1
$\begingroup$

In every textbook it says that it is easy to see that with no income effect, the integral

$\int_{p^0_1}^{p^1_1} \! h(p,u_0) \mathrm{d}p_1. = \int_{p^0_1}^{p^1_1} \! h(p,u_1) \, \mathrm{d}p_1$

Could someone explain to me why?

$\endgroup$
1
$\begingroup$

This is because when the Marshallian demand $x_i(p,w)$ is constant in $w$ (i.e. no income effect), the Hicksian demand $h_i(p,u)$ is constant in $u$. To see this, we only need to apply the relation $$h_i(p,u)=x_i(p,e(p,u)).$$ For $u^0\neq u^1$, we have $$h_i(p,u^0)=x_i(p,e(p,u^0))=x_i(p,e(p,u^1))=h_i(p,u^1).$$

Therefore, $$\int_{p^0_1}^{p^1_1} \! h_i(p,u^0) \mathop{dp_1} = \int_{p^0_1}^{p^1_1} \! h_i(p,u^1) \, \mathop{dp_1}.$$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.