Budget. Peter Berck 2010

Transcription

1 Budget Peter Berck 2010

2 Buying Bundles A bundle is a collection of goods It is a list, showing how much of each good there is. (e.g., 2 apples, 3 green beans). In an economy with n goods, a bundle has n elements some of which may be zero. In mathematical language, a bundle is an n dimensional vector

3 What is Affordable? A 2-good world, so we can draw things. Bread, B. and wine,w Prices P b and P w Quantities B and W Income is Y

4 y = P b B + P w w Is the budget constraint all the (B,W) pairs that cost exactly y. Any (B,W) pair that lies on or below the budget constraint is affordable. Any pair that lies above can't be purchased with y.

5 Savings We would have more than two goods. Bread and Wine today and B and W tomorrow. Now there is a reason to save money and buy tomorrow. Money used to buy the tomorrow goods is savings Now back to 2 dimensions.

6 Slope Intercept Put W on vertical axis, B on horizontal W = y/p w - P b /P w B Intercept Slope horizontal intercept is y/p b.

7 Tradeoffs-- If you have a second helping of owl (oops, I mean cake) You will have to give up something else, ice cream Slope of dudget constraint is how much of the vertical good (wine) you give up to get one unit of the horizontal good (bread)

8 Can you find prices and income? Or do you need to know that P w =1 to get anywhere

9 At your seat. 4. Show what happens if price of bread increases to twice its previous value. Does the vertical intercept change? the horizontal intercept, the slope? has the budget set become larger or smaller. 5. Now show what happens if income increases from 100 to 120. What happens to the vertical intercept, the horizontal intercept and the slope. Has the budget set become smaller or larger? 6. For completeness, suppose the price of wine doubles. What are the intercepts now?

10 Harder Cases Finger exercises* *Bob Solow taught that cute theoretical things are finger exercises. 1. A sale. First 15 units of B at the normal price and all additional units at half price. If B <= 15, budget constraint doesn t change. Then y- P b 15 = B sale (P b /2 )+W P w 2. Look on syllabus for foodstamp example but we won t cover it.

11 Reality and Preference Budget constraints describe reality. What one can do. Preference describes what one wants to do. Economists assume that people do what they want to do within the constraints imposed by reality budget. Let s look at preference.

12 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. 9/14/

13 Individual Preference? Interdependent preference? Commandment? Why do we give money to beggars? 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) 9/14/

14 Veil of Ignorance Beggar or Rich Man to Be? Would Ezra Berck (9/10/2010) vote for laws that protect beggars at the expense of rich men right now?

15 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? 9/14/

16 Preference? Do preferences lead to diabetes? Can your generation help itself in the thralls of soda (which used to come in 6 oz bottles and was not stocked in people s refrigerators)? And 12 and larger plates?

17 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. 9/14/

18 More is Better Bread? These points have more bread or wine or both. Every consumer prefers them to A A Worse than A for all.? Wine Point, A, in Bread-Wine space is a bundle 9/14/

19 Level Set A set of points that have the same height. Examples All the locations on Mt. Marcy that are 1,450 feet. z = xy; {(x,y) k = xy} is a level set, where k is a constant 9/14/

20 Mt. Marcy, NY

21 Same colored squares are all the same height. They are in the same level set. Light Blue squares are 50 units off the floor 9/14/

22 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. 9/14/

23 Utility is an Ordinal Measure of Happiness Think of Utility as height and amount of goods as x 1 and x 2 All bundles same height = level set = indifference curve Theory only requires indifference curves not utility Ordinal means rank (one bundle better than another) not absolute amount (one bundle is 17 utils better than another) 9/14/

24 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. (see p. 66 if you are curious.) 9/14/

25 A Demonstration B c a b 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. 9/14/

26 Indiff. Curves Don t Cross B Use more is better and transitivity to construct the proof a b c W 9/14/

27 Choosing a Bundle Consumers can choose anything on or under their budget constraints. Those are the only things that they can afford. 9/14/

28 Which Bundle? B Of the bundles a consumer can afford, the consumer chooses the one the consumer likes most. e d c Remember: Higher indifference curve, like more. f 9/14/ W

29 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. 9/14/

30 Find the bundle B How much bread and how much wine are purchased? If income is 2, what are the prices of bread and wine? W 9/14/

31 Change in income An increase in income shifts budget constraints up in a parallel fashion. (x 2 = y/p 2 -p 1 /p 2 x 1 ; slope-intercept. change in y does not change slope but increases intercept.) 9/14/

32 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 9/14/

33 Demand Curves

34 Theory From among those bundles he can afford, consumer chooses bundle that makes him happiest (maximizes his utility) Y = p 1 x 1 + p 2 x 2 gives bundles can afford Indifference curves shows preferences among bundles 9/14/

35 Choice at 3 Prices for Bread 100 Price of Wine is 1 Wine High P Medium P Low P Bread 9/14/

36 Price-Quantity Chart The price of wine is 1. Wine Price In Numbers Quantity High $4/loaf 10 Med. $2/loaf 22 Low $1/loaf 40 High P Medium P Low P Bread 9/14/

37 Demand Curve price of bread quantity of bread Price In Numbers Quantity High $4/loaf 10 Med. $2/loaf 22 Low $1/loaf 40 9/14/

38 Income Shifts Demand Wine Price of Wine is 1 Income In Numbers Quantity 80 $4/loaf $2/loaf $2/loaf Bread High P Medium P Med. P; High Y 9/14/

39 One Point on a Demand Curve Shifted Out by Increased Income price of bread Income In Numbers Quantity 80 $4/loaf $2/loaf $2/loaf quantity of bread 9/14/

40 Example from the book: Electricity What is the elasticity demand? Assume a flat supply curve and roughly 1,000,000 households in Montana. How much tax revenue would a $50 tax raise? How much electricity gets saved Research: What is the state budget in Montana? How much carbon per MW, assuming coal? How much does carbon sell for on the European trading system?

41 Figure 4.5: Budget Constraints at $50 and $100/MWH Pearson Addison-Wesley. All rights reserved.

42 Figure 4.6: The Chosen Bundle for Two Prices Pearson Addison-Wesley. All rights reserved.

43 Figure 4.7: Demand Curve for Electricity Pearson Addison-Wesley. All rights reserved.