SL354, Intermediate Microeconomics

Week 1 :March 3 – 7

Monday Tuesday Thursday Friday

Exam 1

Exam 2

Exam 3

Exam 4

Exam 5

Problem Set 3

EquilibriumVarian, 16

Problem Set 2

AuctionsVarian, 17

Profit MaximizationVarian, 19

Welfare Varian, 33

ExternalitiesVarian, 34

InformationVarian, 35

IntroductionVarian, 1

Budget ConstraintsVarian, 2

PreferencesVarian, 3

ChoiceVarian, 5

Consumer DemandVarian, 6 [7]

S. & I. EffectsVarian, 8

Buying & SellingVarian, 9

Intertemporal ChoiceVarian, 10; Thaler, 8 – 9

Market DemandVarian, 15

Loss Aversion, etc.Thaler, 6 – 7

Asset MarketsVarian, 11

Risky AssetsVarian, 13

Capital Markets IThaler, 10 – 11

Capital Markets IIThaler, 12 and 14

UtilityVarian, 4

Problem Set 1Thaler, 1 – 3

Uncertainty (Risk)Varian, 12

Problem Set 4

TechnologyVarian, 18

ExchangeVarian, 31

ProductionVarian, 32

General EquilibriumTBD

AuctionsThaler, 5

Asymmetric InformationVarian, 37

Problem Set 5Thaler, 15

Portfolio Theory TBD

Week 2 :March 10 – 14

Week 3 :March 17 – 21

Week 4 :March 24 – 28

Week 5 :April 7 – 11

Week 6 :April 14 – 18

Week 7 :April 21 – 25

Week 8 :April 28 – May 2

Week 9 :May 5 – 9

Week 10 :May 12 – 16

Buying & SellingVarian, 9

1c

Borrowingin period 1

Intertemporal Trades

0I

21 +)+1( mmr

r 1

{ }210 ,= mmE

•

•

21 ccA ,

1C

2C

2m

2c

1m( )r

mm

+1+ 2

1

Intertemporal Trades

1C

2C

21 = CC

1C

2C

21 = CC

Impatient preferences (Positive time preference)

Patient preferences (Negative time preference)

Asset Markets: Debt

Asset Markets: Debt

Asset Markets: Equity

*Calculated from a value-weighted index of all publicly traded stocks using CRSP data.

Average Annual Returns*

-40%

-20%

0%

20%

40%

60%

80%

100%

Jan-

82

Jan-

84

Jan-

86

Jan-

88

Jan-

90

Jan-

92

Jan-

94

Jan-

96

Jan-

98

Jan-

00

Jan-

02

Jan-

04

S&P 500 Index General Electric

*Calculated as compounded annual return on average monthly returns from preceding 12 months.

GE Average1982-200524%

SP500 Average1982-200512.3%

Asset Markets: Equity

The present value (PV) of an amount to be received at time t (FV) when the per-period discount rate is r:

The present value (PV) of a stream of future values, when the per-period discount rate is r:

Bond pricing. The price of a bond will be the net present value of interest payments and the maturity date and value.

Stock valuation. The current value of a firm (PVFirm) is the present value of the stream of future profits that the firm will generate -- and shareholders are “residual claimants” of those profits:

tr

FVPV

1

n

tt

tn

n

r

FV

r

FV

r

FV

r

FVPV

01

10

0

1111

0 1tt

tFirm

rPV

Present Valuation Techniques and Asset Valuation

Optimal Holding Period for an Asset

$0

$50

$100

$150

$200

$250

$300

$350

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

22%

24%

tFV

tPV

Rate of return from holding asset

t*

Risk and Uncertainty: “Contingent Consumption Plans”

Purchase

Do notpurchase

Luckyday

Unluckyday

$100

$295

$95

Case 1:A person with an endowment of $100 is considering the purchase of a lottery ticket that costs $5. The winning ticket in the lottery gets $200.

Case 2:A person with an endowment of $35,000 faces a 1% probability of losing $10,000. He is considering the purchase of full insurance against the loss for $100.

