A consumer has an indirect utility function given by

$$v(p_1, p_2, R)=\frac{R}{p_{1}+p_2}$$

Where $p_1$ and $p_2$ denote the prices of the two goods consumed by the individual and $R$ the income.

How do I calculate this consumer's Hicksian demand function for goods 1 and 2?


1 Answer 1


To get the Hicksian demand function $h$, you can use Shephard's lemma, which says that

$$h_i(p_1,p_2,u)=\frac{\partial e(p_1,p_2,u)}{\partial p_i}$$

where $e$ is the expenditure function.

To get the expenditure function, use the equation:


i.e. solve

$$v(p_1,p_2,R)=\frac{R}{p_1+p_2}=u$$ for $R$ and call the resulting expression $e(p,u)$.


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