## Rationality in Economics - Behavioral Postulates

• A decision maker knows what he/she likes/enjoys and chooses his/her most preferred alternative among the available ones.

• To say something about his/her behavior, we must model decision makers’ preferences.

## Basics of Preferences Relations

John: apple better than Mango, apple better than banana, mango better than banana.

## Basics of Preferences Relations

Alí, Bob, Carlos, ... , John, ... ,Wei

...

## Basics of Preferences Relations

• Preferences are a personal ranking of alternatives.

• Preferences are a personal assignment of satisfaction level (utility).

## Preference Relations

Comparing two different consumption bundles, $x$ and $y$ in the consumption space:

• Strict preference "$x \succ y$" : x is strictly more preferred than is y

• Weak preference "$x \succsim y$" : x is as at least as preferred as is y

• Indifference "$x \sim y$" : x is equally preferred as is y

## Assumptions on Preference Relations (1): Completeness

• Completeness: For any two bundles x and y it is always possible to make the statement that either

• $x \succsim y$ or $y \succsim x$

## Assumptions on Preference Relations (2): Transitivity

• Transitivity:

• If x is at least as preferred as y, and
• y is at least as preferred as z, then:
• x is at least as preferred as z.
• That is, if $x \succsim y$ and $y \succsim z$ implies $x \succsim z$

## Preferences in the Commodity Space

• Recap: the Commodity Space is the positive quadrant of the n-dimensional plane ($\Re_{+}^n$) where these baskets or bundles live.

## Indifference Curves or Indifference Sets

• Indifference Curves or Indifference Sets (of consumer i):

• A set of bundles that a consumer regards as equal.

• Take bundle $x$. The set of all bundles equally preferred to $x$ makes the "indifference curve" containing $x$. We denote this set by $I(x)$.

• All the bundles $y$ in this set have this property: $y \sim x$.

• Since an indifference “curve” is not necessarily a "curve", we might want to call it indifference “set”.

## Indifference Curve (example)

• E.g.: $(3, 4) \sim (1, 12)$

## Weakly preferred set WP(x)

• WP(3,4) is the shaded area

## Assumption on Preferences (3): More is better (monotoniticy)

More is Better / Monotonicity: * All else the same, more of a “good” commodity is better than less. * $(5.01, 20) \succ (5, 20)$

## Assumption on Preferences (3): More is better (monotoniticy)

• This assumption implies that indifference sets are:
• Curves! (not thick bands)
• Downward sloped! (think about it)

## Is there only one indifference curve?

• No! Typically, there are infinite.

• In most cases it makes sense we talk and draw several ("the indifference map").

## Goods Vs. Bads Vs. Neutrals

Assume $x_2$ is a good: more is better.

Draw and IC for each case:

• $x_1$ is a good.

• $x_1$ is a bad.

• $x_1$ is a neutral.

## Home exercise:

• Can two distinct indifference curves cross each other?

## Assumption on Preferences (4): Convexity

(Weak) Convexity:

• Mixtures of bundles are (weakly) preferred to the bundles themselves.

• Example: If the 50-50 mixture of the bundles $x$ and $y$ is formed like this $z = (0.5) x + (0.5)y$. Then $z$ is at least as preferred as $x$ OR $y$.

## Assumption on Preferences (5): Convexity

• Example of preferences that do not satisfy convexity

## Slope of an Indifference Curve

• The slope of an indifference curve is its marginal rate-of-substitution or MRS.

• MRS is the rate at which the consumer is only just willing to exchange/substitute commodity 2 for a small amount of commodity 1.

• $MRS = \frac{d x_2} {d x_1}$ along one indifference curve.

## Types of Preferences: Perfect Substitutes

• If a consumer always regards units of commodities 1 and 2 as equivalent (or equivalent up to a fixed ratio), then these commodities are regarded as perfect substitutes for the consumer.

• Example: if you like Coke and Pepsi exactly equally, the total amount of bottles is what matter for the consumer. Another example: Agave - Sugar

## Types of Preferences: Perfect Complements

• If a consumer always consumes commodities 1 and 2 in fixed proportion (e.g. one-to-one), then the commodities are perfect complements to the consumer.

• Only the number of pairs in the fixed proportion matter to the consumer. Examples?

## MRS

• Think about the MRS in Perfect Substitutes

• Think about the MRS in Perfect Complements