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If tastes are homothetic and identical, does this imply that the contract curve is the line connecting the lower left and upper right corners of the box?

My understanding: no, it does not. Consumers' indifference curves, though identical, could have the same slope along some line to the side of the line connecting the lower left and upper right corners of the box, e.g. in the case of steep indifference curves.

Is this correct?

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Take the situation where $u_1(x,y)=x+y$, $u_2(x,y)=x+y$. Then the contract curve would be the entire box.

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  • $\begingroup$ Thank you. But do identical, convex preferences imply that the contract curve will coincide with the line connecting the bottom left corner to the top right corner? It seems not. $\endgroup$ – George Jun 13 at 6:09
  • $\begingroup$ From the top of my head, there is no relation between the two. 1. The answer I provided is an example of identical, convex preferences whose contract curve is not the line connecting the bottom left corner to the top right corner. $\endgroup$ – Tomcat Jun 13 at 6:33

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