chapter 3 and 4- Consumer Preferences and the Concept of Utility

Utility function

- a function that measures the level of satisfaction a consumer receives from any basket of goods and services. - assigns a number to each basket so that more preferred baskets get a higher number than less preferred baskets. - U = u(y)

ASSUMPTIONS ABOUT CONSUMER PREFERENCES

1. Preferences are complete. That is, the consumer is able to rank any two baskets. For baskets A and B, for example, the consumer can state her preferences according to one of the following possibilities: 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 equally happy with, baskets A and B (written A = B). 2. Preferences are transitive. By this we mean that the consumer makes choices that are consistent with each other. Suppose that 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. Using the notation we have just introduced to describe preferences, we can represent transitivity as follows: If A > B and if B > E, then A > E. 3. More is better. In other words, having more of a good is better for the consumer. Suppose the consumer is considering the baskets in Figure 3.1. If more is better, she likes more food better than less food and prefers to have more clothing rather than less clothing. In that case, she would prefer basket A to E or H because she receives the same amount of clothing with these three baskets, but more food at A. She would prefer basket A to B or J because she receives the same amount of food in these three baskets, but more clothing at A. She will also prefer A to G or D because she receives more food and more clothing at A than at either of the other two baskets. Therefore, among the seven baskets, her most preferred basket is A. However, without further information about the consumer's preferences, we do not know how she would rank every pair of baskets. For example, without further information we do not know whether she prefers E to G because she would receive more food but less clothing at G.

what is a basket bundle goods?

A combination of goods and services that an individual might consume.

Definition and Formula: Marginal Utility

Additional utility that the consumer gets from consuming a little more of good y. (when the consumption of all the other goods in the consumer's basket remain constant) U(x, y) = x+y MUy = change of Utility / change of y (x held constant) MUx = change of Utility / change of x (y held constant)

A Budget constraint example: Two goods available X and Y I = 10 Px = $1 Py = $2

All income spent on X --> I / Px units of X bought All income spent on Y --> I/Py units of Y bought --> These numbers appear on the coordination system Budget Line 1: 1X + 2Y = 10 or Y = 5 - X/2 Slope of Budget Line = -Px/Py = -1/2

How will the change in income affect the location of the budget line?

An increase in income will shift the budget line away from the origin (to the right) in the parallel fashion expanding the sets of possible baskets from which a consumer may choose. A decrease in income will shift the budget line in toward the origin in parallel fashion, reducing the set of possible baskets from which a consumer may choose.

How will a change in income affect the location of the budget line=

An increase in income will shift the budget line away from the origin in a parallel fashion expanding the set of possible baskets from which a consumer may choose. A decrease in income will shift the budget line in toward the origin in a parallel fashion, reducing the set of possible baskets from which a consumer may choose.

The same preferences as U=xy

An increasing transformation will leave the ranking of any pair of bundles unchanged. . Therefore, just plug in numbers and in case the ranking is affected than it is not the same preferences as U = xy

Defintion indifference curve

An indifference curve or indifference set: is the set of all baskets for which the consumer is indifferent. An indifference map: illustrates a set of indifference curves for a consumer.

What is the difference between ordinal ranking and cardinal ranking

An ordinal ranking simply orders the baskets, but does not give any indication as to how much better one basket is in comparison to another basket. A cardinal ranking not only order the baskets, but also provides information regarding the intensity of the preferences.

At a consumer's interior optimum solution, which of the following will not necessarily hold true when the consumer can purchase goods x and y? a) MUx = MUy b) MUx/MUy = Px/Py c) MRSx,y = MUx/MUy d) MRSx,y = Px/Py

Ans: a Response: There is no reason for the marginal utilities of the two goods to be equal. What we need is for the bang for the buck to be equal for the two goods: the extra satisfaction obtained by spending one more unit of income is the same regardless of the good on which this extra income is spent.

Suppose that the price of good A is $4, the price of B $2 and the consumer's income is $60. which of the following baskets is not on the consumer's budget line? a) A= 20, B=5 b) A= 20, B=10 c) A= 5, B= 20 d) A=15, B=0

Answer is A Formula is: Px + Py < I = 4X + 2Y = 60 a) 4(20) + 2(5)= 90 Not in budget line b) 4(10) + 2(10) = 60 c) 4(5) + 2(20)= 60 d) 4(15) + 2(0) = 60

What does the assumption that preferences are complete mean about the consumer's ability to rank any two baskets?

By requiring preferences to be complete, economist are ensuring that consumers will not respond indecisively when asked to compare two baskets. A consumer will always be able to state that either A is preferred B, B is preferred A, or that she is indifferent between A and B.

Give an example of preferences (e.g. ranking baskets) that do not satisfy the assumption that preferences are transitive.

