Kapitel 2 Flashcards
Preference Relation
Properties of preference relations
- Completeness
- Transitivity
- Reflexivity
- non-satiation
- continuity
- strict convexity
Indifference curves for consumption bundles
Properties of indifference curves
- Ubiquity: Completeness implies that there is an indifference curve through every bundle.
- Downward-sloping: Non-satiation implies that if we increase the amount of one good, we must reduce the amount of some other good to remain indifferent.
- Cannot cross: Take two different indifference curves (one with bundles strictly preferred to the other). Suppose they cross. Using transitivity we reach the contradictory conclusion that bundles in each of these curves are indifferent to each other.
- Convex: These property follows from the convexity of preferences.
Utility functions
- ordinal utility: number attached to the bundle does not have a meaning
Indifference curves for utility
Marginal Utility
MRS
Marginal Utility of good i: rate at which utility changes as good i is increased while all other goods are held constant
-> Derivation of utility functio by xi
Marginal rate of substitution of good i for good j at bundle x is the amount of good j the consumer is willing to give up in exchange for a marginal increase in good i in order to keep the same level of utility
-> divide Marginal utility of i by j
-> slope of the indifference curve
Feasible set
-is given by the budget set
x1p1 * x2p2 ≤ M
- boundary: budget line
- slope: -p1/p2
-> gives opportunity cost
Properties of the budget set
- Bounded: it is possible to enclose the budget set in a sphere of sufficiently large finite size, provided M is finite and all prices are strictly positive.
- Closed: the boundary of the budget set is feasible.
- Convex: any convex combination of two bundles in the budget set is also feasible (intermediate bundle cannot cost more than the most expensive of the bundles).
- Non-empty: if at least one price is finite, M > 0 allows the consumer to buy a positive amount of some good.
Marshallian Demands
- gives optimal demand for each good as a function of prices and income
xi*=Di(p,M)
Marshallian Demands Diagramm
X-P Diagramm
Income consumption curve
The income consumption curve is the set of optimal points traced out as income varies and prices remain constant.
It is the locus of all tangency points between the indifference curves and the varying budget lines.
We say that a good is normal if ∂Di/∂M ≥ 0. Otherwise, it is inferior.
Notice that inferiority is a local property and not all goods can be inferior.
Price consumption curve
The price consumption curve is the set of optimal points traced out as the price of one good varies while all other prices and income remain constant.
We say that a good is ordinary if ∂Di/∂pi ≤ 0. Otherwise, it is a Giffen good.
Substitution effect
the change resulting solely from the change in relative prices with utility held constant (this means that nominal income has to be adjusted).
Income effect
the change resulting solely from the change in real income with relative prices held constant.
Compensating variation
Unterschied zwischen M nach Preisänderung und M nach Preisänderung und Verschiebung
-verschieben p1
- legen neues m auf altes niveau
- unterschied zwischen neuem und altem m=CV/p1
Equivalent variation
Unterschied zwischen M mit alten Preisen und theoretischem M mit neuem U und alten Preisen
- p1 verändert sich
- m auf neues niveau von u verschieben
- unterschied altes neues m =EV/p1
