midterm one definitions

Budget Set

Given prices (P1, P2) and m, the budget set is the set of all affordable bundles. That is all (x1, x2) such that ((P1)(X1))+ ((P2)(X2)) is less than or equal to m.

Budget line

The set of bundles that cost exactly m.

Completeness

Any 2 bundles can be compared. Given any bundles (x₁, x₂) and (y₁,y₂), we assume that (x₁, x₂) ≿ (y₁,y₂) or (y₁,y₂) ≿ (x₁, x₂) or both. In which case the consumer is indifferent between them.

Reflexive

Any bundle is at least as good as itself: (x₁, x₂) ≿ (x₁, x₂), or (x₁, x₂) ~ (x₁, x₂).

Transitive

• If (x₁, x₂) ≿ (y₁,y₂) and (y₁,y₂) ≿ (z₁,z₂) then (x₁x₂) ≿ (z₁,z₂).

  • Along with the previous assumptions, transitivity implies that when a consumer faces a list of bundles, they can rank-order the bundles. (XYZ)

Monotonicity

More is better —> If y₁ ≿ x₁, and y₂ ≿ x₂, and at least one of these inequalities is strict (≻), then it must be that (y₁, y₂) ≻ (x₁, x₂) → Indifference curves have a negative slope

Convexity

Given t between 0 and 1, if (x₁, x₂) ~ (y₁, y₂), then (tx₁+ (1-t)y₁, tx₂ + (1-t)y₂) ≿ (x₁,x₂) —> balanced bundle is better than extremes

Marginal rate of substitution

rate at which consumer can substitute between two goods while remaining indifferent

For well-behaved preferences, MRS is:

• negative — consumer is willing to give up some of good one to get more of the other

• diminishing — the less consumer has of Good 1, the more consumer is willing to give up of Good 2 to getmore of Good 1

Utility is ordinal

the utility number assigned doesn’t matter, we just compare utilities between bundles to see which is preferred

Normal good

more income, higher demand

Inferior good

more income, lower demand

Ordinary good

own price goes down, demand goes up

Giffen good

own price goes down, demand goes down