Ch05-《中级微观经济学》范里安-英文版教学课件.ppt

1、Chapter FiveChoice1Economic RationalityuThe principal behavioral postulate is that a decisionmaker chooses its most preferred alternative from those available to it.uThe available choices constitute the choice set.uHow is the most preferred bundle in the choice set located?2Rational Constrained Choi

2、cex1x23Rational Constrained Choicex1x2Utility4Rational Constrained ChoiceUtilityx2x15Rational Constrained Choicex1x2Utility6Rational Constrained ChoiceUtilityx1x27Rational Constrained ChoiceUtilityx1x28Rational Constrained ChoiceUtilityx1x29Rational Constrained ChoiceUtilityx1x210Rational Constraine

3、d ChoiceUtilityx1x2Affordable,but not the most preferred affordable bundle.11Rational Constrained Choicex1x2UtilityAffordable,but not the most preferred affordable bundle.The most preferredof the affordablebundles.12Rational Constrained Choicex1x2Utility13Rational Constrained ChoiceUtilityx1x214Rati

4、onal Constrained ChoiceUtilityx1x215Rational Constrained ChoiceUtilityx1x216Rational Constrained Choicex1x217Rational Constrained Choicex1x2Affordablebundles18Rational Constrained Choicex1x2Affordablebundles19Rational Constrained Choicex1x2AffordablebundlesMore preferredbundles20Rational Constrained

5、 ChoiceAffordablebundlesx1x2More preferredbundles21Rational Constrained Choicex1x2x1*x2*22Rational Constrained Choicex1x2x1*x2*(x1*,x2*)is the mostpreferred affordablebundle.23Rational Constrained ChoiceuThe most preferred affordable bundle is called the consumers ORDINARY DEMAND at the given prices

6、 and budget.uOrdinary demands will be denoted byx1*(p1,p2,m)and x2*(p1,p2,m).24Rational Constrained ChoiceuWhen x1*0 and x2*0 the demanded bundle is INTERIOR.uIf buying(x1*,x2*)costs$m then the budget is exhausted.25Rational Constrained Choicex1x2x1*x2*(x1*,x2*)is interior.(x1*,x2*)exhausts thebudge

7、t.26Rational Constrained Choicex1x2x1*x2*(x1*,x2*)is interior.(a)(x1*,x2*)exhausts thebudget;p1x1*+p2x2*=m.27Rational Constrained Choicex1x2x1*x2*(x1*,x2*)is interior.(b)The slope of the indiff.curve at(x1*,x2*)equals the slope of the budget constraint.28Rational Constrained Choiceu(x1*,x2*)satisfie

8、s two conditions:u(a)the budget is exhausted;p1x1*+p2x2*=mu(b)the slope of the budget constraint,-p1/p2,and the slope of the indifference curve containing(x1*,x2*)are equal at(x1*,x2*).29Computing Ordinary DemandsuHow can this information be used to locate(x1*,x2*)for given p1,p2 and m?30Computing O

9、rdinary Demands-a Cobb-Douglas Example.uSuppose that the consumer has Cobb-Douglas preferences.U xxx xa b(,)1212 31Computing Ordinary Demands-a Cobb-Douglas Example.uSuppose that the consumer has Cobb-Douglas preferences.uThenU xxx xa b(,)1212 MUUxaxxab11112 MUUxbx xa b22121 32Computing Ordinary Dem

10、ands-a Cobb-Douglas Example.uSo the MRS isMRSdxdxUxUxaxxbx xaxbxaba b 211211212121 /.33Computing Ordinary Demands-a Cobb-Douglas Example.uSo the MRS isuAt(x1*,x2*),MRS=-p1/p2 soMRSdxdxUxUxaxxbx xaxbxaba b 211211212121 /.34Computing Ordinary Demands-a Cobb-Douglas Example.uSo the MRS isuAt(x1*,x2*),M

