Use calculus to show that the supply function Q = Ap
has constant elasticity.
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
derivation holds for any price; hence the
elasticity of demand is constant at every point
along this type of demand curve.