More on consumer theory: predicting and ex-plaining the choices we makedraft Oct 30, 2012Choices depend on preferences and and constraintsWrt constraints, and quoting from a course evaluation"You seem like a nice guy but you are soooo oooooboring. I would not hang out with you even if you theonly person in my budget set."In my defense, this person understands the di¤erence between his preferencesand his constraints, so managed to learn in an extreme state of boredom.In previous lectures we discussed the budget constraint and preferences.Here we discuss preferences in more detailThe relevant chapter is 10, and, in particular, its appendix.11 Economists assume individuals have prefer-ences: they can rank bundles of goods suchthat Bundle j is preferred to bundle i, or Bundle i is preferred to bundle j, or The individual is indi¤erent between bundles i and j. And this is true for any pair of bundles i and jEconomists often represent preferences with something called a utility func-tion.1A utility function is simply a mathematical function that assigns a numberto each bundle such that is assigns a higher number to bundle k than to bundlev if bundle k is preferred to bundle v, and assign bundles h and t the samenumber if the individual is indi¤erent between these to bundles.The function is chosen such that u(k ) > u(v) if bundle k is preferred tobundle v, and u(t) = u(h) if the individual is indi¤erent between the two bundles.Your u(:) is di¤erent from mine u(:).One has preferences and a mathematical function is one way to representthose preference, there are other ways as well. For example one could writedown, in a notebook a description of each possible bundle and the ranking ofthat bundle.Economists do no assume people get utility: utility is a way to representpreferences.We call these numbers produced by this function, utils or utility. If a bundlem has a higher utility number than bundle w this simply means that bundle mis preferred to bundle w.1Utility is a concep t that confuses many people. Many people want to make more ofutlity than is the re. Economists do not assume that peo ple get utility per sec; it is only amathematical metric we use to ra nk bundles.2Economists assume your preferences are your preferences- they are what theyare. If you like to do activity x with stray dogs, and you would give up eve rythingelse to do more of activity x with stray dogs, those are your preferences, whichwe economists take as given.(However, economists might want to in‡uence (restrain or encourage) yourchoices if your choices directly in‡uence others in a sign…cant way, including thestray dogs)Psychologists, on the other hand, might ask why you have the preferencesyou have.22Actually, many of them would ask whether people have pre ferences in the economic senseof the word.31.1 KW, and I as well, will assume there are only twogoods in playKW assumes the two commo dities are restaurant meals and ro oms.they assume u = (r; m). KW choose a matematical function of r and m thatwould produce a graph that looks like this one.4For my example, my two goods will be aquarium …sh and dog biscuits . Ihave a big aquarium that will hold many …sh. My dog, So…e, likes dog biscuits.My trust fund provides me with a small amount of money each month that Ican only spend on …sh or dog biscuits, So…e has no money.All of our other needs are fu…lled by care packages sent by relatives, so allof my money can be spent on …sh or biscuits.So…e always prefers more dog biscuits to less dog biscuits, and I care aboutSo…eCeteris paribus, I would always prefer to have more …sh in my aquiarium.5So…e swimming in my large aquarium1.1.1 I need to assume a mathetmatical form for my utility function61.1.2 I choose u = f:8d:2, hopefully it represents my preferences. Imade …sh more important than dog biscuits.A digression about graphs an d mathematical functions. A graph is a visual image of aspeci…c mathematica function. That is, if we know the mathematical function I havesu¢ cient information to graph it, and if one has the graph one can work backwardsand …gure out wh at mathematical fun ction would produce that graph. As you advan ceto h igher math courses or higher ec onomics courses, th e mathematical function ofinterest will be speci…ed. It will then possib ly be graphed so the stude nt can visualizethe function. M ostly in Econ 2010 and in the book, the graph is shown withoutmaki ng explicit the mathematical function that generated that graph. Rememberthat underlying the graph, there is a mathematical function.I have assumed that, if I am currently consuming equal quantities of both,I could prefer an additional …sh to an additional dog biscuits.481062000224104d686f810My assumed utility for …sh and dog biscuitsuitlity is on the vertical axis.33Note that the utility keeps rising as I consume more of each good, but I can draw a graphthat goes on forever.7Imagine all the bundles between which I am indi¤erent. How would youindentify such bundles? GRAB A SWORD?2 Indi¤erence curves identify all those bundlesthat achieve the exact same utility.(Said another way, not using the concept of utility: An indi¤erence curve rep-resents all of the bun dles between which you are indi¤erent)4The graph in KW isrelatethis to utility function for r and m4The existe nce of indi¤erence curves do not depend on the concept of utility; they dependonly on the individual having preferences (a ranking of co nsumption bundles).82.1 The indi¤erence curves that correspond to my utilityfunction for …sh and biscuits2.20 1 2 3 4 5 6 71234567biscuitsfishIndi¤. curvs : Blk u = 1, Red u = 2, Blu u = 3For example I am indi¤ent between 1:25 biscuits with 2:25 …sh, and 5 biscuitswith 1:59 …sh: each of these bundles generates 2 utils.Notice how the indi¤erence curves become ‡atter when there are relativelymore biscuits than …sh in the bundle (steeper as there are relatively more …shin the bundle). It does not have to be this way, but often is this way.9Now let’s look at my utility indi¤erence curve for u = 2 in more detail0 1 2 3 4 5 6 71.52.02.53.03.54.0biscuitsfishIndi¤erence curve for u = 2Which indicates, as noted above, that I am indi¤erent between 1:25 biscuitswith 2:25 …sh, and 5 biscuits with 1:59 …sh.Said another way, to increase So…e’s biscuit consumption from 1:25 to 5 (anincrease of 3:75 biscuits) I would be willing to give up :66 …sh (2:25  1:59)102.3