and the demand x are related by x=9500-250p. a) at this price, is the demand inelastic or elastic. b) should the price be increased or decreased to increase revenue?

A) The price elasticity of demand is given by

... Ed = (dx/dp)·(p/x)

... = -250·(15/(9500-250·15)) ≈ -0.652

B) This value has a magnitude less than 1, so price can be increased to increase revenue.

The price at which Ed has a magnitude of 1 is ...

... 250p/(9500 -250p) = 1

... 250p = 9500 -250p

... 500p = 9500

... p = 9500/500 = 19

Revenue will increase as price increases up to $19 per pair.