ECO 200Y1Y - MICROECONOMIC THEORY SECTION L0101 …

Department of Economics Luhang Wang University of Toronto Room 273, 150 St. George St. 2011/2012 Email: luhang.wang@ utoronto.ca

Office hours: TBA

ECO 200Y1Y - MICROECONOMIC THEORY SECTION L0101

TEXTBOOK: Microeconomics by Besanko and Braeutigam (4th edition).

LECTURE TIME AND LOCATION: W2-4pm, LM159 COURSE WEBSITE: blackboard www.portal.utoronto.ca MARKING SCHEME: The final course mark will be based on the following:

• term test 1 14% Wednesday October 26 • term test 2 8% December - during exam/test period • term test 3 14% Wednesday February 01 • term test 4 14% Wednesday April 04 • final exam 50% Exam Week (could be during the day)

Please do your utmost not to miss a test. But if it happens that

• you have to miss t1, t3, or t4 for a legitimate reason, to get credit you need to write a comprehensive make-up at the end of the term (likely during the last week); comprehensive means all materials covered in T1, T3 and T4 may be tested on

• you have to miss t2 for a legitimate reason, to get the credit you need to write a special make-up for it during the exam/test period in December

Medical notes must state clearly that you were too ill to write the test and should be provided within one week. TUTORIALS:

• time and location: F12-1pm MP103 • problem sets will be pre-posted on the course website and the solutions will be discussed during

tutorials • there will also be in-class handouts with problems for you to do in tutorials, followed by a discussion • when time permits, you are also encouraged to ask more general questions about the course materials

e-TA: You can also email your question to your TA. To have your questions answered through email, you need to describe clearly what the question is and show the efforts you have taken. TA’s email TBA.

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COURSE OUTLINE AND TUTORIAL ASSIGNMENTS (preliminary and subject to change)

DATE TOPIC RECOMMENDED READING

2011-09-14 roadmap of the course

2011-09-21 preference and utility function chapter 3

2011-09-28 budget constraint and utility maximization chapter 4, 5

2011-10-05 utility maximization and demand theory chapter 4, 5

2011-10-12 applications of utility theory chapter 5

2011-10-19 revealed preference and index numbers chapter 4

2011-10-26 test 1

2011-11-02 uncertainty and lottery chapter 15

2011-11-09 dealing with risk chapter 15

2011-11-16 production function, producer budget and cost minimization chapter 6, 7

2011-11-23 cost minimization and profit maximization chapter 7, 8

2011-11-30 profit maximization in a perfectly competitive industry chapter 9

2011-12-TBA test 2 (not on a lecture day, during the exam weeks)

2012-01-11 analysis of perfectly competitive market (1) chapter 10

2012-01-18 analysis of perfectly competitive market (2) chapter 10

2012-01-25 general equilibrium, gains from trade and welfare theorem chapter 16

2012-02-01 test 3

2012-02-08 market power and monopoly chapter 11

2012-02-15 price discrimination (1) chapter 12

2012-02-29 price discrimination (2) chapter 12

2012-03-07 game theory and nash equilibrium chapter 14

2012-03-14 application of game theory (1): auction chapter 14, 15

2012-03-21 application of game theory (2): duopoly and oligopoly market chapter 13

2012-03-28 application of game theory (3): public goods chapter 17

2012-04-04 test 4

Introduction

• why do I like microeconomics?• human behaviour and decision making, big or small• compact tool set

• what do you remember from ECO100?

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Three Important Concepts in MicroeconomicAnalysis

• optimization:individual decision making

• equilibrium:bring individuals together and find the state where no one wantsto change

• comparative statics:change the environment (thus the incentive of decision makers)and see how the equilibrium changes

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Optimization

• cost benefit analysis• benefit• cost: opportunity cost

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Optimization: Opportunity Cost

• For a decision maker, the opportunity cost of doing A is thebenefit foregone of doing the next best thing.

• Optimization means if the benefit from doing A exceeds itsopportunity cost, then the decision maker should do A;otherwise, the decision maker should not do A.

