Review Sheet for Consumer Theory - Intermediate Microeconomics

how do you find elasticity?

% change in q over % change in p

What is the slope of the budget constraint?

-Px/Py

What four things do the properties of preferences imply about the shape of indifference curves?

1. When consumers like both goods, the indifference curve has a negative slope, and in order to have on good, you have to give up some of the other. 2. Indifference curves cannot intersect, they must be parallel 3. Every basket lies on one and only one indifference curve because each basket has a unique level of utility 4. Indifference curves are not thick, or else you could have two points with different amounts of utility on the same curve (which should not happen!)

factors that influence elasticity

1. more substitutes = higher elasticity because it's easy to switch 2. when the product represents a significant portion of buyers' expenditure, then you will be more responsive so more elastic 3. market level vs. brand level (market level is less elastic, brand level is more elastic) 4. necessities vs. luxuries (necessities are less elastic, luxuries are more elastic) 5. long run vs. short run (long run is more elastic, short run is less elastic)

What are the assumed properties of preferences?

1. preferences are complete (meaning that someone can definitely tell you what they prefer, they can actually rank them) 2. preferences are transitive (if A is preferred over B, and B is preferred over C, then A is preferred over C) 3. more is better

What is the relationship between marginal utility and marginal rate of substitution?

MRS can be written as MUx/MUy

How are MU and TU related?

MUx > 0, then TU is increasing MUx = 0, then TU = maximum MUx < 0, then TU is decreasing

What are preferences?

consumer preference: tells us how an individual would rank (compare the desirability of) any two baskets we assume that there is no cost and that people are rational

does MRS increase or decrease as we consume more x?

decrease

Where do demand curves come from? Know the algebra of deriving a demand curve.

demand curves come from the horizontal price consumption curve. To find an equation for a demand curve, 1. set up the tangency MUx/MUy = Px/Py 2. cross multiply 3. isolate PyY 4. substitute into the budget line x = I/2px y = I/2py

what are the inequalities for elastic demand, inelastic demand, and unitary elastic?

elastic demand: E>1 inelastic demand: E<1 unitary elastic: E=1

inelastic vs. elastic demand

elasticity > 1 .... elastic demand elasticity < 1 .... inelastic demand elasticity = 1 .... unitary elastic

cross price elasticity

elasticity for two goods percent change in quantity demanded over percent change in price E>0, as P goes up and Q goes up (substitutes) E<0, as P goes up and Q goes down (complements)

What is an optimal choice point?

finding a basket of goods that maximizes the consumer's satisfaction (utility) while living within their budget

ordinal ranking

gives us information about the order in which a consumer ranks baskets, but it does not tell us by how much they like one more than the other

what is price elasticity?

how we react to a price change, or our responsiveness

definition and equation of elasticity

how we react to a price change, or our responsiveness elasticity formula: change in Q/change in P * p/q

relationship between elasticity and total revenue

if demand is elastic, change in price triggers a larger change in quantity (and for elastic goods, Q and TR move in the same direction) if demand is inelastic, change in P triggers a smaller change in quantity (and for inelastic goods, P and TR move in the same direction)

income elasticity

is how responsive we are with Qd when the income changes (percent change in Q over percent change in I) E>0, Q goes up as I goes up (normal good) E<0, Q goes down as I goes up (inferior good)

what does it mean if the slope of the IC < slope of the budget line?

means MUx/Px < MUy/Py bang for the buck is < for x, so you should get more y and less x

what does it mean if the slope of the IC > slope of the budget line?

means MUx/Px > MUy/Py bang for the buck is > for x, so you should get more x and less y

be able to define and graph the income and substitution effects for the following types of goods a. normal good b. inferior good c. giffen good

normal good: c to the right of a and b inferior good: c in between a and b giffen good: c to the left of a and b income effect: when Px goes down, your purchasing power goes up, so you feel wealthier, and you have more money in your pocket, which means you will have more of all goods substitution effect: When Px goes down, you substitute away from other goods and consume more x, which is relatively cheaper so you are equally happy

price consumption curve

series of optimal choice points as Px changes

income consumption curve

series of optimal choice points as income varies, holding prices constant (goes with the engel curve)

What is a budget constraint? What is the equation?

set of baskets that a consumer can purchase with a limited amount of income PxX + PyY <= I

engel curve

shows the relationship between income and consumption of good x

market demand definition and graph

sum of demand of all consumers graphically, it is a horizontal summation of all individual demand curves (add up the x's that go with the same price horizontally to get the market demand)

cardinal ranking

tells us by how much one good is liked more than the other, and gives intensity of preference when ranking baskets

What is the mathematical relationship between the budget constraint and the indifference curve at the optimal choice point for Cobb-Douglas preferences?

the budget line is tangent to the indifference curve, which means that at the optimal point, the budget line slope = the slope of the indifference curve also, MUx/Px = MUy/Py at the equilibrium This is saying that at the equilibrium, the additional utility per dollar spent on good x must equal the additional utility per dollar spent on good y (bang for the buck must be the same for both goods at the equilibrium point)

relationship between price consumption curve and demand curve (graph)

the demand curve shows changes in x* as the price of x changes the demand for x and price are related inversely. you can't have y in the demand function for x. remember that the demand for x is a function of Px, not y; and income is exogenous, so it is okay to have it there

What is the marginal rate of substitution?

the willingness to trade one good for another is measured by this. It's the rate at which the consumer gives up y for x and keeps utility unchanged. It is also the absolute value of the slope of the indifference curve. as we consume more x, MRS decreases

relationship between an income consumption curve and engel curve for an inferior good (graph)

they are both downward sloping, so as income increases, x decreases

relationship between an income consumption curve and engel curve for a normal good (graph)

they are both upward sloping, so as income increases, x increases

elasticity in a linear demand curve

upper half is > 1 (elastic) midpoint is = 1 (unitary elastic) lower half is < 1 (inelastic)

giffen good

when Px goes down, X goes down for example, a designer purse could be a giffen good because people might only be buying it because of its expensiveness, so when the price drops, the demand for the purse drops

consumer surplus definition and what the graph would look like

benefits that consumers get for participating in the market the equation is the willingness to pay - the price you actually paid graph: area below the demand curve and above the price

equation for perfect substitutes utility function and graph it

U(X,Y) = aX + bY

Equation for Cobb-Douglas utility function and graph it

U(X,Y) = cX^a * Y^b

equation for perfect complements utility function and graph it

U(X,Y) = min{aX, bY}

What is marginal utility?

additional satisfaction from consuming one additional unit of the good, and it the rate at which total utility changes as x changes (change in TU / change in x)

What is an indifference curve?

all the combinations of two goods x and y that yield the same level of utility (everything that lies on the same IC give you the same level of satisfaction)

What is an in-kind transfer as compared to a cash grant? What circumstances would someone want a in kind transfer, and what circumstances would someone want a cash grant?

an in-kind transfer is what the government gives you, and you can only use it for certain things. A cash grant is also something the government gives you, but you can use it for anything you want. Someone who consumes more than the subsidy doesn't care whether they get cash or the subsidy. Someone who consumes below the subsidy would rather have cash, because then they can go to a higher indifference curve