Week 4 - Budget Constraints and Consumer Preferences
What are the four basic assumptions about individual preferences?
*Consumer Theory assumes that:* 1. Preferences are *complete,* which means that consumers are able to rank all possible baskets 2. Preferences are *transitive* which means that if bundle A is preferred to bundle B and bundle B is preferred to bundle C, then *bundle A is preferred to bundle C* 3. More is *always* preferred to less because *all goods are desirable
Effects of A Change in Income on the Budget Line
A change in income (with prices fixed) causes a parallel shift in the budget
Effects if a Change in Price on The Budget Line
A change in the price of one good (with income unchanged) causes the budget line to rotate about one intercept.
Transitivity
A consumer says he prefers a Toyota automobile to a Ford and a Ford to a Jeep. He also says he prefers a Jeep to a Toyota. Which basic assumption about preferences does this consumer violate?
Bundles (aka market basket)
A particular combination of two or more goods The first number of the pair represents the good measured along the horizontal axis Consumption are *flows*, which means amounts per unit of time [Slide 5, 3.1]
Preference Ordering
A ranking of all possible consumption bundles in terms of their desirability, or order of preference. Example: Consider two bundles, say, A (4, 2) and B (3, 3), in a world with only two goods: shelter and food. For any two such bundles, a preference ordering enables a consumer to make one of three possible statements: - A is preferred to B - B is preferred to A - A and B are equally attractive Ordinal, not cardinal. The consumer might be able to say that he prefers A to B but not that A provides twice as much satisfaction as B. Preference orderings often differ widely among consumers. The preference ordering enables the consumer to rank different bundles but not to make more precise quantitative statements about their relative desirability. - Thus, the consumer might be able to say that he prefers A to B but not that A provides twice as much satisfaction as B.
Indifference Map
A representative sample of the set of a consumer's indifference curves, used as a graphical summary of her preference. By completeness: there is an indifference curve that passes through every possible bundle. This indifference map shows just four of the infinitely many indifference curves The numbers 𝐼1,𝐼2,𝐼3, 𝐼4. are index values used to denote the order of preference that corresponds to the respective indifference curves. Any index numbers would do equally well provided they satisfied the property 𝐼1<𝐼2<𝐼3<𝐼4. In representing the consumer's preferences, what really counts is the ranking of the indifference curves, not the particular numerical values we assign to them. (Ordinal)
Indifference Curve
A set of bundles among which the consumer is indifferent Bundles that lie above an indifference curve are all preferred to the bundles that lie on it. (K; By more-is-better and transitivity.) Bundles that lie on an indifference curve are all preferred to those that lie below it. (L) We can repeat this process as often as we like, and the end result will be an indifference curve, a set of bundles all of which are equally attractive as the original bundle A, and hence also equally attractive as one another. [3.2, Slide 13] A~D, D>K ==> A>K
provide the consumer with the same level of satisfaction.
An indifference curve shows all combinations of two goods that
Perfect Substitutes and Perfect Complements
An indifference curve with a different shape implies a different willingness to substitute. Two extreme cases that do not exhibit diminishing MRS are *perfect substitutes* and *perfect complements*
become flatter
Assume that food is measured on the horizontal axis and clothing on the vertical axis. If the price of food falls relative to that of clothing, the budget line will
Marginal Rate of Substitution (MRS)
At any point on an indifference curve, the rate at which the consumer is willing to exchange the good measured along the vertical axis for the good measured along the horizontal axis; equal to the absolute value of the slop. Example: MRSA=2 means that, when having bundle A in hand, the consumer is *willing* to exchange 2 units of food for an additional unit shelter *without changing total satisfaction.* Slope: change in Fa/change in Sa [3.2 Slide 18]
Affordable Sets
Bundles on or below the budget constraint Bundles for which the required expenditure at given prices is less than or equal to the income available
Diminishing Rates of Marginal Substitution
By convexity: consumers like variety. We are usually willing to give up goods we already have a lot of to obtain more of those goods we now have only a little of. - Reversely, only know you love it when you let it go MRS declines as we move downward to the right along an indifference curve. Graphically, the curve is *convex,* or bends towards the origin. [3.2 Slide 19]
Obvious Better/Worse Bundles
By more-is-better: More northeast the better, more southwest is worse. [3.2 Slide 11]
cannot be upward sloping because this violates the assumption that more is better than less, indicating that one of the goods is a "bad."
Can a set of indifference curves be upward sloping? If so, what would this tell you about the two goods? A set of indifference curves
are shaped as right angles
Describe the indifference curves associated with two goods that are perfect complements. The indifference curves for two goods that are perfect complements
are downward-sloping straight lines
Describe the indifference curves associated with two goods that are perfect substitutes. The indifference curves for two goods that are perfect substitutes
There will be no effect on the budget line.
If prices and income in a two-good society double, what will happen to the budget line?
Why Two Indifference Curves Do Not Cross
If two indifference curves intersect, either more-is-better or transitivity is violated, depending on the stating point of your argument.