11、RS=-p1/p2 soMRSdxdxUxUxaxxbx xaxbxaba b 211211212121 /.axbxppxbpapx21122121*.(A)35Computing Ordinary Demands-a Cobb-Douglas Example.u(x1*,x2*)also exhausts the budget sop xp xm1 12 2*.(B)36Computing Ordinary Demands-a Cobb-Douglas Example.uSo now we know thatxbpapx2121*(A)p xp xm1 12 2*.(B)37Computi

12、ng Ordinary Demands-a Cobb-Douglas Example.uSo now we know thatxbpapx2121*(A)p xp xm1 12 2*.(B)Substitute38Computing Ordinary Demands-a Cobb-Douglas Example.uSo now we know thatxbpapx2121*(A)p xp xm1 12 2*.(B)p xpbpapxm1 12121*.Substituteand getThis simplifies to.39Computing Ordinary Demands-a Cobb-

13、Douglas Example.xamab p11*().40Computing Ordinary Demands-a Cobb-Douglas Example.xbmab p22*().Substituting for x1*in p xp xm1 12 2*then givesxamab p11*().41Computing Ordinary Demands-a Cobb-Douglas Example.So we have discovered that the mostpreferred affordable bundle for a consumerwith Cobb-Douglas

14、 preferencesU xxx xa b(,)1212 is(,)(),().*()xxamab pbmab p1212 42Computing Ordinary Demands-a Cobb-Douglas Example.x1x2xamab p11*()xbmab p22*()U xxx xa b(,)1212 43Rational Constrained ChoiceuWhen x1*0 and x2*0 and (x1*,x2*)exhausts the budget,and indifference curves have no kinks,the ordinary demand

15、s are obtained by solving:u(a)p1x1*+p2x2*=yu(b)the slopes of the budget constraint,-p1/p2,and of the indifference curve containing(x1*,x2*)are equal at(x1*,x2*).44Rational Constrained ChoiceuBut what if x1*=0?uOr if x2*=0?uIf either x1*=0 or x2*=0 then the ordinary demand(x1*,x2*)is at a corner solu

16、tion to the problem of maximizing utility subject to a budget constraint.45Examples of Corner Solutions-the Perfect Substitutes Casex1x2MRS=-146Examples of Corner Solutions-the Perfect Substitutes Casex1x2MRS=-1Slope=-p1/p2 with p1 p2.47Examples of Corner Solutions-the Perfect Substitutes Casex1x2MR

17、S=-1Slope=-p1/p2 with p1 p2.48Examples of Corner Solutions-the Perfect Substitutes Casex1x2xyp22*x10*MRS=-1Slope=-p1/p2 with p1 p2.49Examples of Corner Solutions-the Perfect Substitutes Casex1x2xyp11*x20*MRS=-1Slope=-p1/p2 with p1 p2.50Examples of Corner Solutions-the Perfect Substitutes CaseSo when

18、 U(x1,x2)=x1+x2,the mostpreferred affordable bundle is(x1*,x2*)where 0,py)x,x(1*2*1and 2*2*1py,0)x,x(if p1 p2.51Examples of Corner Solutions-the Perfect Substitutes Casex1x2MRS=-1Slope=-p1/p2 with p1=p2.yp1yp252Examples of Corner Solutions-the Perfect Substitutes Casex1x2All the bundles in the const

19、raint are equally the most preferred affordable when p1=p2.yp2yp153Examples of Corner Solutions-the Non-Convex Preferences Casex1x2Better54Examples of Corner Solutions-the Non-Convex Preferences Casex1x255Examples of Corner Solutions-the Non-Convex Preferences Casex1x2Which is the most preferredaffo

20、rdable bundle?56Examples of Corner Solutions-the Non-Convex Preferences Casex1x2The most preferredaffordable bundle57Examples of Corner Solutions-the Non-Convex Preferences Casex1x2The most preferredaffordable bundleNotice that the“tangency solution”is not the most preferred affordablebundle.58Examp