If a consumer states that A is preferred to B and that B is preferred to C, but then states that C is preferred to A, she will be violating the assumption of transitivity. The first statement is inconsistent with the first two.

A Budget constraint example: Shift of a budget line

If income rises, the budget line shifts parallel to the right (shifts out) If income falls, the budget line shifts parallel to the left (shifts in) Y = 5 - X/2 Y = 6 - X/2

More is better regarding indifference curves

If more is better, the the indifference curves have a negative slope because any basket, A, lying to the northeast of another basket, B, must be on a higher indifference curve. Any basket, C, lying to the southwest of basket B, must be on a lower indifference curve if more is better holds (since points to the southwest of B contain less of both goods). Hence, the only points that are indifferent to point B must lie to the northwest or the southeast of B. This means that the indifference curve must have a negative slope.

More is better regarding marginal utility of a good

If more is better, then the marginal utility of a good must be positive. That is, total utility must increase if the consumer consumes more of the good.

A Budget constraint example: Rotation of a budget line

If the price of X rises, the budget line get steeper and the horizontal intercepts shifts in If the price of X falls, the budget line gets flatter and the horizontal intercept shifts out

How will an increase in the price of one of the goods purchased by a consumer affect the location of the budget line?

If the price of one of the goods increases, the budget line will rotate inward on the axis for the good with the price increase. The budget line will continue to have the same intercept on the other axis. For example, suppose someone buys two goods, cups of coffee and doughnuts, and suppose the price of a cup of coffee increases.-

consumer preferences

Indications of how a consumer would rank (compare the desirability of) any two possible baskets, assuming the baskets were available to the consumer at no cost.

Suppose Debbie purchases only hamburgers. Assume that her marginal utility is always positive and diminishing. Draw a graph with total utility on the vertical axis and the number of hamburgers on the horizontal axis. Explain how you would determine marginal utility at any given point on your graph.

Marginal utility would be measured as the slope of a tangent line to the total utility curve in the graph attached.

Key properties of indifference curves

Monotonicity: indifference curves have negative slope - and indifference curves are not "thick" Transitivity: indifference curves do not cross Completeness: each basket lies on only one indifference curve

Ordinal and cardinal ranking

Ordinal ranking simply orders the basket; one is better than the other. Cardinal ranking orders the baskets but also provides information regarding the intensity of the preferences. e.g. one basket is twice as good as another basket.

The budget constraint: Assume only two goods available X and Y

Price of x: Px Price of y: Py Income: I Total expenditure on basket (X,Y): PxX + PyY The basket is affordable if total expenditure does not exceed total income PxX + PyY < I

Slope of indifference curve at basket R Slope of budget Line

R = - MUx / MUy = - 1 BL = -Px / Py = -1/2

consumer choice

Rational choice: The consumer chooses the basket that maximises his satisfaction given the constraint that his budget imposes: Max U(X,Y) Subject to: PxX + PyY < or equal I

If the consumer has a positive marginal utility for each two goods, why will the consumer always choose a basket on the budget line?

Relatively to any point on the budget line, when the consumer has a positive marginal utility for all goods she could increase her utility for all goods she could increase her utility by consuming some basket outside the budget line. However, Baskets outside the budget line are unaffordable to her so she is constrained ( as in constrained optimization) to choosing the most preferred basket that lies along the budget line.

Complete Preferences

The assumption that a consumer is able to make a comparison between any two possible bundles of goods. A is preferred to B B is preferred to A Indifferent between A and B

Marginal Rate of Substitution

The marginal rate of substitution is the maximum rate at which the consumer would be willing to substitute a little more of good x for a little less of good y. It is the increase in good x that the consumer would require in exchange for a small decrease in good y in order to leave the consumer just indifferent between consuming the old basket or the new basket. It is the rate of exchange between goods x and y that does not affect the consumer's welfare. MRSx,y = - change of y/ change of x = MUx /MUy (for a constant level of preference)

Interior Optimum Tangent

The optimal consumption basket is at a point where the indifference curve is just tangent to the budget line. A tangent: to a function is a straight line that has the same slope as the function. Therefore... MRSx,y = MUx/MUy = Px/Py The rate at which the consumer would be willing to exchange X for Y is the same as the rate at which they are exchanges in the marketplace.

Budget Set

The set of baskets that are affordable.

Budget Line

The set of baskets that one can purchase when spending all available income. PxX + PyY = I Y = I/Py - (Px/Py)X

Budget Constraint

The set of baskets that the consumer may purchase given the limits of the available income.

