ECON 410 Consumer Theory

budget line

set of all bundles which exhaust income

budget set

set of all bundles under and including the budget line

model of consumer theory

• budget constraints

• tastes or preferences

• maximizes well-being

marginal rate of transformation (MRT)

absolute value of the slope of the budget line

MRT formula

Px/Py

3 ways to interpret MRT

• how much y a consumer must trade for one more unit of x

• the opportunity cost of buying x in terms of y

• the relative price of x in terms of y

bigger MRT means?

steeper slope

smaller MRT means?

flatter slope

properties of preferences

• completeness

• transitivity

• more is better

completeness

when facing a choice, a consumer can rank them so that either a>b, b>a, or a - b

transitivity

consumers rankings are logically consistent in the sense that if a>b, b>a, then a>c

more is better

all else the same, more of a commodity is better than less

rational preferences

preferences are rational if they are complete and transitive

indifference curve

graphical set of all bundles of goods that an individual views as equally desireable

indifference map

a complete set of indifference curves that summarize a consumer’s tastes

if preferences are rational and monotonic, 4 properties must hold

• every bundle lies on an IC curve

• bundles on IC’s farther from the origin are preferred to those on IC’s closer to origin

• IC’s cannot cross

• IC’s cannot slope upward

what does the curvature of the indifference curve signify?

the rate at which an individual is willing to tradeoff between two goods

utility

a set of numerical values that reflect the relative rankings of various bundles of goods

utility function

the mathematical relationship between utility measurers and every possible bundle of goods

what measure is utility?

an ordinal measure

examples of monotonic transformations

• adding a constant

• multiplying by a positive constant

• assuming each good is positive, raising to a positive power

• natural log/exponential

perfect substitutes utility function

• used to represent two goods a consumer views as perfect goods for one another

• consumer always willing to substitute one good for another at the same rate

perfect complements utility function

• used to represent preferences for two goods that must be consumed in a fixed proportion

• a consumer is completely unwilling to substitute one good for another

• more of one good without more of another does not change utility

cobb douglas utility function

represents complete transitive, monotonic, and convex preferences

quasilinear utility function

• can describe preferences for a consumer who purchases the same amount of a good regardless of their income

• the MRS is a function of only one of the goods

marginal rate of substitution (MRS)

• absolute value of the slope of an IC

• MRS of x for y measures the amount of y a consumer is wiling to trade for one more unit of x to remain as well off

MRS formula

= ΔY/ΔX

marginal utility

extra utility a consumer gets from consuming the last unit of a good

marginal utility of x formula

= MUx = du/dx

marginal utility of y formula

= MUy = du/dy

if MUx/y > 0

x/y is a “good” good

if MUx/y = 0

x/y is a “neutral” good

if MUx/y < 0

x/y is a “bad” good

slope of IC if x = “good” and y = “good”

downward

slope of IC if x = “bad” and y = “bad”

downward

slope of IC if x = “good” and y = “bad”

upward

slope of IC if x = “bad” and y = “good”

upward

slope of IC if x = “good” and y = “neutral”

vertical

slope of IC if x = “bad” and y = “neutral”

vertical

slope of IC if x = “neutral” and y = “good”

horizontal

slope of IC if x = “neutral” and y = “bad”

horizontal

explanation of downward sloping IC

to keep utility constant, you must consume less of good Y as you consume more of good X

explanation of upward sloping IC

to keep utility constant, you must consume more of good Y as you consume more of good X

explanation of vertical sloping IC

utility does not change as you consume less or consume more of good Y

explanation of horizontal sloping IC

utility does not change as you consume less or consume more of good X

perfect substitute general utility function

U(x,y) = ax + by

perfect complement general utility function

U = (x,y) = min (ax,by)

cobb douglas general utility function

U(x,y) = cx^ay^b

quasilinear general utility function

• U(x,y) = f(x) + ay

• U(x,y) = ax + f(y)