TERM 2 Lecture 3 Flashcards
(21 cards)
Whats the point of specifying which bundles the consumer prefers to which others
Provides the foundation for a fuller modelling of choice
- nature of these preferences can be restricted by assumptions which vary from what is minimally necessary for a viable theory to assumptions which seriously constrain the nature of choice
We define a preference relation as
qA>/ qB, meaning consumer weakly prefers qA to qB
qA ~ qB, means the consumer is equally satisfied with either bundle
qA>qB, means the consumer strictly prefers qA to qB
Whats the weakly preferred/ upper contour set
R(qA), includes all bundles that are at least as good as qA
Whats the weakly dispreferred set
L(qA), includes all bundles that are worse than or equal to qA
Whats the indifference set?
I(qA), all bundles that are equally good as qA, so its the overlap of R and L
Completeness Axiom
States that for two consumption bundles, a consumer can always make a comparison between them meaning:
- can always prefer one over the other
- or be indifferent between them
Transitivity Axiom
If a consumer prefers one bundle to another, then prefers that 2nd bundle over a 3rd, should therefore also prefer the 1st bundle to the 3rd
- prevents preference cycles
Continuity Axiom
Continuity assumption states, if prefer qA to qB, and qB to qC, then there is some bundle qD on the path joining qA to qC which is indifferent to qB
- ensures preferences behave smoothly without sudden jumps or contradictions, ensuring well-behaved ICs and allowing utility functions to be continuous
Describe to me, utility functions
- assigns a numerical value to each bundle q to represent how much the consumer likes it
- continuity ensures that small changes in a bundles lead to small changes in utility
- utility functions are ordinal, only represent ranking.
Nonsatiation Axiom
For any bundle in the consumption set, there is always some way to improve it
- so no bliss points
- utility can always increase
Monotonicity Axiom
Larger bundles are always preferred over smaller ones, assumption here is that consumers prefer more goods rather than less
- ICs must slope downward, to get more of one good, you must give up some of the other to maintain same utility - MRS
Convexity Axiom
If qA >/ qB and 1>k>0, then kqA + (1-k)qB > qB
- means IC is convex, so assuming consumers like a mix of goods rather than extreme amounts of only one good
- diminishing MRS, willingness to substitute one for another decreases as you get more of one good.
Homotheticity Axiom
- meaning
- geometric interpretation
- relation to homogeneity
If a consumer is indifferent between two bundles qA and qB, then they will also be indifferent between scaled up versions of those bundles
- preference depends on proportions, not absolute amounts.
- if two bundles lie on an IC, then scaling both by the same positive multiple keeps them on a new higher IC
- that means MRS is constant along rays through the origin
- a utility function is homothetic if it is homogenous of degree 1, as proportional changes in consumption lead to proportional changes in utility rankings
Quasilinearity Axiom
Adding the same amount of one good preserves indifferent between bundles
- meaning if consumer is indifferent between qA and qB, then adding k units of a combination of goods, lets say just good 1 to both still keeps them indifferent
- indifference curves are parallel translations of each other along the axis of good 1 in this case
Issues with homotheticity and quasilinearity
Both are strong restrictions, in many contests they would be inappropriate to assume, but are importsnt to consider as, they define the unique cases in which certain properties of demands or welfare comparisons hold.
Consumer rationality assumptions
Completeness and transitivity
- we can consistently put all bundles in order from most to least preferred
Subset relation to weakly and strictly preferred sets
If qB is weakly preferred to qA, then R(qB) must lie entirely within R(qA)
- if qB is strictly preferred to qA, then R(qB) is a strict subset of R(qA)
How to show monotonicity
MRS should be negative
Convex how to show
If the dq2/dq1 is diminishing in q1, in absolute value.
Homotheticity how to show?
If the MRS is a function only of the ratio q2/q1, or vice versa of course
- or if the MRS is homogenous of degree 0 in q1,q2
Quasilinearity how to show
Try make the utility function:
U(q1,q2) = v(q1) + q2, which is quasilinear in terms of q2 and then vice versa
- MRS only depends on either q2 or q1