Purchase

Do notpurchase

Luckyday

Unluckyday

$35,000

$34,900

$34,900

Luckyday

Unluckyday $25,000

995$

900,34$

x

xE

0

900,34$

x

xE

Outcome A:

Outcome B:

31$

100$

x

xE

IfPr(Lucky) = 0.025):

0I

1

00 , bg CCE

•

•

BadC

GoodC

000,35$0 gC

KCC

C

gb

b

00

0 000,25$

KCC

C

gb

g

01

1 900,34$

KKCC

C

bb

b

01

1 900,34$

11 , bg CCA

Risk and Uncertainty: “Contingent Consumption Plans”

Purchase

Do notpurchase

Luckyday

Unluckyday

$35,000

$34,900

$34,900

Luckyday

Unluckyday

$25,000

K = the “expected loss” ($10,000), and K is the insurance premium.

1. Risk aversion is defined through peoples’ choices:

2. Non-linearity in the utility of wealth.

Given a choice between two options with equal expected values anddifferent standard deviations, a risk averse person will choose the optionwith the lower standard deviation:

Given a choice between two options with equal standard deviations anddifferent expected values, a risk-averse person will choose the optionwith the higher expected value:

212121 then , and ,XEXE If

212121 then ,XEXE and , If

Economic Treatment of Risk The Meaning of Risk Aversion

Pr(xB) = .010

$100,000

$50,000

E[X] = $99,500= $4,975cv = 0.0500

Pr(xA) = .990

Dealing With Risk: Insurance

Pr(xB) = .010

$100,000

$100,000 - $500

$99,500

E[X] = $99,500= $0cv = 0

Pr(xA) = .990

$100,000 - $500 - $50,000 + $50,000

$99,500

Dealing With Risk: Insurance

E[X] = $99,500= $0cv = 0

IsPreferable

to

E[X] = $99,500= $4,975cv = 0.0500

For a risk-averse person . . .

IsEquivalent

to

E[X] = $99,500= $4,975cv = 0.0500

Can we find another option, keeping = $0, but with a lowerE[X], that will be considered equal to the original? For example,suppose that for this risk-averse person . . .

E[X] = $99,415= $0cv = 0

Dealing With Risk: Insurance

If, for a risk-averse person . . .

IsEquivalent

to

E[X] = $99,500= $4,975cv = 0.0500

Then $99,415 is called a certainty equivalent.

$99,415

Furthermore, we will be able to sell an insurance policy to thisperson for $585.

The $85 difference between the amount the person will pay andthe expected loss is called a risk premium.

Dealing With Risk: Insurance

$99,415

B

Risk Premium

500,99415,99$2 UEUU

$

Utility

$100,000$0

U1

A

C

U3

$50,000

000501 ,$UU 0001003 ,$UU

U($)

$99,500

U2 D

Economic Treatment of Risk The Meaning of Risk Aversion

$

Utility

U($)

Economic Treatment of Risk Risk Aversion and Risk Neutrality U($)

U($)

Risk Aversi

on

Risk Seeking

Risk Neutra

l

Risk Premium 2

$

Utility

U2($)

Economic Treatment of Risk Risk Tolerance

U1($)

Risk Premium 1

Risk Premium 1 > Risk Premium 2 : Agent 1 is more risk averse than Agent 2Agent 2 is more risk tolerant than Agent 1

Modeling Risk and Expected Utility in Insurance Problems

2211 ** ,2 If

*)(

xUxprxUxprUEn

xxprUtilityEn

nn

UECEU

CExERP

Expected Utility:

Certainty Equivalent:

Risk Premium:

Dealing With Risk: Diversification (Portfolio Theory)

irE

iw

rE

rEwrEwrE

i

i

investment ofreturn Expected

portfolio in the investment ofWeight

2 and 1 sinvestment of comprised portfolio a ofreturn Expected

where,2,1

22112,1

2 and 1 sinvestment of Covariance

investment of Variance

porfolio in the investment of Weight

portfolio theof Variance

where,2

2,1

2

22,1

2,12122

22

21

21

22,1

i

iwwwww

i

i

Expected Return of a Portfolio (2 investments):

Expected Variance of a Portfolio (2 investments):

Dealing With Risk: Diversification (Portfolio Theory)

yyxxyx rEwrEwrE ,

yxyxyyxxyx rrwwww ,cov222222,

Portfolio Example

Weight: 0.5 0.5 State Pr(•) x y x,y

1 0.200 11.00% -3.00% 4.00% 2 0.200 9.00% 15.00% 12.00% 3 0.200 25.00% 2.00% 13.50% 4 0.200 7.00% 20.00% 13.50% 5 0.200 -2.00% 6.00% 2.00%

