Chapter seven Revealled Preference 显现性偏好
Chapter Seven Revealed Preference 显现性偏好
What Is the Question of the Chapter? Suppose we observe a collection of a consumers choices, can we discover his/her preference? Is this possible at all? If so, under what conditions is this possible? (This is the reverse question of finding the optimal choice)
What Is the Question of the Chapter? Suppose we observe a collection of a consumer’s choices, can we discover his/her preference? Is this possible at all? If so, under what conditions is this possible? (This is the reverse question of finding the optimal choice)
Digression: Science VS Engineering (对比科学家思维与工程师思维) 找问题与解问题的不同 要对问题提问题 务虚与务实的不同 解释世界与改造世界的不同 旁观者与参与者的不同
Digression: Science vs. Engineering (对比科学家思维与工程师思维） 找问题与解问题的不同 –要对问题提问题 务虚与务实的不同 解释世界与改造世界的不同 –旁观者与参与者的不同
Maintained Assumptions on Preferences Preferences do not change while the choice data are gathered are strictly convex are monotonic
Maintained Assumptions on Preferences Preferences –do not change while the choice data are gathered. – are strictly convex. – are monotonic
Assumptions on Preferences If preferences are convex and monotonic(i.e well-behaved) then the most preferred affordable bundle is unique X1
Assumptions on Preferences x2 x1 x1 * x2 * If preferences are convex and monotonic (i.e. well-behaved) then the most preferred affordable bundle is unique
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 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