Direct Preference revelation Suppose that the bundle xis chosen when the bundle y is affordable Then x is revealed directly as preferred to y (otherwise would have been chosen)
Direct Preference Revelation Suppose that the bundle x* is chosen when the bundle y is affordable. Then x* is revealed directly as preferred to y (otherwise y would have been chosen)
Direct Preference revelation The chosen bundle x is revealed directly as preferred to the bundles y and z. X y X1
Direct Preference Revelation x2 x1 x * y The chosen bundle x* is revealed directly as preferred to the bundles y and z. z
Direct Preference revelation That x is revealed directly as preferred to y will be written as x≥y
Direct Preference Revelation That x is revealed directly as preferred to y will be written as x y. D p
Indirect preference revelation Suppose x is revealed directly preferred to y, and y is revealed directly preferred to z. Then, we call x is revealed indirectly as preferred to z. write this as so xy and y 6
Indirect Preference Revelation Suppose x is revealed directly preferred to y, and y is revealed directly preferred to z. Then, we call x is revealed indirectly as preferred to z. Write this as x z so x y and y z x z. D p D p I p I p
Indirect preference revelation X2 z is not affordable when x* is chosen X* is not affordable when y* is chosen So x and z cannot be compared X directly. But x y b y and y 6 SO X*Z
z is not affordable when x* is chosen. x* is not affordable when y* is chosen. So x* and z cannot be compared directly. Indirect Preference Revelation x2 x1 x* y* z But x*x* y* and y* z so x* z. D p D p I p