Chapter 4: Revealed Preference and Afriat's Theorem

Question 1

Sufficient conditions for budget exhaustion.

Answer 1

Preferences which are complete, transitive, and locally insatiable.

Question 2

GARP

Answer 2

Given a price bundle, consumption which does not exhaust a budget constraint is strictly dominated by choices which do. Based the implied ordering through transitivity, GARP holds if no data reveal contradictions (preference cycles) over indirectly revealed preferences.

Question 3

Afriat’s Theorem

Answer 3

If a finite set of demand data violates GARP, these data are inconsistent with locally insatiable, complete, and transitive preferences.
If preferences satisfy GARP, there exist preferences which are complete, transitive, continuous, strictly increasing (implying local insatiability), and convex preferences.

Question 4

Price increase, holding real wealth constant

Answer 4

Suppose x is chosen with p and y. x’ is chosen with p’ and income p’\cdot x. p’ represents p except one price is increased. Then x_i’\leq x_i, if preferences are locally insatiable.
Idea, we hold wealth constant relative to the previous consumption. Therefore, only the substitution effect is relevant.

Question 5

Giffen goods are

Answer 5

inferior goods. That is when wealth increases, consumption falls.