consumer theory Flashcards
what assumes the traditional view of consumer behaviour?
The traditional view of consumer behavior assumes that:
- Consumers have clear, well-defined preferences for all available bundle
- They aim to choose the most preferred bundle from the options available to them
what are the key components of any model of consumer choice?
Any model of consumer choice is built on four key components:
1. Consumption set or commodity space: this is the set of all possible alternatives the consumer can imagine.
2. Feasible set: the set of alternatives that the consumer can realistically access or achieve.
3. Preference relation: describes the consumer’s preferences and tastes among the different options.
3. Behavioral assumption: the principle the consumer follows to make a decision, which is to choose the most preferred option they can get.
what is a consumption bundle?
A consumption bundle is just one specific combination
of how many units of each good the consumer chooses.
It’s a point in the commodity space X, which includes
all possible combinations of goods the consumer could have, but only with non-negative quantities (you can’t pick negative amounts of goods).
what is a preference relation?
Formally, a preference relation is a binary relation, ⪰ X on .
A “preference relation” is a way to compare two things (bundles of goods). We use the symbol to show this. If you see x ⪰ y it means the person thinks that “ x is is at least as good as y ”
what are the axioms of the consumer’s preferences
- completeness: for any two bundles x and y in X , either x ⪰ y or y ⪰ x, in other words the consumer can always compare two bundles.
- transitivity: for any three elements x, y, z in X, if x ⪰ y and y ⪰ z, then x ⪰ z
Completeness and transitivity together mean that the consumer can compare any set of goods (or bundles of goods) and rank them from best to worst, he can also like two options equally.
These rules are so fundamental that economists consider them to be the basic definition of “rational” behavior. In other words, if a consumer follows these rules when making choices, they are acting in a way that is considered logical or rational.
Definition: Rational preference relation
A preference relation is called rational if it is complete and transitive.
Definition: Strict preference relation
x ≻y (“x is strictly preferred to y”) if and only if:
x ≽y and y ≱ x
Definition: Indifference relation
x ∼y (“x is indifferent to y”) if and only if:
x ≽y and y ≽x
what are indifference sets?
Indifference relation is important in economics because it helps us understand situations
where a consumer feels the same about two different bundles of goods.
These situations are
often grouped into what we call indifference sets.
indifference set is the collection of all bundles that the consumer considers equally good as bundle x.
formally: Ix={ y∈X: y∼x }
These indifference sets are important because they show the trade-offs the consumer is willing to make between different goods. In other words, they help us see how much of one good a person would give up to get more of another, while still feeling just as satisfied.
Definition: (Strong) monotonicity
- A preference relation is monotone IF for any x and y such that xℓ >yℓ for ℓ= 1,…,L, we have x ≻y.
- It is strongly monotone IF for any x and y such that
xℓ ≥ yℓ for all ℓ= 1,…,L and xj >yj for some j ∈X ⇒x ≻y.
Monotone preferences mean that if one bundle of goods x
has more of every single good compared to another bundle y the consumer will always strictly prefer bundle x.
Strongly monotone preferences are a bit more flexible. Even if bundle x has more of just one good and the same or more of all others, you will still strictly prefer x.
That’s strong monotonicity: having more of just one good
makes the consumer prefer that bundle, as long as the rest are the same or better.
what bundle a consumer is more likely to pick?
If preferences are monotone or strongly monotone, a consumer will pick a bundle that lies on the boundary of their budget set.
From the set of bundles they can afford, they will choose a bundle based on their wealth w and the prices pl≥0 of different commodities.
what is local nonsatiation?
for every x there is a point nearby that the consumer prefers to x.
Local Nonsatiation: This concept does not mean that a preferred option must have more of every good. It does not imply that giving the consumer more of everything will always make them better
off. Instead, it allows for the possibility that some goods can be considered “bads.” In other words, some items may not provide satisfaction or may even be undesirable for the consumer.
Just because consumers want
more of some goods doesn’t mean they want more
of everything. Sometimes, having less of a bad can make them better off overall.
what is nearby preference?
