Consider an exchange economy with two consumers A and B, two goods x, y. Consumers have identical preferences $U=xy$. Total available endowment are $E_x$ and $E_y$.
This is the background of a homework question which does not ask but I got this question when I try to draw the Edgeworth Box.
I find the contract curve to be the diagonal of the Edgeworth Box, with slope $\dfrac{E_y}{E_x}$. I also find the price in this economy to be $\dfrac{p_x}{p_y}=\dfrac{E_y}{E_x}$.
Then I got confused that if we start from an endowment point (for example, at the bottom right corner) and trade to the contract curve to get an equilibrium, then the line we trade along is called the priceline right? And its slope should be $-\dfrac{p_x}{p_y}$ right? If I did all these correct, I find my priceline is not orthogonal to the contract curve.
It is more likely I made something conceptually wrong? Is the contract curve in this economy the diagonal?