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Opportunity Cost

Need to know what the options are.{A1, A2, A3...A10}A1 attending lectureA2 teaching yourself in the libraryA3 having a workout in AC...A10 having a long afternoon napV (A1) > V (A2) > V (A3) > ... > V (A10)

• what is the opportunity cost of choosing A1



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Examples of Optimization Problems

• Jill decides how late to stay out at a party when she has to go toclass the next day

• Jill decides how long to surf the web in the evening when she hasto go to class the next day

• Jack decides how much food to eat at a buffet

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• given a fixed monthly budget for entertainment,how many movies and how many concerts to go?

• receiving an inheritance of $100 million,how much to consumer today and how much in the future?

• you want to be an established professional at the age of 35,how many years of school?

• to produce a fixed amount of output,how much capital service and how much labour service toemploy?

What is the difference between these problems and those on theprevious slide?

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• for wireless service, whether to sign a 3-year contract or usepay-as-you-go

• when buying a house, whether to buy an expensive one indowntown, or a cheaper one in suburb and commute to workeveryday

• whether to vote and which political party to vote

What is the difference between these problems and the previous ones?

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Marginal Analysis in Optimization

Jill’s time at the party

Jill goes to a party on Sunday night. She always enjoys party andwould love to stay longer. One the other hand, she needs to go toschool on the Monday morning. The longer she stays the more tiredshe would be. Let t be the amount of time she wants to stay at theparty. How is t decided?

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The benefit she derives from staying out is B(t).• what B(t) is consistent with the fact that Jill enjoys party time?• what if the longer she stays in a party, the smaller the benefit she

gets from one extra hour?• use a curve to describe the relationship between t and B(t)

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an example of B(t) that represents Jill’s preference for party time

B(t) = b0 + b1t− b22 t2; b1, b2 > 0

MB(t) = ΔBΔt = b1 − b2t > 0

ΔMB(t)Δt = Δ2B

dt2 = −b2 < 0

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On the cost side, the later she stays out, the more tired she will bethe next day, and therefore will do a poor job at school. Let the costof staying out be C(t).

• what C(t) is consistent with the fact that Jill gets more tired thenext day from longer partying time?

• what if the longer she stays in a party, the more tired shebecomes from one extra hour?

• use a curve to describe the relationship between t and C(t)

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an example of C(t) that represents Jill’s cost from partying is

C(t) = c0 + c1t + c22 t2; c1, c2 > 0

MC(t) = ΔCΔt = c1 + c2t > 0

ΔMCΔt = Δ2C

Δt2 = c2 > 0

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Jill’s objective is to maximize the net benefit.

net benefit B(t)− C(t)

maxt

N(t) = B(t)− C(t)

• let’s start with t0 and check under what condition it is optimal• thought experiment: increase t by Δt (from t0 to t0 + Δt)

• the increase in benefit is

MB(t0)Δt

• the increase in cost isMC(t0)Δt

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Her change in net benefit is

ΔNB(t0) = MB(t0)Δt−MC(t0)Δt

= [MB(t0)−MC(t0)]Δt

This is proportional to marginal benefit minus marginal cost.• What if marginal benefit at t0 exceeds marginal cost at t0?• What if MC(t0) exceeds MB(t0)?• When is the optimum achieved?

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Optimum achieved when

MB(t∗) = MC(t∗)

ΔB

Δt∣t∗ =

ΔC

Δt∣t∗

Where is this point on the diagram?

Where to find marginal benefit and marginal cost in the diagram?

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Solution: t∗ and the associated net benefit N∗

MB(t∗) = b1 − b2t∗ = c1 + c2t

∗ = MC(t∗)

t∗ =b1 − c1

b2 + c2

NB∗ = b0 + b1t∗ − b2

2(t∗)2 − (c0 + c1t

∗ +c2

2(t∗)2)

= b0 − c0 +(b1 − c1)

2

2(b2 + c2)

Comparative Statics :• What happens to t∗ when b1 increases?• what happens to t∗ when c1 increases?• what happens to N∗ when b1 increases?• what happens to N∗ when c1 increases?

