1、Course:Microeconomics Text:Varians Intermediate Microeconomics 1Last chapter we talk about what is affordable or feasible to consumers.This time we talk about preferencespreferences:what the consumer like more and what they like less.As a rational agent,a consumer chooses the option in the budget se
2、t that is highesthighest in their preference order(i.e.one likes the most).2Let x,y are consumption bundles.denotes strict preference strict preference so x y means that bundle x is preferred strictly to bundle y.denotes indifferenceindifference;x y means x and y are equally preferred.denotes weak p
3、referenceweak preference;x y means x is preferred at least as much as is y.f fp pp pf f3Strict preference,weak preference and indifference are all preference relations.Particularly,they are ordinal relations;i.e.they state only the order in which bundles are preferred.It has no indication of how muc
4、h they like one versus the other.4x y and y x imply x y.x y and(not y x)imply x y.f ff ff ff fp p5Completeness:For any two bundles x and y it is always possible to make the statement that either x y or y x.Bundles are always comparable.If both are true,then they are indifferent to the individual.f f
5、f f6Reflexivity:Any bundle x is always at least as preferred as itself;i.e.x x.f f7Transitivity:Ifx is at least as preferred as y,andy is at least as preferred as z,thenx is at least as preferred as z;i.e.x y and y z x z.It avoids circular preference,and ensure that there exists the best bundle.f ff
6、 ff f8Take a reference bundle x.The set of all bundles equally preferred to x is the indifference curve(set)containing x;the set of all bundles y:y x.Weakly preferred set:bundles that are weakly preferred to x.y:y x.f f9x xThe consumer is indifferent between every point on the indifference curve.10
7、p pp px xy yz zIf consumer prefers more to less for each goods,all bundles on the northeast of the indifference curve are strictly preferred to x,and all bundles southwest of the indifference curve are less preferred to x.11x x2 2x x1 1x xAll bundles in IAll bundles in I1 1 are arestrictly preferred
8、 to all strictly preferred to all in Iin I2 2.y yz zAll bundles in IAll bundles in I2 2 are are strictly preferred to strictly preferred to all in all in I I3 3.I I1 1I I2 2I I3 312x x2 2x x1 1I(x)I(x)x xI(x)I(x)WP(x),the set ofWP(x),the set of bundles weakly bundles weakly preferred to x.preferred
9、to x.13x x2 2x x1 1WP(x),the set ofWP(x),the set of bundles weakly bundles weakly preferred to x.preferred to x.WP(x)WP(x)includes includes I(x).I(x).x xI(x)I(x)14x x2 2x x1 1SP(x),the set ofSP(x),the set of bundles strictly bundles strictly preferred to x,preferred to x,does not does not include in
10、clude I(x).I(x).x xI(x)I(x)15I I2 2p p16When more of a commodity is always preferred,the commodity is a good.If every commodity is a good then indifference curves are negatively sloped.It is because when one has more of one good,one has to get less of another to make this bundle indifferent to the o
11、riginal one.1718If less of a commodity is always preferred then the commodity is a bad.e.g.rotten fruits;tobacco smoke(if you do not smoke)If one good is good and the other is bad,then the indifference curve would be upward sloping.19If you want more of the good,you also have to get more of the bad
12、so that you are indifferent between them.20If one just do not care about whether or how much to have a commodity,this is called a neutral good.E.g.:goods that you dont use and do not care about their existence.If one commodity is neutral,the other is good,the indifference curve would be vertical/hor
13、izontal.2122If a consumer always regards units of commodities 1 and 2 as equivalent,then the commodities are perfect substitutes.Only the total amount(or a weighted sum)of the two commodities in bundles determines their preference rank-order.Example:orange juice of two different brands.Apartment in
14、different locations.23I I2 2I I1 124If a consumer always consumes commodities 1 and 2 in fixed proportion(e.g.one-to-one),then the commodities are perfect complements.Only the number of pairs of units of the two commodities determines the preference rank-order of bundles.E.g.:left shoes/right shoes;
15、computer and monitor.25I I1 1Each of Each of(5,5)(5,5),(5,9)(5,9)and and(9,5)(9,5)contains contains5 pairs so each is 5 pairs so each is equally preferred.equally preferred.26I I2 2I I1 1Since each of Since each of(5,5)(5,5),(5,9)(5,9)and and(9,5)(9,5)contains 5 pairs,contains 5 pairs,each is less e
16、ach is less preferred than the preferred than the bundle bundle(9,9)(9,9)which which contains 9 pairs.contains 9 pairs.27A bundle strictly preferred to any others is a satiation point or a bliss point.The satiation point is the best bundle.More of anything are not better.What do indifference curves
17、look like for preferences exhibiting satiation?28293031A commodity is infinitely divisible if it can be acquired in any quantity;e.g.water or cheese.A commodity is discrete if it comes in unit lumps of 1,2,3,and so on;e.g.aircraft,ships and refrigerators.32Suppose commodity 2 is an infinitely divisi
18、ble good(gasoline)while commodity 1 is a discrete good(aircraft).What do indifference“curves”look like?333 334Typical assumptions of preferencesA preference relation is“well-behaved”if it ismonotonic and convex.Monotonicity:More of any commodity is always preferred(i.e.no satiation and every commodi
19、ty is a good).This implies a negatively sloped IC.35Convexity:Mixtures of bundles are(at least weakly)preferred to the bundles themselves.E.g.,the 50-50 mixture of the bundles x and y is z=(0.5)x+(0.5)y.z is at least as preferred as x or y.36x xy yz=z=x+yx+y2 237x xy yz=(txz=(tx1 1+(1-t)y+(1-t)y1 1,
20、tx,tx2 2+(1-t)y+(1-t)y2 2)is preferred to x and y is preferred to x and y for all 0 t 1.for all 0 t 1.38x xy yPreferences are Preferences are strictly convexstrictly convex when when allall mixtures z mixtures z are are strictlystrictly preferred preferred to their to their component component bundl
21、es x and y.bundles x and y.z z39BetterBetter40BetterBetter41It represents a more balanced preference rather than a preference that induces a specialization.It is natural to consume the goods involved in positive amount.It also implies a diminishing marginal rate of substitution.42The negative of the
22、 slope of an indifference curve is its marginal rate of substitution(MRS).Note:this is slightly different from the textbook,but my definition is more popular.This represents the maximum amount of x2 one is willing to give up per unit of x1 at a specific consumption bundle.4344 D DD DD DD DD D45x x1
23、1 4647Because instead of giving up,you have to obtain more good 2 for you to be willing to accept more good 1.48We call it a diminishing marginal rate of diminishing marginal rate of substitutionsubstitution.49MRS=MRS=0.50.5MRS=MRS=5 5 50MRSMRS=0.50.5MRS MRS=2 2MRS=1.551In this chapter,we talk about
24、 how we can specify consumers preference towards different consumption bundles.We can use indifferent curve to depict different kinds of preferences.The marginal rate of substitution is the slope of indifference curve.It represents the willingness to substitute one good for another one.52We have talked about preference and indifference curve in this chapter.To put preference in a more mathematically convenient way,we introduce the utility function in the coming chapter.Then we can put together preference/utility and budget constraint to analyze consumer choices.53