Nearby Preferences: For any chosen bundle of
goods, there is always another bundle that the
consumer would prefer, meaning they always want
to improve their choice.
when preferences are non-satiated?
consumers always prefer to have more of at least one good. They are never
completely satisfied and always want something better or more.
it is possible for all commodities to be bads?
It is not possible for all commodities to always be bads if preferences are non-satiated.
- If preferences are non-satiated, it is impossible for all commodities to be bads, because if all commodities were considered bads, then the consumer would prefer to have less of them or
none at all. - In this case, having no consumption at all, represented by the point x=0, would become a satiation point. This means that the consumer would be satisfied with having nothing, which
contradicts the idea of non-satiated preferences. - If preferences are non-satiated, consumers should always want more of something instead of
being satisfied with having nothing.
what is a satiation point?
A satiation point is a level of consumption where a consumer feels satisfied and does not want any more of a good or service. If a consumer reaches a satiation point, they are content with what they have.
what are the caracteristics of an indifference set?
- Downward sloping: If the consumer wants more of one good (say, apples), they will have to give up some of another good (say, bananas) to stay equally satisfied.
This creates a
downward-sloping line, because there’s a trade-off between goods. - Thin: The indifference sets are “thin”, meaning there aren’t many combinations of goods that keep the consumer equally satisfied. So, the sets don’t have a lot of options that give the
consumer the same happiness level.
what is the upper contour set?
this is the set of bundles that are at least as good as x
what is the lower contour set
is the set of all bundles that are no better than x
when we have convex preferences?
A preference relation is said to be convex if the consumer prefers balanced combinations of goods over extreme choices.
Formally, this means that if for every x, the upper contour set of x is convex.
= If y⪰x and z⪰x, then λy+(1− λ)z ⪰ 0, where λ is any number between 0 and 1.
averages are at least as good as extremes
convex upper contour set
for any two points in this set, the straight line connecting them that is also inside the set.
non-convex upper contour set
combinations of goods fall into the lower contour set, meaning they are worse than x.
This breaks the axiom of convex preferences,
where averages should be as good as extremes.
what does the combination of the convexity and non-satiation assumption leads us to?
The combination of the convexity and non-satiation assumptions leads us to important characteristics of indifference sets.
- Thin: the indifference curves are thin, meaning that only a few combinations of commodities will make the consumer equally happy.
- Downward Sloping: as you increase the amount of one good, you must decrease the amount of another good to stay equally satisfied. This creates a downward slope on the graph.
- Bowed Upward: this means that as you have more of one good, the amount of the other good you are willing to give up increases.
what are flats indifference curves?
There is nothing in the definition of convexity that prevents flat regions from appearing on indifference curves. The curves generally bow but also have sections that are flat, indicating areas
where the consumer is indifferent between different combinations of the two commodities.
An example of flat convex indifference curves are the perfect substitutes.
what are perfect substitutes
An example of flat convex indifference curves are the perfect substitutes.
goods that can be used to satisfy the same needs
for these goods
the indifference curves are straight lines
what is strict convexity?
A preference relation is strictly convex if for any distinct bundles y and z
(y ≠ z) such that y ≽x and z ≽x, λy + (1−λ)z ≻x for any λ∈(0,1).
averages are strictly better than extremes.
why we use strict covexity?
Even if it’s not wrong to have them, there are reasons why we want to avoid indifference curves that have flat areas.
To do this, we use a stronger version of the convexity assumption, called strict convexity.
Implications of the different properties for indifference curves
- Completeness: there is an indifference curve passing through every possible bundle.
- Nonsatiation: bundles on indifference curves that are farther from the origin are
preferred to those closer to the origin. This reflects the idea that more of the goods is always better. - Transitivity: indifference curves cannot cross.
- Nonsatiation: Indifference curves must be downward sloping and cannot be thick. A thick indifference curve would imply that two different bundles are equally preferred, which contradicts the assumption of more goods being better.
- Strict Convexity: Indifference curves are bowed upward
RATIONAL vs WELL-BEHAVED preferences
- If the preferences are complete and transitive, the preference is RATIONAL
- if the preferences are monotone and strictly convex, the preference is WELL BEHAVED
