# Find Engel Curve with a Cobb-Douglas [closed]

I have $U(x,y)=xy$, $p_1=4$ and $p_2=1$. Income is unknown. Where do I start?

## closed as off-topic by Giskard, Kitsune Cavalry♦Nov 9 '18 at 1:06

This question appears to be off-topic. The users who voted to close gave this specific reason:

• Use the fact that slope of IC equals slope of the budget line in equilibrium and then use the budget equation to get the demand as a function of income and that's your Engel curve. – Amit Jul 5 '17 at 2:53
• Possible duplicate of Deriving Equation for Engel Curve – luchonacho Jul 5 '17 at 6:14
• Start by reading your book chapter on Engel curves. – Giskard Jul 5 '17 at 6:35

The way I would attack this is to solve the utility function $$u(x,y)=xy$$ subject to the budget constraint: $$4x+y=m$$. This is using Lagrange method It turns out that $$x=m/8$$ and $$y=m/2$$.
The Engel curve show the relationship between income and the quantity of the good demanded, so substitute values for $$m$$ and find the corresponding $$x$$ or $$y$$ demanded and plot the Engel curve for good x or good y.