Microeconomics: BSc Year One Extending Choice Theory

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1 mcroeconomcs notes from by Tm Mller Mcroeconomcs: BSc Year One Extendng Choce Theory Consumers, obvously, mostly have a choce of more than two goods; and to fnd the favourable combnatons of these we must look at utlty functons. To smplfy ths, we ntally contnue lookng at two goods. A consumer s utlty can be defned as a functon of the amount consumed of each good: utlty = U (, ) The actual functon tself s ordnal only (that s, only the order, and not the magnatude matters) snce we have no set unts to measure utlty n.. So, for example, f we take: U =, we can also say that: or that: U =, U = log( ) + log( ). The utlty functon has the followng propertes: Margnal utlty can be found by dfferentaton (or partal dfferentaton): U = The margnal rate of substtuton can also be derved by keepng total utlty constant: d MRS, = - d U s constant And from these we can derve: U U U & ª & + & But f we hold U constant, and therefore look at the MRS, & & du - d = du - d = = MRS. And from the slope of the ndfference curves at the ponts where they touch the budget lnes, we can see that: = MRS, page

2 mcroeconomcs notes from by Tm Mller Therfore, combnng the above propertes, we may fnd: =, showng that prces reflect the attractveness of goods. So, formally, consumers am to maxmse utlty U, ) subect to the constrant ( + M n the two-good case. For example, gven the utlty functon U =, and a prce constrant of the form + = M, we would look at the margnal utltes of the two goods ( and ), and fnd the pont at whch =. Changes n Money Supply An ncrease n money supply wll have the effect of shftng the budget lne away from the orgn. From ths s derved the Engel curve, whch looks at the demand for a good varyng wth ncome (here represented n terms of money supply): page

3 mcroeconomcs notes from by Tm Mller The Engel curve for an nferor good The Engel curve for a normal good As shown, not all goods have a monotonc Engel curve; goods such as nferor goods are not contnually ncreased n consumpton as ncome rses. Ths s due to uneven ncome and substtuton effects ths wll be dscussed later. Changes n rce A change n the prce of one good wll lead to a pvotng of the budget lne about the pont at whch t touches the other axs. A fall n the prce n wll lead to a movement thus: rce consumpton curve for a normal good From ths we can derve the standard downward-slopng demand curve. Changes n Tastes Anythng can happen when tastes change. In order to analyse standard demand theory here, the reasons for changes must be known habt formng goods wll have a dfferent effect than other goods, for example. We need to look how demand for one good s related to demand for another. page 3

4 mcroeconomcs notes from by Tm Mller A Couple of Interestng onts From the theory of consumer demand explaned so far, we can draw a couple of conclusons: Any new entres nto the market must understand the fundamental preferences lyng n the marketplace Market demand s found by summng all ndvduals demands Elastctes We can say that an ndvdual s demand for a good s a functon dependant on the prce of that good, prces of other goods, and personal ncome (amongst other thngs). Usng the summaton from above, we can say that the total market demand wll prmarly rely on prces of all goods n the economy, and market ncome (y). It s useful to look at the partal dervatve of market demand for a good wth respect to prces, and especally proportonal changes. Ths partal dervatve s defned as an elastcty the elastcty of A wth respect to B s defned as B A. A B The ncome elastcty of demand (often denoted by h) s defned by: m x h = x m where, for an nferor good, h < 0 (that s, the amount bought falls wth a rse n ncome); for a necessty, h les between and 0 (and so the proporton of ncome spent on the good falls when ncome rses); and for a luxury good, h >. A good s own prce elastcty of demand (e) s defned by: p x e = x p at any pont. The value of e wll normally be negatve, but needn t be the same everywhere, even on a straght-lne demand curve, as t wll depend on the relatve values of prce and quantty. If e >, when prce falls more s spent on the good, and t s sad to have elastc demand. On the other hand, nelastc demand ( e < ) means that a fall n prce leads to a lower expendture on the good. page 4

5 mcroeconomcs notes from by Tm Mller Income and substtuton effects Wth a prce fall, two thngs occur: the relatve prce of the good falls compared to other goods the relatve ncome of the ndvdual rses (dependng on the spendng on the good) We may look at a vsual nterpretaton of the ncome and substtuton effects, usng ndfference curves. We start at pont A, and a prce fall for good skews the budget lne so that we now le on a hgher ndfference curve, at pont B. Wth ths new slope of budget lne, f we were stll on the same utlty as orgnally, we would be at pont C. A C B In thse case, the substtuton effect s measured by the move from A to C, whle the move from C to B s the ncome effect. The substtuton effect occurs because the ndvdual chooses to purchase more of good ; the ncome effect because the consumer buys more of both goods. The substtuton effect s always postve, whle the ncome effect depends on ncome elastcty. Gffen goods For nferor goods, the substtuton and ncome effects go n opposte drectons. It s theoretcally possble for the ncome effect to outwegh the substtuton effect, and for demand to fall wth a fall n prce. Ths s most lkely f the good s very strongly nferor, and a large amount of ncome s spent on t. One example of ths s subsstence foods n poor countres - f the prce of bread falls, ncomes rse qute a lot, and people can afford to buy other food such as fsh rather than bread. Endowment ponts page 5

6 mcroeconomcs notes from by Tm Mller We want to drop the assumpton that ncome s fxed, and we can assume that people have a certan amount of goods to barter wth (an endowment). Take, for example, farmers producng food. An decrease n the prce of other goods wll lead to: a substtuton effect where the farmer tres to eat less n order to rase ncome more, so he can buy other goods an ncome effect where the farmer s relatvely better off, so he can afford to offer less of hs food for sale, and so supply falls. Ths may outwegh the substtuton effect. The drecton of an ncome effect depends on whether you are a net buyer or a net suppler of the good wth the prce change. The budget lne wll rotate about the endowment pont (E below) nstead of about the axs. E A prce change swvels the lne We can then fnd the change n consumpton usng the equaton p = p Utlty constant + ( ) 4-43 change from the endowment. M page 6