Use calculus to show that the supply function Q = Ap

has constant elasticity.

## EXPERT ANSWER

The constant elasticity demand function is Q = Ap, where A is a positive constant, is the constant

elasticity of demand, the price is raised to the

power, and we are holding income and other

factors constant. Differentiating this expression

with respect to price, we find that dQ/dp = Ap-1.

Thus, the elasticity of demand, (dQ/dp)(p/Q), is (Ap- 1) p/Q = ((Ap)/Q) = 1/1 =1

This

derivation holds for any price; hence the

elasticity of demand is constant at every point

along this type of demand curve.