Consumer Theory Made Much Too SimpleThe basics of the Theory of Demand

(c) 1998 Peter Berck

Bundles Definition: A Bundle is a collection of goods (e.g., 2 apples, 3 green beans). In an economy with n goods, a bundle has n elements, some of which may be zero.

PreferencesBehavioral Assumption: Each person has his/her own preferences over bundles.A person can rank two bundles A and B. EitherA is preferred to BB is preferred to AA is indifferent to BOne person may prefer A to B whilst another prefers B to A.

Individual Preference?Meditation XVII. John Donne."The bell doth toll for him that thinks it doth: and though it intermit again, yet from that minute that that occasion wrought upon him, he is united to G_d. Who casts not up his eye to the sun when it rises? but who takes off his eye from a comet when that breaks out? Who bends not his ear to any bell which upon any occasion rings? but who can remove it from that bell which is passing a piece of himself out of this world? No man is an island, entire of itself; every man is a piece of the continent, a part of the main. If a clod be washed away by the sea, Europe is less, as well as if a promontory were, as well as if a manor of thy friend's or thine own were.. Any man's death diminishes me because I am involved in mankind, and therefore never send to know for whom the bell tolls; it tolls for thee. (page 1213 of the Norton Anthology of English Literature. Volume 1. WW Norton & Co. 1974)Leviticus. XIX-7. And when you reap the harvest of your land, thou shalt not wholly reap the corner of thy field, neither shalt you gather the gleaning of thy harvest. And thou shalt not glean thy vineyard, neither shalt thou gather the fallen fruit of thy vineyard: thou shalt leave them for the poor and the stranger. I am the Lord your G_d. (Hertz)

Respect Preferences?Would you use the word, prefer, to describe the actions of an alcoholic or a drug addict. Would you say, "she prefers alcohol to food?" If you said that, would you still want to influence the addict to change their behavior? Does your answer depend upon the damage addicts do to other people? If it does, consider the poster-girl addict: she hurts no-one but herself and dies with enough money in her pocket for her own burial. Do you subscribe to the view that if a person thinks their choice makes them better off then you (and the rest of society) ought also think that the person's choice makes them better off? Do you have the same problems answering these questions for a person who chooses cauliflower rather than broccoli?

PropertiesThe preferences are assumed to have the following reasonable properties: I. More is better. If bundle A has strictly more of one good and does not have less of any good than bundle B, then all consumers prefer A to B. II. Transitivity. A better than B better than C means A better than C. III. A preferred to B means B is not preferred to A.

More is BetterBreadWine Point, A, in Bread-Wine space is a bundleAThese points havemore bread or wineor both.Every consumer prefers them to A Worse thanAfor all.??

Level SetA set of points that have the same height. ExamplesAll the locations on Mt. Rose that are 8,000 feet.z = xy; {(x,y)| k = xy} is a level set, where k is a constant

Same colored squares are all the same height.They are in the same level set.Light Blue squares are 50 units off the floor

Indifference curves. Two bundles are indifferent (for a particular consumer) if the consumer is equally happy with either bundle. (If one added the teeniest bit of any good to one of the bundles, then the consumer would prefer it.) Let A be a bundle. There is an indifference curve through A.The indifference curve through A is the set of all bundles that makes the consumer just as happy as bundle A.

UtilityThink of Utility as height and amount of goods as x1 and x2All bundles same height = level set = indifference curveTheory only requires indifference curves not utility

Properties. Indifference curves slope down. They do not cross. Higher indifference curves are better. For reasons that I don't care to discuss, I always draw them so that they look like a crescent moon.

A DemonstrationBWabcEvery point on the higher indifference curve is better because b is preferred to a by more is better, c is indifferentto b because they are on the same indifference curve and therefore c is preferred to a.

Indiff. Curves Dont CrossBWabcUse more is betterand transitivity to construct the proof

Choosing a BundleConsumers can choose anything on or under their budget constraints. Those are the only things that they can afford.

Which Bundle?

BWcdefOf the bundles a consumer canafford, the consumer choosesthe one the consumer likes most.Remember: Higherindifference curve, likemore.

Which??Choice will occur where an indifference curve is tangent to the budget constraint.No point on the upper indifference curve lies on the budget the constraint. The consumer might like it but can't afford any such bundle. All points on the lower indifference curve are inferior to the middle indifference curve.

Find the bundleBW24246How much bread andhow much wine are purchased?If income is 2, what are the prices of bread and wine?

Change in incomeAn increase in income shifts budget constraints up in a parallel fashion. (x2 = y/p2 -p1/p2 x1; slope-intercept. change in y does not change slope but increases intercept.)

Inferior and NormalWhen income increases the quantity purchased of a normal good also increases.When income increases, the quantity purchased of an inferior good decreases

BW

5.The food stamp example Pay $A to buy $C worth of stampsfood stamp food FB and food bought with cash OB. total food B = OB +FB >= $C/Pb = FB, after purchase of stamps y - $A left to spend so y - $A= Pb OB + Pw W, where OB >= 0.

Algebra Concludes Subsitute B - FB for OB and $C/Pb for FB, to get the new budget constraint, y - $A +$C = Pb B + Pw W , where B >= $C/Pb

Food stamp pictureLet the price of wine be 1. What is y? slope of the budget constraints? Price of bread? Quantity of food stamps, $c,and cost of food stamps $a?

Participate? Cash?