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| What does the theory of consumer choice focus on? | How consumers with limited resources choose goods and services |
| Why do we study consumer preferences? | To understand how a consumer compares (or ranks) the desirability of different sets of goods= If we ignore the costs of purchasing the goods, consumer preferences indicate whether the consumer likes one particular set of goods better than another (assuming that all goods can be "purchased" at no cost) |
| When goods are costly.... | a consumer's income limits the sets of goods they can purchase |
| Why do businesses care about consumer demand curves? | Because they reveal how much a consumer is willing to pay for a product |
| In a modern economy, consumers can.... | Purchase a vast array of goods and services |
| Market Basket | (aka BUNDLE) Is a collection of goods and services that an individual might consume (EX: 1 basket might include 2 jeans, 3 pairs of shoes, and 1 gun vs. another bundle containing 4 jeans, etc.)= A basket might also contain only one good |
| Consumer Preferences | Tell us how an individual would rank (i.e. compare the desirability of) any two baskets, assuming the baskets were available at no cost (in actuality, there are many factors influencing consumer preferences) |
| Consumer Behavior: Rational vs. Irrational | It is important to understand that consumers behave rationally under most circumstances |
| Assumptions about Consumer Preferences | 1) Preferences are complete= 2) Preferences are transitive= 3) More is better |
| Assumptions about Consumer Preferences: Preferences are Complete | (One of the 3 assumptions) Assumes that the consumer is able to rank any 2 baskets (She prefers basket A to basket B [written A>B]; She prefers basket B to basket A [written B>A]; she is indifferent between, or ewually happy with, baskets A and B [written A≈B]) |
| Assumptions about Consumer Preferences: Preferences are Transitive | (One of the 3 assumptions) Assumes that the consumer makes choices that are consistent with each other= EX: If a consumer tells us that she prefers basket A to basket B, and Basket B to basket E, we can then expect her to prefer basket A to basket E= We can represent transitivity as follows: [If A>B and if B>E, then A>E] |
| Assumptions about Consumer Preferences: More is Better | (One of the 3 assumptions) Assumes that having more of a good is better for the consumer |
| Ordinal Rankings | Give us information about the order in which a consumer ranks baskets= An ordinal ranking however would not tell us HOW MUCH MORE a consumer likes basket A than D |
| Cardinal Rankings | Give us information about the intensity of a consumer's preferences= With a cardinal ranking, we not only know that she prefers basket A to basket D, but we can also measure the strength of her preference for A over D= We can make a quantitative statement, such as "The consumer likes basket A twice as much as basket D" (a Cardinal Ranking thus contains MORE info than an Ordinal Ranking) |
| Importance of measuring the amount of pleasure a consumer gets from a basket | Is not all that important= Although we often use a CARDINAL RANKING to facilitate exposition, an ordinal ranking will normally give us enough info. to explain a consumer's decisions |
| Utility Function | (The three consumer preferences assumptions allow us to represent preferences with a utility function) Measures the level of satisfaction tha a consumer receives from any basket of goods= Can represent the utility function with algebra or a graph |
| Utility Function: Example | Let y denote "the # of burgers she purchases each week"= Let U(y) measure the level of satisfaction (or UTILITY) that Sarah derives from purchasing y hamburgers |
| Marginal Utility | (MU) While studying consumer behavior, we often want to know how the level of satisfaction will CHANGE (∆U) in response to a CHANGE in the level of consumption (∆y), where ∆ is read as "the change in"= Economists refer to the rate at which total utility changes as the level of consumption rises as the MARGINAL UTILITY (MU) |
| The Marginal Utility of good y | (MUy)= ∆U/∆y |
| How is the marginal utility at a particular point represented? | Represented by the SLOPE of a line that is tangent to the utility function at that point= Since the slopes of the tangents change as we move along the utility function U(y), Sarah's marginal utility will depend on the quantity of hamburgers she has already purchased= In this respect, Sarah is like most people: the additional satisfaction that she receives from consuming more of a good depends on how much of the good she has already consumed |
| Marginal Utility: Additional Satisfaction | The additional satisfaction that a consumer gets from consuming more of a good depends on how much of the good she has already consumed |
| Marginal Utility: Graph | [MU graph is simply the first deriv. of U(y)] The equation/graph reflects the precise way in which marginal utility depends on the quantity y |
| Drawing Total Utility and Marginal Utility Curves | 1) Total Utility and Marginal Utility CANNOT be plotted on the same graph= 2) The marginal utility is the slope of the (total) utility function= 3) The relationship between total and marginal functions holds for other measures in economics |
