Intermediate Micro Midterm 1

3 components of consumer choice

• preferences

• constraints

• optimization

bundle

• a consumer’s choice of consumption

• describes the quantities of goods consumed

• can be written as (x₁, x₂) where x₁ and x₂ represent 2 different goods

budget constraint

• the set of bundles that exhaust the consumer’s income at given prices

• P_xX + P_yY = I

budget set

• the budget set contains all bundles the consumer can afford

• P_xX + P_yY ≤ I

relationship between bundles and location on the budget line

• bundles ON the budget line exhaust income

• bundles INSIDE the budget line cost less than income

• bundles OUTSIDE the budget line cost more than income

why is the slope of the budget line negative?

• scarcity! to obtain one more unit of x, the consumer must give up P_x/P_y units of y

budget equation in linear equation form

Y = (I/P_y) - (P_x/P_y)x

what does the y-intercept of the budget line equation represent?

• the y-intercept is the maximum amount of y the consumer can purchase if the consumer spends all income on y

• same for x and x-intercept

real income/purchasing power increases if…

• no previously affordable bundles are lost AND

• some new bundles become affordable

real income/purchasing power decreases if…

• some previously affordable bundles are lost AND

• no new bundles become affordable

composite good

• represents spending on all goods other than the particular good we are studying

preference ordering

ranks bundles from more desirable to less desirable

completeness

• preferences are complete if the consumer can compare any two bundles

• doesn’t necessarily tell us which bundle the consumer prefers, it just says the consumer can rank them

• for any two bundles, A and B, one of the following must be true:

  • A > B

  • B > A

  • A ~ B

Transitivity

• rankings of bundles are internally consistent

• if A > B and B > C then A > C

rational preferences

• these are preferences that are complete and transitive

monotonicity

• for goods, we usually assume that more is better

• if bundle A contains at least as much of every good as bundle B, and more of at least one good, then A > B

• caveat: this assumption only holds for goods, not bads

convexity

• we typically assume consumers prefer balanced combinations to extreme bundles

• if A and B are equally attractive, then a mixture of A and B is at least as good as either extreme

utility function

• a mathematical way to represent preferences

• a utility function assigns a number to every possible bundle

• high utility means the bundle is ranked more highly

utility

• measures the total satisfaction, pleasure, or value a consumer gets from consuming a good or service

• utility is ordinal - the ranking matters, but the numerical distance doesn’t really matter

marginal utility

• measures how utility changes when the consumption of one good increase slightly, holding the other good constant

• we solve for this using partial derivatives

diminishing marginal utility

as we consume more of a good, the additional utility from consuming each additional unit of that good decreases

indifference curve

• the set of consumption bundles that provide the same level of utility

• a graphical representation of preferences

preference assumptions and indifference curves

• completeness - every bundle has an indifference curve passing through it

• monotonicity - indifference curves are downward sloping, indifference curves further from the origin are better (because they represent a higher level of utility

• transitivity - indifference curves cannot cross

• convexity - indifference curves become flatter as we move down and to the right

marginal rate of substitution

• the MRS of x for y is the amount of y the consumer is willing to give up to get one more unit of x while remaining equally well off (aka utility stays the same)

• graphically, MRS is the negative of the slope of the indifference curve at a point

• MRS = - (dy/dx) - MU_x/MU_y