Question 7.7.1: Find the elasticity of f (x) = Ax^b, where A and b are const......

In this case, f^{\prime}(x)=A b x^{b-1}.\mathrm{Hence},\mathrm{E}\mathrm{l}_{x}(A x^{b})=(x/A x^{b})A b x^{b-1}=b,\mathrm{so}

f(x)=A x^{b}~\Rightarrow~\mathrm{El}_{x}\,f(x)=b    (7.7.3)

The elasticity of the power function Ax^{b} w.r.t. x is simply the exponent b. So this function has constant elasticity. In fact, it is the only type of function which has constant elasticity. This is shown in Exercise 9.9.6.