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An Example of Discrete Choice

Go to the party or stay at home surfing the internet

Now let Jill’s benefit and cost from spending time t surfing theinternet be:

B(t) = b0 + b1t−b2

2t2; b1, b2 > 0

C(t) = c0 + c1t +c2

2t2; c1, c2 > 0

t∗ =b1 − c1

b2 + c2

N∗ = b0 − c0 +

(b1 − c1

)2

2(b2 + c2)

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Go to the party or surf the internet?value (net benefit) of going to the partyN∗ = b0 − c0 + (b1−c1)2

2(b2+c2)

value (net benefit) of surfing the internet

N∗ = b0 − c0 +(b1−c1)

2

2(b2+c2)

• what is the opportunity cost of going to the party?• how does this cost different from the time cost C(t)?• under what condition should she go to the party?• does this cost matter if Jill is already in the party?

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Optimization with a Budget Constraint

In many economic problems, the decision maker faces a budgetconstraint. In general, the agents wants to use all the budget availablebecause of the assumption that more consumption is better.

For example, if there are multiple goods to be consumed, and thebudget is exhausted, the consumer can only choose to redistributeconsumption across goods, i.e. to consume more of good A meansgiving up some of other goods.

Thus the opportunity cost of consuming good A is what other goodsthe consumer can choose to consume with the money used to buygood A. This immediately raises a question as to which other goodsshould the consumer give up when thinking of buying more good A.

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Example

Let the consumer consume 2 goods, i = 1, 2. The prices are P1 and P2

respectively. Let the consumer have income Y to divide between the 2goods. c1 and c2 are the amounts of goods consumed.

the consumer’s budget constraint is:

P1 × c1 + P2 × c2 ≤ Y

Let the utility function of the consumer be U(c1, c2). Assume that Uis increasing in all its arguments. i.e., more is better.

The objective of the consumer is to choose the quantity of each goodto maximize utility subject to his budget constraint.

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First, note that he will spend all his money. If he does not spend allhis money, he can increase his utility by spending all the leftovermoney on any good.Starting from consumption bundle c0 = (c0

1, c02).

• consider buying Δc1 more of good 1.• how much does this cost?

P1Δc1.• where does this money come from?

less consumption of good 2• by how much?

P1Δc1P2

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How much more utility will the consumer get by switchingexpenditure from good 2 to good 1?

Let his marginal utility of good i be MUi = ΔUΔci

So the increase in utility from consuming Δc1 units of good 1 is:

Δc1MU1(c0)

The decrease in utility from consuming P1Δc1P2

less good 2 is:

P1Δc1

P2MU2(c0)

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The net change in utility is positive if

Δc1MU1(c0)− P1Δc1

P2MU2(c0) > 0

Δc1(MU1 −P1

P2MU2) > 0

or ifMU1

P1>

MU2

P2

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For some c∗ to be optimal, it must be the case that

MU1(c∗)

P1=

MU2(c∗)

P2

In this case, the consumer will not want to give up some good 2 formore good 1.Note the use of opportunity cost in this argument. To buy more goodi, the opportunity cost is buying less of other goods.

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Example of Equilibrium

Market Equilibrium under Perfect Competition• the major product of the individual optimization analysis is to

determine for consumer how much to buy, and for each firm howmuch to produce, under different prices

• they are called individual demand curve and individual supplycurve respectively

• we can aggregate across individuals to get market demand andmarket supply curves

• we use price elasticity of demand and elasticity of supply todescribe these curves

• price elasticity of demand %ΔQd

%Δp, where %ΔQd = ΔQd

Qd and%Δp = Δp

p

• price elasticity of supply %ΔQs

%Δp

• the intersection of the market demand curve and the marketsupply supply determines the market equilibrium

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• in individual optimization, agents take the price of aconsumption good as given (exogeneous)

• at the price level of the intersection point, the quantitydemanded is the same as the quantity supplied

• everyone achieves his/her optimum and no one wants to move• what if at a price level the quantity demanded is bigger than the

quantity supplied? can it be an equilibrium price?