| Why can't total utility and marginal utility curves be plotted on the same graph? | Although the horizontal axes are the same for each graph (e.g. both representing the number of hamburgers consumed each week, y), the vertical axes for the two graphs are NOT the same (total utility has the dimensions of U(whatever that may be), while marginal utility has the dimension of utility per hamburger [∆U divided by ∆y]) |
| What does "The marginal utility is the slope of the (total) utility function" mean? | The slope at any point on the total utility curve is ∆U/∆y, the rate of change in total utility at that point as consumption rises or falls, which is what marginal utility measures (note that ∆U/∆y at any point is also the slope of the line segment tangent to the utility cure at that point) |
| What does "the relationship between total and marginal functions holds for other measures in economics" mean? | The value of a MARGINAL function is often simply the slope of the corresponding TOTAL function |
| Principle of Diminishing Marginal Utility | Says that after some point, as consumption of a good increases, the marginal utility of that good will begin to fall (is exemplified in/with Diminishing Marginal Utility [e.g. a declining marginal utility graph]) |
| Diminishing Marginal Utility= What does it reflect | Reflects a common human trait: The more of something we consume, the less ADDITIONAL satisfaction we get from additional consumption= Marginal utility may not decline after the first/second/etc. unit, but it will normally fall after some level of consumption |
| Understanding the principle of diminishing marginal utility | Suppose you have already eaten 1 burger this week= If you eat a 2nd burger, your utility will go up by some amount= THIS IS THE MARGINAL UTILITY OF THE SECOND BURGER!!!= If you have already eaten 5 burgers this week and are about to eat a 6th, the increase in your utility will be the marginal utility of the 6th burger= If you're like most people, the MU of your 6th burger will be less than the MU of the 2nd burger (in that case, your MU of burgers is diminishing) |
| What does the assumption that "more is better" imply about MU? Is it true? | Says that Total Utility must increase as consumption of the good increases (i.e. the MU of that good must always be positive)= In reality, this assumption is not always true= However, it is still reasonable to assume that more is better for amounts of a good that a consumer might actually purchase (EX: we wouldn't normally need to draw the utility function for the 7 burgers= The consumer would never consider buying more than 7 burgers because it would make no sense for hr to spend money on burgers that reduce her satisfaction) |
| Extending the concept of marginal utility to the case of multiple goods | The marginal utility of any one good is the rate at which total utility changes as the level of consumption of that good rises, holding constant the levels of consumption of all other goods= EX: In the case where only 2 goods are consumed and the utility function is U(x,y), the marginal utility of food (MUx) measures how the level of satisfaction will change (∆U) in response to a change in the consumption of food (∆x), holding the level of y constant: {MUx= [∆U/∆x]|y is held constant}= Similarly, the marginal utility of clothing (MUy) measures how the level of satisfaction will change (∆U) in response to a small change in the consumption of clothing (∆y), holding constant the level of food (x): {MUy= [∆U/∆y]|x is held constant} |
| How can you determine whether the marginal utility of a good is positive? | First, you can look at the total utility function= If it increases when more when more of the good is consumed, the marginal utility is positive= Second, you can look at the marginal utility of the good to see if it is a positive number= When the marginal utility is a positive number, the total utility will increase when more of the good is consumed |
| Indifference Curve | A curve connecting a set of consumption baskets that yield the same level of satisfaction to the consumer= The consumer would be equally satisfied with (or INDIFFERENT in choosing among) all baskets on that curve |
| Indifference Map | (Is the simple 2D graph showing indifference curves) Are called this because it shows a set of indifference curves |
| Indifference Curves on an Indifference Map: 4 Properties | 1) When the consumer likes both goods (i.e., when MUx and MUy are both positive), all the indifference curves have a negative slope= 2) Indifference curves cannot intersect= 3) Every consumption basket lies on one and only one indifference curve= 4) Indifference curves are not "thick" |
| "When the consumer likes both goods (i.e. when MUx and MUy are both positive), all the indifference curves will have a negative slope": Meaning | Suppose the consumer has basket A= Since the consumer has positive marginal utility for both goods, she will prefer any baskets to the north, east, or northeast of A (because then she would have more of either x, y, or both x and y)= We indicate this in the graph by drawing arrows to indicate preference directions= The arrowing point to the east reflects the fact that MUx>0= The arrow pointing to the north reflects the fact that MUy>0 |
