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The following problem shows an example of preferences that satisfy transitivity for but not for~. Johrn consumes two goods, X and Y. He prefers the bundle (x, y) to the bundle (x,y) if and only if (y-ry > 1). Similarly, he prefers the bundle (xy) to the bundle (x, y) if and only if (ry - ry > 1). Otherwise he is indifferent between the two bundles. a. Show that the relation of indifference () is not transitive for John. (Hint: To show that something is not true it is sufficient to show just one counterexample). b. Prove that the strictly preferred relation () is transitive for John. (Hint: Try coming up with a geometrio interpretation of Johns preferences before attempting a proof)

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By transitivity property, suppose x,y and z three bundles. So if x> y, and y> z, then x> z. This is law of transitivity. Similarly if x= y and y= z then, x= z by transitivity.

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