3
$\begingroup$

I have a utility function of $U = B^{.67}Z^{.33}$ with Income $Y$, Price of Good B is $P_b$ and price of Z is $P_z$ I now need to derive an engel curve for this. I have no idea where to start.

$\endgroup$
6
$\begingroup$

It is quite simple. The engels curve is the change in demand for a good as a function of income, keeping prices fixed

Solve the constrained maximisation problem $$ \max B^{0.67}Z^{0.33}-\lambda(P_bB+P_zZ-Y) \Leftrightarrow \\ B=\frac{0.67Y}{P_b} \\ Z=\frac{0.33Y}{P_z} \\ \lambda = \frac{0.5303709372}{P_z^{33/100}P_b^{67/100}} $$

Fix prices at some level. I choose 1 for simplicity. Then the engels is simply $$ Y=\frac{1}{0.67}B \\ Y=\frac{1}{0.33}Z $$ enter image description here

$\endgroup$

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.