| Preference Directions: Arrow pointing to the East | Reflects the fact that MUx>0 |
| Preference Directions: Arrow pointing to the North | Reflects the fact that MUy>0 |
| Points to the northeast or southwest of point A on an indifference curve | Cannot be on the same indifference curve as A because they will be preferred to A or less preferred than A, respectively (i.e. depending on if more/less of X & Y are/is better) |
| Where must points on the same indifference curve as point A lie? What does this show? | Either to the northwest or southeast of A= This shows that indifference curves will have a negative slope when both goods have positive marginal utilitites |
| "Indifference curves cannot intersect": Meaning | (see pg. 81) |
| "Every consumption basket lies on one and only one indifference curve": Meaning | This follows from the property that indifference curves cannot intersect= However, even though a point can lie on two curves ONLY at a place where the 2 curves intersect, because indifference curves CANNOT intersect, every consumption basket MUST lie on a SINGLE indifference curve |
| "Indifference curves are not "thick"": Meaning | This is because if a thick indifference curve passed through 2 baskets (e.g. A and B), and B is to the northeast of A, then B is actually preferred to A because B must have a higher utility than A= Thus, A and B CANNOT be on the same indifference curve |
| Marginal Rate of Substitution | The rate at which the consumer will give up one good to get more of another, holding the level of utility constant (i.e. is a consumer's willingness to substitute one good for another while maintaining the same level of satisfaction)= EX: Consumer's marginal rate of substitution of burgers for lemonade is the rate at which teh consumer would be willing to give up glasses of lemonade to get more hamburgers, with the same overall satisfaction |
| Marginal Rate of Substitution: How is the trade-off that the consumer is willing to make between the two goods illustrated when the 2 goods have positive marginal utilities? | Is illustrated by the slope of the indifference curve |
| Marginal Rate of Substitution of X for Y | (MRSx,y) Is the rate at which the consumer is willing to give up y in order to get more of x, holding utility constant= n a graph with x on the horizontal axis and y on the vertical axis, MRSx,y at any basket is the negative of the slope of the indifference curve through that basket (EX: At basket A the slope of the indifference curve is -5, so MRSx,y=5 [i.e. he would give up 5 glasses of lemonade for 1 additional burger]) |
| How else can we express the marginal rate of substitution for any basket? | As a ratio of the marginal utilities of the goods in that basket= EX: Consider basket A on the indifference curve U1; suppose the consumer changes the level of consumption of x and y by ∆x and ∆y= The corresponding impact on utility ∆U will be: [ ∆U= MUx(∆x) + MU∆y(∆y) ]= HOWEVER, it must be that ∆U=0 because changes in x and y that move us along the indifference curve U1 must keep utility unchanged= So 0=MUx(∆x) + MUy(∆y), which can be rewritten as MUy(∆y)= -MUx(∆x)= We can now solve for the slope of the indifference curve ∆y/∆x |
| How do you solve for the slope of the indifference curve ∆y/∆x | [∆y/∆x]|holding the utility constant = -MUx/MUy |||||=Because MRSx,y is the negative of the slope of the indifference curve, we observe that: [-∆y/∆x]|holding utility constant = MUx/MUy = MRSx,y |
| For many (but not all) goods, what happens to MRSx,y as the amount of x increases along an indifference curve | For many (but not all) goods, MRSx,y diminishes as the amount of x increases along an indifference curve |
| Diminishing Marginal Rate of Substitution | A feature of consumer preferences for which the marginal rate of substitution of one good for another good diminishes as the consumption of the first good increases along an indifference curve (i.e. Diminishing marginal rate of substitution of x for y means that the marginal rate of substitution of x for y DECLINES as Eric increases his consumption of x along an indifference curve)= EX: If on indifference curve U1 at point A Eric consumes much lemonade and few burgers, MRSx,y will be high because he would probably give up much lemonade for just 1 more burger= However, if at point D Eric is consuming many burgers and few lemonades, MRSx,y will be less than at A because he wouldn't really want to give up any more of his little lemonade just to get another burger) |
| What does diminishing marginal rate of substitution of x for y imply about the shape of the indifference curves? | Remember that the marginal rate of substitution of x for y is just the negative of the slope of the indifference curve on a graph with x on the horizontal axis and y on the vertical axis= If MRSx,y diminishes as the consumer increases x along an indifference curve, then the slope of the indifference curve must be getting flatter (less negative) as x increases= THEREFORE, indifference curves with diminishing MRSx,y must be bowed in toward the origin |