Composite Good
In a choice between a good X and numerous other goods, the amount of money the consumer spends on those other goods Example: Y represents all those other goods. The units of the composite good are defined so that its price is $1 per unit. - The vertical axis measures the amount of money spent each week on all goods other than X. Representing more than two goods on a surface is difficult. To circumvent the difficulty, economist introduces the composite good concept. In a choice between a good X and numerous other goods, the composite good Y represents all those other goods. The units of the composite good are defined so that its price is $1 per unit, which enables us to think of the composite good as the amount of money the consumer spends on those other goods. Ex: [3.1, slide 9]
the assumption of convexity.
Indifference curves are convex to the origin because of
Properties of Indifference Curves
Indifference curves are ubiquitous. (result of completeness) Indifference curves are downward-sloping. (more-is-better) Indifference curves cannot cross. (more-is-better + transitivity) Indifference curves become less steep as we move downward and to the right along them. (convexity)
are incomplete
Jane is trying to decide which courses to take next semester. She has narrowed down her choice to two courses, Econ 1 and Econ 2. Now she is having trouble and cannot decide which of the two courses to take. It's not that she is indifferent between the two courses. She just cannot decide. An economist would say that this is an example of preferences that
is decreasing as "x" increases.
Measuring "y" on the vertical axis and "x" on the horizontal axis, convexity of indifference curves imply that the magnitude of MRS of "y" for "x"
Convexity
Mixture of goods are preferable to extremes. If you are indifferent between two bundles A and B, your preferences are *convex* if your prefer a bundle that contains half of A and half of B to either of the original bundles. For example, A=(4,0), B=(0,4). Then convexity means you will prefer (2,2) to each of the more extreme bundles. This property conveys the sense that we like balance in our mix of consumption goods.
More-Is-Better
Other things equal, more of a good is preferred to less. For example, A=(12,10), B=(12,11). If the assumption holds, you will prefer B to A, because it has more food and no less shelter. Note: this assumption cannot help us to rank A=(12,10) and B=(9,11). You cannot add up the two numbers in each bundle and compare the sums.
Completeness
Preferences are assumed to be complete. In other words, consumers can compare and rank all possible bundles. Thus, for any two bundles A and B, a consumer will prefer A to B, will prefer B to A, or will be indifferent between the two. By indifferent we mean that a person will be equally satisfied with either bundle. Preference orderings often differ widely among consumers. Despite these differences, however, most preference orderings share several important features. Economists usually abstract three or four properties out of these shared features and make them the basic assumptions about rational preference. > "Preferred to:" A>B or B>A ~ "Indifferent between:" A~B
Transitivity
Preferences are transitive. Transitivity means that if a consumer prefers basket A to basket B and basket B to basket C, then the consumer also prefers A to C. Transitivity is normally regarded as necessary for consumer consistency. Example: A (4,2), B (3,3), C (2,4). If you prefer (4,2) over (3,3) and you prefer (3,3) over (2,4), then you must prefer (4,2) over (2,4). Applies to all meaningful relation chains. Also mention not all relations are transitive. "defeats in football".
counter-clockwise about the fixed horizontal axis intercept.
Suppose a consumer only purchases food and clothing, and food is plotted along the horizontal axis of the consumer's indifference map. If the price of clothing increases and the price of food and income do not change, then the budget line changes by rotating
The budget line is now convex to (bows in toward) the origin.
Suppose you only consume food and clothing, and clothing is plotted on the vertical axis. Also, you purchase food at a fixed price (PF), but the price of clothing declines as you buy in larger quantities (i.e., quantity discounts). What does the budget line look like in this case?
B = I/Pb - (Pa/Pb)A
The budget constraint for a consumer who only buys apples (A) and bananas (B) is: PaA + PbB = I where consumer income is I, the price of apples is Pa, and the price of bananas is Pb. To plot this budget constraint in a figure with apples on the horizontal axis, we should use a budget line represented by the slope-intercept equation
represent the quantity of each good that could be purchased if all of the budget were allocated to that good.
The endpoints (horizontal and vertical intercepts) of the budget line
Budget Constraint (aka Budget Line)
The set of all bundles that exactly exhaust the consumer's income at given prices Ps * S + Pf * F = M S: shelter F: Food [3.1, Slide 6] D: below the budget line E: above the budget line
the marginal rate of substitution of one good for another good.
The slope of an indifference curve reveals
Parallel outward (rightward) shift
To simplify our consumption models, suppose U.S. consumers only purchase food and all other goods where food is plotted along the horizontal axis of the indifference map. If the U.S. Congress passes an economic stimulus package that pays $300 to each person, how does this affect the budget line for each consumer?
Perfect Substitutes
Two goods for which the MRS is a constant. The indifference curves are straight lines.
Perfect Complements
Two goods for which the MRS is zero or infinite. The indifference curves are shaped as right angles.
When indifference curves are places in the Cartesian Plane,
the result is called an indifference map. the curves that occupy a place farther away from the origin yield more utility than curves closer to the origin. the curves cannot intersect.
