Term 2 Lecture 2 Flashcards
(12 cards)
What is the idea of revealed preference?
About how people make choices with their money, helps us understand what they prefer, based on what they actually buy
- lets say you can buy good A or good B
- if you could have bought B at the same price or cheaper, but chose A, then you prefer A
If they could have bought B for cheaper, and still chose A, then they strictly prefer qA over qB, so the equal to disappears from the inequality, leaving pAqA > pBqB
WARP, what is it?
A consistency rule for consumer choices
- if a consumer chooses qA over qB in one situation, then they should not choose qB over qA in another situation where qA is cheaper
What is indirect revealed preference?
If qA is directly revealed preferred to qB and qB is directly revealed preferred to qC, then qA is indirectly revealed preferred to qC
SARP, what is it?
SARP extends the idea of consistency in WARP in consumer choices beyond direct preferences to indirect chains of preference.
- budget set 1, chose qA when qA and qB both affordable, so qARDqB
- budget set 2, chose qB when both qB and qC were affordable, so qBRDqC
- budget set 3, chose qC when both qA and qC were affordable, so qCRDqA, which contradicts earlier choices and transitive preferences, creating a preference cycle.
SARP implies WARP, but extends it into 3+ goods territory
Relation between WARP and SARP violation
SARP can be violated due to the appearance of preference cycles, violating transitivity, but WARP will still hold as each direct choice remains consistent
- proves SARP is a stricter rule than WARP, WARP alone is not enough to ensure full consistency when multiple goods are involved.
Slutsky compensation and how it leads to the negativity condition
Suppose the price changes from pA to pB, instead of letting the consumers real purchasing power change, we adjust their budget so they can still afford original bundle qA
- pBqA = pBqB, meaning the budget/total spend remains the same
- also pAqA < pAqB, as if this was not true, then qB would have been picked earlier as it would have been cheaper, which would contradict WARP
Subtract the equality in line 2 from this inequality to get the negativity constraint: (pB - pA)(qB - qA) < 0
What does the negativity constraint imply?
If price goes up then demand must go down, and vice versa, supporting the law of demand
Whats the point of slutsky compensation
Removes the income effect so we can study the pure price/substitution effect
What is the Slutsky-compensated demand function a given initial bundle qA and what does it mean?
g(qA,p) = f(p’qA,p), so the demand if budget is constantly adjusted to keep initial choice qA affordable
Differentiate:
Dgi/Dpj = (qjA)(Dfi/Dy) + Dfi/Dpj
Dfi/Dpj = uncompensated effect
Dgi/pj = compensated price effect, substitution effect
-Qj.Dfi/Dy = income effect, so change in demand due to income changes
Slutsky equation in elasticity form:
Nij* = nij + wjA.ei
- nij* = compensated price elasticity - sub effect only
- nij = uncompensated price elasticity - total price effect
- wjA - budget share of good j
- ei - income elasticity of demand for good i
If we restrict slutsky to own price effect, i.e. i = j
Dgi/Dpi = (qiA)(Dfi/Dy) + Dfi/Dpi
Nii* = nii + wiA.ei
- Dfi/Dy > 0, i.e. the income effect is positive, for normal goods when income rises, demand for it rises too
- substitution effect is always negative, as when price of a good goes up, consumer switch to other relatively cheaper goods, Dgi/Dpi < 0 due to WARP
- rearrange, you get Dfi/Dpi = Dgi/Dpi - (qiA)(Dfi/Dy), so it is negative for a normal good, demand must fall as price rises, confirming the law of demand
When can giffen goods occur?
Dfi/Dpi = Dgi/Dpi - (qiA)(Dfi/Dy)
- Dgi/Dpi < 0 always - sub effect always negative
- so Dfi/Dy must be SO negative, that it outweighs the substitution effect and the total price effect is positive - giffen good
Same way 0 > nii* > wiAei