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Part 1: Consumers’ Optimization Problem

• objective: maximize utility with a fixed budget• describe utility• constraint: budget line• optimization: marginal analysis• demand curve (labour supply curve)• test 1 (Oct. 26, 2011)• decision under uncertainty

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Part 2: Firms’ Optimization Problem underPerfect Competition

• objective: profit maximization• constraints: technology condition and demand condition• breakdown: cost minimization and profit maximization

• cost minimization• objective: minimize cost to product a fixed output• describe how firms use input to produce output• cost function

• profit maximization• marginal revenue versus marginal cost• enter or exit

• test 2 (Dec., 2011)

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Part 3: Analysis of Perfectly CompetitiveMarkets

• bring consumers and firms together to determine equilibrium• government intervention• efficiency and welfare analysis of market equilibrium• (from partial equilibrium to) general equilibrium and welfare

theorem• gains from trade• test 3 (Feb., 01, 2012)

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Part 4: Market Power and Firm Interactions

Extend the previous analysis of firms’ behaviour in two dimensions• market power (perfect competition)• interaction (strategic behaviour)

game theory and Nash equilibrium• application of game theory in public goods• test 4 (April 04, 2012)

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A Few Suggestions

• do practice questions• focus on understanding• attend tutorials• seek help from e-TA, make sure to show your efforts in your email• use office hours

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Consumer Theory

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preference

Preference is about consumers’ likes and dislikes; in other words,ranking of baskets of goods.

budget of $300 per week on meals, snacks, entertainment

basket A: (14 meals, 10 snacks, 1 movie, 0 concert)

basket B: (21 meals, 0 snacks, 0 movie, 1 concert)

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axioms of choices

rational preference:

• more is better than less(14m, 10s, 1m, 0c) ≻ (12m, 10s, 1m, 0c)

(14m, 10s, 0exams) ≻ (14m, 10s, 2exams)good: absence of bad

• completeness: give ranking to any two basketssay basket A & basket B, then A ≻ B or B ≻ A or A ∼ B

• transitivity: if A ≻ B and B ≻ C, then A ≻ C

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completeness and transitivity: an example

Mike goes to Joe’s cafe for lunch every Wednesday. Chef Joe knowshow to cook 4 dishes: pasta, pizza, hamburgers and tacos. Only 3 outof the 4 dishes are served each day.

On one particular Wednesday, you and Mike go to Joe’s cafe for lunchtogether. On the way to the restaurant, you ask Mike what he wouldlike to have for lunch. Mike says he finds himself in the mood forpasta; hamburgers are less satisfying but still good; tacos areacceptable; the mere thought of eating pizza is off-putting.

Is Mike’s preference ranking of lunch options complete?

yes, pasta ≻ hamburger ≻ taco ≻ pizza

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continue..Suppose you ask Mike the same question in a different way. You askabout what he is going to choose under three scenarios and Mike giveshis answers as following.

1. when tacos, hamburgers and pizza are available, Mike prefershamburger

2. when tacos,hamburgers and pasta are available, Mike preferspasta

3. when pasta, hamburgers and pizza are available, Mike preferspizza

Is Mike’s preference transitive? Why?

no1. hamburger ≻ pizza2. pasta ≻ hamburger3. if transitivity holds, we should have pasta ≻ pizza

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ordinal ranking vs. cardinal ranking

• ordinal: ranks only• cardinal: quantitative measure of the intensity of preference

utility function

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utility function

example of consumption of two goods F and C, U(F,C)

• U is increasing in F and C

• MUF (F 0, C0) = U(F 0+ΔF,C0)−U(F 0,C0)ΔF > 0

the increase in utility due to one unit increase in F

• MUC(F 0, C0) = U(F 0,C0+ΔC)−U(F 0,C0)ΔC > 0

the increase in utility due to one unit increase in C

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substitution between goods

How do we measure the tradeoff between food and clothing?