Preferences that do not satisfy the assumption that preferences are transitive

Violating the assumption of transitivity, when a statement is inconsistent with another one. A is preferred to B B is preferred to C C is preferred to A => inconsistent

If a consumer is unable to compare two baskets, then this consumer's preferences violate which of the following key assumptions? a) Completeness. b) Transitivity. c) More is better. d) Both completeness and transitivity.

a) Completeness.

Wendy is very indecisive. She can't decide whether she should go on a cruise or spend her vacation at her friend's home. Her preferences violate the assumption of: a) Completeness. b) Transitivity. c) More is better. d) Both completeness and transitivity.

a) Completeness.

Which of the following statements is true? a) More is better implies that the indifference curves have a negative slope. b) Transitivity implies that indifference curves have a negative slope. c) Completeness implies that indifference curves cannot cross. d) Transitivity implies that indifference curves must be convex to the origin.

a) More is better implies that the indifference curves have a negative slope.

The assumption that preferences are complete requires the consumer a) to rank any two baskets. b) to say that basket C is preferred to basket A if basket B is preferred to basket A and basket C is preferred to basket B. c) to rank a basket with more units of all goods higher than a basket with fewer units of all goods. d) to have a diminishing marginal rate of substitution.

a) to rank any two baskets.

Suppose that a consumer has utility function U=.1H+F. Which of the following is true? a) The marginal utility of h is .1 b) the marginal utility of h is decreasing c) The marginal rate of substitution between h and f is .1

answer is a and c

If I prefer steak to burritos, burritos to pasta and pasta to steak: a) My preferences are irrational. b) My preferences violate the transitivity assumption. c) My preferences violate the "more is better assumption. d) I must have been exhibiting diminishing marginal utility.

b) My preferences violate the transitivity assumption.

Assume that a consumer prefers watching Yu-Gi-Oh to watching Teen Titans, and that this same consumer prefers watching Teen Titans to watching Sponge Bob. Further assume that this same consumer states, "I would prefer to watch Sponge Bob to watching Yu-Gi-Oh." This consumer's preferences violate which of the following key assumptions? a) Completeness. b) Transitivity. c) More is better. d) Both completeness and transitivity.

b) Transitivity.

Assume that two baskets A and B lie on the same indifference curve. Assume that basket A contains more of good Y than basket B but less of good X than basket B . As the consumer moves down and to the right (from basket A to basket B ) along his indifference curve, total utility a) increases. b) remains constant. c) decreases. d) is ambiguous.

b) remains constant

The assumption that preferences are transitive requires the consumer a) to rank any two baskets. b) to say that basket C is preferred to basket A if basket B is preferred to basket A and basket C is preferred to basket B . c) to rank a basket with more units of all goods higher than a basket with fewer units of all goods. d) to have a diminishing marginal rate of substitution.

b) to say that basket C is preferred to basket A if basket B is preferred to basket A and basket C is preferred to basket B .

If a consumer would rather eat three bars of chocolate than four bars of chocolate, this consumer's preferences violate which of the following key assumptions? a) Completeness. b) Transitivity. c) More is better. d) Both completeness and transitivity. Ans: CDifficulty: EasyHeading: Representations of PreferencesLO 2 Apply three basic assumptions about consumer preferences: preferences are complete, preferences are transitive, and more is better.

c) More is better.

The assumption that more is better requires the consumer a) to rank any two baskets. b) to say that basket C is preferred to basket A if basket B is preferred to basket A and basket C is preferred to basket B . c) to rank a basket with more units of all goods higher than a basket with fewer units of all goods. d) to have a diminishing marginal rate of substitution.

c) to rank a basket with more units of all goods higher than a basket with fewer units of all goods.

Consumer preferences: a) are fixed exogenously and unchanging in reality. b) indicate how a consumer would rank any two possible baskets of goods, taking into account her budget constraint. c) indicate how a consumer would rank any two possible baskets of goods, taking into account the current prices of those goods. d) indicate how a consumer would rank any two possible baskets of goods, assuming that the baskets were available to the consumer at no cost.

d) indicate how a consumer would rank any two possible baskets of goods, assuming that the baskets were available to the consumer at no cost.

How will an increase in price of one good purchased by a consumer affect the location of the budget line?

if the price of one the goods increases the budget line will rotate inward (to the left) for the good with the price increased. the budget line will continue to have the same intercept. e.g. for example, suppose someone buys two goods, cup of coffee and doughnuts, and suppose the price of a cup of coffee increases. see pic attached.

Definition Diminishing marginal utility

the principle of diminishing marginal utility states that the marginal utility falls as the consumer consumes more of a good

perfect complements

two goods for which the MRS is zero or infinite; the indifference curves are shaped as right angles (45°)

perfect substitutes

two goods for which the marginal rate of substitution of one for the other is a constant U = Ax + By MRSx,y = A/B so that 1 unit of x is equal to B/A units of y everywhere (constant MRS)