Why is Engel curve a straight ray through the origin if $D_wx$ = x(p, 1)$? I see in the textbook that the Engel curve will be straight if $D_wx(p,w) = x(p,1)$ but it's not immediately clear to me why this is the case. Could someone kindly explain to me?
The function $x(p,1)$ is constant in $w$. If you integrate it wrt $w$, you end up with a straight line (wrt $w$), whose equation is ...