• (14 meals, 10 snacks, 1 movie, 0 concert) ≻ (12 meals, 10 snacks,1 movie, 0 concert)

• (14 meals, 10 snacks, ...) ∼ (12 meals, 15 snacks, ...)

Consider an consumer with C units of clothing and F units of foodand let her have ΔF "more" units of food and ΔC "more" units ofclothing.

• increase in utility when she has ΔF "more" food: UF ΔF

• increase in utility when she has ΔC "more" clothing UCΔC

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• what is the total change in utility

ΔU = UF ΔF + UCΔC

• to keep her total utility unchanged

UF ΔF + UCΔC = ΔU = 0

UCΔC = −UF ΔF

ΔC

ΔF= −UF

UC

for every one unit change of F , C needs to change this much tokeep utility constant

• marginal rate of substitution of food for clothing UF

UC

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MRS continue..

• different utility functions can have the same marginal rate ofsubstitution (at every point)what happens to MRS if we multiply a utility function with 10,100, 1000?

• MRS (ordinal); utility function and marginal utility (cardinal)• MRS: the foundation of mutually beneficial trade two kids in

kindergarten, one with a bag of fruit candies and one with a badof Smarties, swap or not?

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indifference curve

graphical presentation of utility function• negatively sloped

what if X is bad?• no intersection• IC position and level of utility• slope and MRS• convex to the origin and diminishing MRS

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special utility functions and ICs

perfect substitutes• example: U(C, T ) = C + 1/2T

• MRS• indifference curve

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perfect complements• example: U(C, S) = min(C, S)


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Cobb-Douglas utility• example: U(x, y) = x

13 y

23


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quasi-linear utility• example: U(C, Y ) = ln(C) + Y

• MRSwhat if holding C constant and increase Y ?

• indifference curve

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change of preference

example: two brands of bread Dark (D) and White (W)• they are perfect substitutes U(D,W ) = D + W

• firm D successfully conveys through advertisement theinformation that its product has extra health benefit

• the marginal utility of consuming D becomes 2• what is the utility function now?• how do the indifference curves change?

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budget constraint

• PC is the price of clothing• PF is the price of food• I is income of consumer• her budget constraint:

PCC + PFF ≤ I

• budget line

C =I

PC− PF

PCF

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important facts about budget line

• slope −PF

PC

• intercept on X axis: IPF

• intercept on Y axis: IPC

• points within/outside BL

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changes of BL

• what happens to BL if I increases?• what happens to BL if PF increases?• what happens to BL if PC increases?• what happens to BL if PC and PF rise (fall) proportionally?• what happens to BL if PC , PF and I rise (fall) proportionally?

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more examples

change in intercept? slope?• rationing of food• in-kind food aid• membership discount• quantity discount

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consumer optimization

consider an initial allocation on the budget line A = {F 0, C0}• increase food consumption by ΔF marginal units• increase in utility from food is UF ΔF

• how much does ΔF cost?• to release money of amount PF ΔF , decrease in clothing

consumption is PF ΔF

PC

• decrease in utility from less clothing is PF ΔF

PCUC

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• overall utility change is UF ΔF − PF ΔF

PCUc

• if UF ΔF − PF ΔF

PCUc > 0

deviate from F 0, C0 by increasing food consumption• if UF ΔF − PF ΔF

PCUc < 0

deviate from F 0, C0 by decreasing food consumption• if UF ΔF − PF ΔF

PCUc = 0

optimum achieved

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consumer optimization: graphical presentation

at optimum, we havePF

PC= −ΔC

ΔF = UF

UC

• budget slope ΔCΔF = −PF

PC

• IC slope ΔCΔF = −UF

UC

• tangency condition

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how to resolve the problem

• tangency condition MRS = PF

PC

• budget condition PF ∗ F + PC ∗ C = I

• two equations and two unknowns

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a Cobb-Douglas example

• a consumer’s utility function is

U(F,C) = F13C

23

• prices are PF and PC for food and clothes respectively• income is I

consumer solvesmaxF,C

U(F,C) = F13C

23

subject toPFF + PCC ≤ I

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continue..

