Consumer Theory Made Much Too Simple

1. Consumer Theory Made Much Too Simple • The basics of the Theory of Demand (c) 1998 Peter Berck

2. 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.

3. Preferences • Behavioral Assumption: Each person has his/her own preferences over bundles. • A person can rank two bundles A and B. Either • A is preferred to B • B is preferred to A • A is indifferent to B • One person may prefer A to B whilst another prefers B to A.

4. 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)

5. 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?

6. Properties • The 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.

7. More is Better These points have more bread or wine or both. Every consumer prefers them to A Bread ? A Worse than A for all. ? Wine Point, A, in Bread-Wine space is a bundle

8. Level Set • A set of points that have the same height. • Examples • All 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

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

10. 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.

11. Utility • Think of Utility as height and amount of goods as x1 and x2 • All bundles same height = level set = indifference curve • Theory only requires indifference curves not utility

12. 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.

13. A Demonstration c B b a W Every point on the higher indifference curve is better because b is preferred to a by more is better, c is indifferent to b because they are on the same indifference curve and therefore c is preferred to a.

14. Indiff. Curves Don’t Cross Use more is better and transitivity to construct the proof B a c b W

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

16. Which Bundle? Of the bundles a consumer can afford, the consumer chooses the one the consumer likes most. e Remember: Higher indifference curve, like more. B c f d W

17. 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.

18. Find the bundle How much bread and how much wine are purchased? B If income is 2, what are the prices of bread and wine? 6 4 2 2 4 W

19. Change in income • An 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.)

20. Inferior and Normal • When income increases the quantity purchased of a normal good also increases. • When income increases, the quantity purchased of an inferior good decreases B W

21. 5. The food stamp example • Pay $A to buy $C worth of stamps • food 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.

22. 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

23. Food stamp picture Let 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?

24. Participate? Cash?