. E[i] 10.00% 8.00% 9.00% Var(i) 0.76% 0.71% (i) 8.72% 8.41% c.v. 0.87 1.05 Cov(x,y) -0.24% Var(x,y) 0.25% (x,y) 4.97% c.v. 0.55

yxyxyx rr ,,cov :where

Capital Asset Pricing Model

[ ]portfolio a ofreturn = Er

fr

xr

mr

m

fm rr

-

mx

Xm

fm

fx

rrrr

-

+=

[ ]security a ofreturn = Er

i

fr

mr

fm rr -

( )ififi rrrr -+=

1

Capital Market Line Security Market Line

( )( ) Beta,

m

mx

r

rr

var

,cov≡

Capital Asset Pricing Model

3-Year 5-Year 10-YearMutual Fund Name Symbol Beta Returns Beta Returns Beta ReturnsAmerican Century Heritage A ATHAX 1.44 20.50 1.17 19.26 0.96 8.42Fidelity Advisor Equity Growth T FAEGX 1.18 8.31 1.16 11.20 1.16 3.34Fidelity Magellan FMAGX 1.33 6.88 1.03 10.42 1.04 3.53Putnam International Growth & Income PNGAX 1.07 12.55 1.03 20.56 0.96 6.90Fidelity Diversified International FDIVX 1.08 14.57 1.02 22.18 0.96 10.85Templeton Growth A TEPLX 0.77 5.78 0.85 14.81 0.80 7.01Vanguard 500 Index VFINX 1.00 5.72 1.00 11.18 1.00 3.43Vanguard Total Stock Market Index VTSMX 1.04 6.19 1.04 12.27 1.01 3.89Vanguard PRIMECAP VPMCX 1.01 9.63 1.06 15.78 1.08 8.50Janis Growth & Income JAGIX 1.13 6.69 1.05 11.22 0.98 5.84Dreyfus Premier Balanced B PRBBX 0.98 4.05 0.90 6.59 0.87 1.43Dreyfus Founders Balanced A FRIDX 0.98 3.71 0.88 7.21

Capital Asset Pricing Model

Name Symbol Beta

Aetna AET 1.08

Anheuser Busch BUD 0.60

Bank of America BAC 0.32

Boeing BA 0.88

Cummins Inc. CMI 1.35

Deere & Co. DELL 1.23

Dell DELL 1.81

Eli Lilly Co. LLY 0.43

Family Dollar Stores FDO 0.82

General Electric GE 0.70

General Motors GM 1.27

Google GOOG 2.01

Intel INTC 1.72

J.P. Morgan Chase JPM 0.68

Microsoft MSFT 1.61

Nordstrom Inc. JWN 1.51

Pfizer PF 0.75

Wal-Mart Stores WMT -0.18

Wellpoint Inc. WLP 0.61

Wells Fargo WFC 0.32

( )( ) Beta,

m

mx

r

rr

var

,cov≡

Efficient Markets and Economic Profits –Total Market Returns, Selected Time Periods

Economic Analysis of Market Opportunities

Monthly: Annual:Value-Weighted Equal-Weighted Value-Weighted Equal-Weighted

Index Index Index Index1/80 to 12/02:AVG 0.0108 0.0202 0.1370 0.2708STDEV 0.0464 0.0548 0.7234 0.8974

1/97 to 12/99:AVG 0.0208 0.0250 0.2805 0.3450STDEV 0.0501 0.0579 0.7981 0.9643

1/00 to 12/02:AVG -0.0115 0.0109 -0.1298 0.1385STDEV 0.0564 0.0778 0.9319 1.4576

1/97 to 12/01:AVG 0.0046 0.0179 0.0572 0.2378STDEV 0.0554 0.0685 0.9103 1.2135

1980s:AVG 0.0139 0.0152 0.1798 0.1986STDEV 0.0482 0.0530 0.7591 0.8585

1990s:AVG 0.0143 0.0279 0.1859 0.3916STDEV 0.0393 0.0474 0.5883 0.7428

Loss Aversion

You are offered the following bet: A coin will be tossed. If it is heads you win x; if it is tails, you lose y.

+ (Gain)+ (Loss)

+ v

- v

+ $30

- $10

Value = V($)

“Most respondents in a sample of undergraduates refused to stake $10 on the toss of a coin if they stood to win less than $30.”