III) Revealed Preferences, price effects Flashcards
In reality, do we observe preferences?
No, we observe choices.
What are the determinants of the choice?
Prices and level of income.
How do you denote a revealed preference?
qRPq’
q is prefered to any bundle affordable in this budget set.
According to the weak axiom of weak preferences, if qRPq’, then….
q’RPq is impossible.
What is the transitive closure of the direct revealed preference relation?
What is the Strong axiom of revealed preferences?
If qRPq’, & q’RPq’’, then qRPq’’
SARP: if qRPq’ indirectly, q’RPq even indirectly is impossible.
What is the Slutsky effect?
Decomposition that helps us to understand the effect of price on consumption, based on the decomposition between a substitution and an income effect.
How do we do the decomposition in income and substitution effect?
We first keep the income constant and change the relative prices and then we change the income level.
First we compute the substitution effect and then we compute the income effect.
What is the substitution effect?
We keep the purchasing power constant and we compute the difference between the first consumption and now.
Δq1 = g1(p’1, x’) - g1(p1, x)
What is the income effect?
Analyze of the difference of consumption when incomes goes back to his position.
Δxn1 = x1(p’1, x) - x1(p’1, x’)
x’>x => decrease in income
Normal good: Δx is negative, positive if inferior good.
Giffen good: negative income effect is higher than the substitution effect.
How do you compute the Slutsky effect?
Δq1 = Δqs1 + Δqn1
Δqs is the substitution effect (always negative)
Δqn1 is the income effect, negative (normal good) or positive (inferior good).
If the goods are perfect complements or perfect substitutes, what happens to the substitution and income effects?
Complements: only an income effect.
Substitutes: only a substitution effect.
What’s the difference between the Hick’s decomposition and th Slutsky’s?
In the Slutsky’s decomposition, the new budget line is drawn passing by the original choice, so it draws a new indifference curve.
In the Hick’s decomposition, the new budget line is drawn around the original indifference curve until it is parallel to the new income line.
This will lead to different results.
What would look like an Hick’s decomposition based on the final choice?
What is the condition for the Marshallian demands to be linear in income?
What’s the effect on the sum of Ds?
Preferences must be homothetic / pure substitutes / pure complements.
The sum of Ds only depends on the sum of income. Aggregation of Ds is exact.
How do you draw the D curve?
What is elasticty of price on D?
Measure, independent of the units, of how 1% of change in price affects the D of the good in %.
If D is differentiable, what is the elasticity of price on D?
What is elasticity of income on D?
Measure of how 1% change in income affects the D of the good in %.
If D is differentiable, what is the formula for the elasticity of income on D?
To what is equal the weighted average of income elasticities?
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