Question 11.8.3: Suppose D = Ax^a11 x^a22· · · x^ann is defined for all x1 &g......

Essential Mathematics for Economic Analysis [1185377]

Suppose $D = Ax^{a_{1}}_{1} x^{a_{2}}_{2}· · · x^{a_{n}}_{n}$ is defined for all $x_{1} > 0, x_{2} > 0, . . . , x_{n} > 0,$ where A > 0 and $a_{1}, a_{2}, . . . , a_{n}$ are constants. Find the elasticity of D w.r.t. $x_{i},$ for i = 1, . . . , n.

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Because all the factors except $x^{a_{i}}_{i}$ are constant, we can apply Eq. (7.7.3) to obtain the result $El_{i} D = a_{i}.$

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

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