• find the optimal consumption C∗ and F ∗

• comparative statics of I, PC and PF

• optimized utility• Comparative statics...marginal utility of income

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an example of perfect substitutes

consumer solvesmaxC,T

U(C, T ) = C + 1/2T

subject toPCC + PTT ≤ I

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an example of perfect complements

consumer solvesmaxC,S

U(C, S) = min(C, S)

subject toPCC + PSS ≤ I

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an example of quasi-linear utility function

consumer solves

maxC,Y

U(C, Y ) = ln(C + 1) + Y

subject toPCC + Y ≤ I

what is the solution if PC > 1 (consumption can not be negative)?economic meaning? too little utility value per dollar relative to theother alternative

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more examples

suppose the indifference curves are downward sloping and convex tothe origin

• rationing of foodwho is affected? how does the consumption bundle change?

• food quantity discountwho is affected? how does the consumption bundle change?

• in-kind food aid or cash subsidy of equivalent monetary valuewho is indifferent between the two program? who is not? whichprogram is preferable?

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change in income

income consumption curve (ICC)• in which space?• what relationship?

Engel curve• in which space?• what relationship?

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income effect

• positive: normal goods• zero: neutral• negative: inferior

Can both goods be inferior?• may change with income (poverty, medium income, rich)• a quasi-linear example, ICC? Engel curve?

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change in price

price consumption curve (PCC)• in which space?• what relationship?

demand curve• in which space?• what relationship?• what drives movements along an individual demand curve?• how does an increase (a drease) in income affect demand curve?• demand curves for bread and butter

assume perfect complements and fixed food budget• demand curves for white bread and black bread

assume perfect substitutes and fixed food budget

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decompose a change in price

• change in slope of BL• shrinkage or enlargement of the affordable set, similar to a

change in income

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quantity effect of a change in price

• total effect (TE)• effect due to the change of the slope of budget lime, substitution

effect(SE)• effect due to the change of the size of affordable set, income

effect(IE)

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a graphical presentation

• TE: initial point A and final point B• isolate SE with an auxiliary BL

• Hicks method• Slutsky method

• SE: initial point A and decomposition point D• IE (what remains): decomposition point D and final point B

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mathematical method

• conditions for initial point A and final point B• conditions for decomposition point DH or DS

• SE = XA −XD, IE = XB −XD

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direction and magnitude of SE and IE

increase in the price of the X-good• more or less consumption of X due to SE?• more or less consumption of X due to IE?• giffen good, a special kind of inferior good with IE larger than SE

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relate to demand curve

• normal good• inferior, non-giffen good• giffen good

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welfare effect of a change in price

we have done the analysis on the quantity effect of a price change,now move on to the welfare impact

• measure the distance between two indifference curves?• arbitrary utility label• monetize the distance• how much money is needed to achieve a certain utility level

(more money is needed to achieve higher utility level)• what price to use

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compensating variation and equivalent variation

take for example an increase in the price of the x-good• use new prices

meaning of the distance between the two budget lines?compensating variation

• use initial pricesmeaning of the distance between the two budget lines?equivalent variation

• application: membership fee for membership discount

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how to calculate CV

• original prices and income Px, Py and I

• optimal consumption (X0, Y0), utility U0

• Px increases to P ′x, with P ′x > Px

• how much money is needed to achieve U0 under prices P ′x and Py

• find the budget line that is tangent to the indifference curverepresenting U0 and has the slope P ′

x

Py...I ′CV

• CV = I − I ′CV

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how to calculate EV

• original prices and income Px, Py and I

• Px increases to P ′x, with P ′x > Px

• consumption after the price change (X1, Y1), utility U1

• how much money can be taken away from the consumer to makeU1 her optimal utility under prices Px and Py.