21、les of Kinky Solutions-the Perfect Complements Casex1x2U(x1,x2)=minax1,x2x2=ax159Examples of Kinky Solutions-the Perfect Complements Casex1x2MRS=0U(x1,x2)=minax1,x2x2=ax160Examples of Kinky Solutions-the Perfect Complements Casex1x2MRS=-MRS=0U(x1,x2)=minax1,x2x2=ax161Examples of Kinky Solutions-the

22、Perfect Complements Casex1x2MRS=-MRS=0MRS is undefinedU(x1,x2)=minax1,x2x2=ax162Examples of Kinky Solutions-the Perfect Complements Casex1x2U(x1,x2)=minax1,x2x2=ax163Examples of Kinky Solutions-the Perfect Complements Casex1x2U(x1,x2)=minax1,x2x2=ax1Which is the mostpreferred affordable bundle?64Exa

23、mples of Kinky Solutions-the Perfect Complements Casex1x2U(x1,x2)=minax1,x2x2=ax1The most preferredaffordable bundle65Examples of Kinky Solutions-the Perfect Complements Casex1x2U(x1,x2)=minax1,x2x2=ax1x1*x2*66Examples of Kinky Solutions-the Perfect Complements Casex1x2U(x1,x2)=minax1,x2x2=ax1x1*x2*

24、(a)p1x1*+p2x2*=m67Examples of Kinky Solutions-the Perfect Complements Casex1x2U(x1,x2)=minax1,x2x2=ax1x1*x2*(a)p1x1*+p2x2*=m(b)x2*=ax1*68Examples of Kinky Solutions-the Perfect Complements Case(a)p1x1*+p2x2*=m;(b)x2*=ax1*.69Examples of Kinky Solutions-the Perfect Complements Case(a)p1x1*+p2x2*=m;(b)

25、x2*=ax1*.Substitution from(b)for x2*in(a)gives p1x1*+p2ax1*=m70Examples of Kinky Solutions-the Perfect Complements Case(a)p1x1*+p2x2*=m;(b)x2*=ax1*.Substitution from(b)for x2*in(a)gives p1x1*+p2ax1*=mwhich gives21*1appmx 71Examples of Kinky Solutions-the Perfect Complements Case(a)p1x1*+p2x2*=m;(b)x

26、2*=ax1*.Substitution from(b)for x2*in(a)gives p1x1*+p2ax1*=mwhich gives.appamx;appmx21*221*1 72Examples of Kinky Solutions-the Perfect Complements Case(a)p1x1*+p2x2*=m;(b)x2*=ax1*.Substitution from(b)for x2*in(a)gives p1x1*+p2ax1*=mwhich givesA bundle of 1 commodity 1 unit anda commodity 2 units cos

27、ts p1+ap2;m/(p1+ap2)such bundles are affordable.appamx;appmx21*221*1 73Examples of Kinky Solutions-the Perfect Complements Casex1x2U(x1,x2)=minax1,x2x2=ax1xmpap112*xampap212*74Choosing Taxes:Various TaxesuQuantity tax:on x:(p+t)xuValue tax:on px:(1+t)pxAlso called ad valorem taxuLump sum tax:TuIncom

28、e tax:Can be proportional or lump sum75Income Tax vs.Quantity TaxuOriginal budget:p1x1+p2x2=muAfter quantity tax:(p1+t)x1+p2x2=muAt optimal choice(x1*,x2*)(p1+t)x1*+p2x2*=m (5.2)Tax revenue:R*=tx1*uWith an income tax,budget is:p1x1+p2x2=m-tx1*76Income vs.Quantity TaxuProposition:(x1*,x2*)is affordab

29、le under income taxuEquivalent to:prove that(x1*,x2*)satisfies budget constraint under income tax.uOr,budget constraint holds at point(x1*,x2*).p1x1*+p2x2*=m-tx1*uWhich is true according to(5.2).uIt is not an optimal choice because prices are different.uConclusion:The optimal choice must be more preferred to(x1*,x2*)7778