| Indifference curves with INCREASING MRSx,y | If the MRSx,y is higher at basket H than at basket G, then the slope of indifference curve U1 will be more negative (steeper) at H than at G (**see pg. 87)= Thus, with increasing MRSx,y, the indifference curves will be bowed away from the origin |
| What happens when a consumer views 2 products as PERFECT SUBSTITUTES? | If a consumer views 2 products (EX: Coke and Pepsi) as perfect substitutes and is always willing to substitute a glass of one for a glass of the other, then the marginal rate of substitution of Coke for Pepsi will be CONSTANT and equal to 1 |
| Perfect Substitutes | 2 goods such that the marginal rate of substitution of one good for the other is constant (is not necessarily 1); therefore, the indifference curves are straight lines |
| Perfect Substitutes: EX: Suppose David likes both butter (B) and margarine (M) and that he is always willing to substitute a pound of either commodity for a pound of the other | Then [MRSb,m= MRSm,b= 1]= We can use a utility function such as U=aB + aM, where "a" is any positive constant, to describe these preferences (with this utility function, MUb= a and MUm= a; it also follows that MRSb,m= MUb/MUm = a/a = 1, and the slope of the indifference curves will be constant and equal to -1) |
| More generally, indifference curves for perfect substitutes.... | Are straight lines, and the marginal rate of substitution is constant, though not necessarily equal to 1 |
| Perfect Substitutes: EX: Suppose a consumer likes both pancakes and waffles and is always willing to substitute 2 pancakes for 1 waffle | A utility function that would describe his preferences is U= P + 2W, where P is the # of pancakes and W is the # of waffles= With these preferences, MUp=1 and MUw=2, so each waffle yields TWICE the MU of a single pancake= We also observe that [MRSp,w= MUp/MUw= 1/2]= Since MRSp,w= 1/2, on a graph with P on the horizontal axis and W on the vertical axis, the slope of the indifference curve is -1/2 |
| Indifference Curves with perfect Substitutes | A consumer with the utility function U= P + 2W always views 2 pancakes as a perfect substitute for 1 waffle; MRSp,w= 1/2, and so indifference curves are straight lines with a slope of -1/2 |
| Perfect Complements | Perfect Complements (in consumption) are 2 goods that the consumer always wants to consume in fixed proportion to each other (EX: 1 left shoe for every 1 right shoe= there is no benefit for having an extra left shoe than 1 right shoe= Shows that the consumer derives satisfaction form complete pairs of shoes, but gets no added utility from extra right shoes or extra left shoes)= The indifference curves in this case comprise straight-line segments at right angles (**see pg. 89)= So, perfect complements are goods that the consumer always wants in fixed proportion to each other (e.g. 1:1) |
| Perfect Complements: EX: Left Shoes (L) and Right Shoes (R) | A utility function for these perfect complements is U(R,L)= 10min(R,L), where the notation "min" means "TAKE THE MINIMUM VALUE OF THE TWO NUMBERS IN PARENTHESES"= EX: At basket G, R=2 and L=2; so the minimum of R and L is 2, and U= 10(2)=20; At basket H, R=3 and L=2, so the minimum of R and L is still 2, and U=10(2)=20; MEANING: Shows that baskets G and H are on the same indifference curve, U2 (where U2=20)= (see pg. 90) |
| Cobb-Douglas Utility Function | A function of the form U= Ax^[α]y^[β], where U measures the consumer's utility from x units of one good and y units of another good and where A, α, and β are positive constants= (The utility functions U=(xy)^[1/2] and U=xy are examples of the Cobb-Douglas Utility Function) |
| Cobb-Doublas Utility Function: 3 Properties | 1) The marginal utilities are positive for both goods (the marginal utilities are MUx=αAx^(α-1)y^[β] and MUy= βAx^(α)y^(β-1); thus both MUx and MUy are positive when A, α, and β are positive constants= This means that "the more is better" assumption is satisfied)= 2) Since the marginal utilities are both positive, the indifference curves will be downward sloping= 3) The Cobb-Douglas utility function also exhibits a diminishing marginal rate of substitution (the indifference curves will therefore be bowed in toward the origin) |
| Quasi-Linear Utility Function | A utility function that is linear in at least one of the goods consumed, but may be a nonlinear function of the other good(s)= Such functions may reasonably approximate consumer preferences in many settings (EX: can describe preferences for a consumer who buys the same amount of a good regardless of his income) |
| Quasi-Linear Utility Function: Indifference Curve | The distinguishing characteristic of a quasi-linear utility function is that as we move due north on the indifference map, the marginal rate of substitution of x for y remains the same (i.e. at any value of x, the slopes of all of the indifference curves will be the same)= RESULT: The indifference curves are parallel to each other= This utility function is linear in y, but generally not linear in x (this is why its called quasi-linear) |
| Quasi-Linear Utility Function: Equation | U(x,y)= v(x) + by, where "b" is a positive constant and v(x) is a function that increases in x (i.e. the value of v(x) increases as x increases [EX: v(x)= x^2 or v(x)= √x])= This utility function is linear in y, but generally not linear in x (this is why its called quasi-linear) |