• find the budget line that is tangent to the indifference curverepresenting U1 and has the slope Px

Py...I ′EV

• EV = I ′EV − I

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consumer surplus (CS) as a measure of welfarechange

• what is consumer surplus• how is consumer surplus calculated• why is CS just approximation• Hicksian (compensated) demand curve and CV/EV

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example

U(x, y) = xy

• original prices Py = 1, Px = 4

• income I = 72

• change of price in x, P ′x = 9

• find the CV and EV associated with the price change

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consumer surplus

• CV and EV are different in general• a good approximation is consumer surplus which lies in between

these two numbers

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labour supply (leisure demand)

• a consumer consumes two goods, leisure L and composite goodY , U(L, Y )

• she has 24 hours to allocate between leisure and working• L is her leisure consumption; Ls = 24− L is her labour supply• her wage rate is w• what is the price (opportunity cost) of one hour of leisure?• she uses the money earned from working to buy composite good

Y

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continue..

• indifference curve• budget line• optimization problem• leisure demand curve L(w)

• labour supply curve Ls = 24− L(w)

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continue..

• income and substitution effect of an increase in wage rate• is leisure a normal good?• can the leisure demand curve be upward sloping?• what is the implication for labour supply curve?• decision on the extensive margin: whether to work at all

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practice question

Joe is taking one year off from school. His parents give him anallowance of $280 per week, thus $80 per day. He is offered a job thatpays $5 per hour at a convenience store where he can work as much orlittle as he likes. Assume he needs 9 hours per day to take care ofhimself and has 15 hours for work and leisure. Also assume hismarginal rate of substitution of leisure for composite good isMRSl,Y = 2Y

l .• will he work at all• what if his parents reduce his allowance to $210 per week?• draw his labour supply curve• what happens when the wage rate increases to $10 per hour? SE?

IE?

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two period consumption problem

• a consumer consumes in two periods and her two-period utility isU(C1, C2)

• she has income Y1 in the first period and Y2 in the second period• in the first period she can borrow money at rate rb or lend (save)

money at rate rs

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continue..

• indifference curve• budget line

• rb = rs• rb > rs

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continue..

optimization problem• is she a saver or borrower?

• rb = rssaving Y1 − C1 or borrowing C1 − Y1

• rb > rs

• assume rb = rs = r, how does C1 change if r increases?• borrower: IE? SE? borrow less or more?• saver: IE? SE? save less or more?

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choice and revealed preference

• utility function (assumed preference) + budget constraint ⇒optimal choice

• observed choice (optimal) + budget constraint ⇒? preferencewhat can observed (optimal) choices tell us about consumers’preference (and welfare)?

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example

A consumer spends all her income on X and Y . In period 1, shebought 20 units of X at $5 per unit and 15 units of Y at $5 per unit.In period 2, she bought 30 units of X at $5 per unit and 10 units of Yat $10 per unit.

• draw the BL and find the consumption bundle for each period• which bundle does she prefer?• is she better off or worse off in the second period?• what if in the second period she bought 12 units of X at $10 per

unit and 23 units of Y at $5 per unit• what if in the second period she bought 8 units of X at $10 per

unit and 30 units of Y at $5 per unit• what do you learn from this practice?

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indexes

• change of interestprice index, quantity index and income Index

• weights: base or end periodLaspeyres Index and Paasche Index

• relationship between quantity, price and income indexesapplication, using price index to convert nominal income into realincome

• apply Paasche quantity index to the previous example• apply Laspeyres quantity index to the previous example• relate to CV and EV• relate to Slusky vs. Hicks method of calculating SE• caveat? why CPI may overestimate the increase in cost of living?

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a practice question

"With my income this year and new prices for X and Y I could havejust bought last year’s consumption bundle but I chose not to."

• show the situation in a diagram• what index can be constructed with the information provided?• are you better off or worse off this year?

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Documents

ECO 200Y1Y - MICROECONOMIC THEORY SECTION L0101 …