SL354, Intermediate Microeconomics
Monday
Week 1 :
March 3 – 7
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
Tuesday
Thursday
Friday
Introduction
Varian, 1
Budget Constraints
Varian, 2
Preferences
Varian, 3
Utility
Varian, 4
Choice
Varian, 5
Consumer Demand
Varian, 6 [7]
S. & I. Effects
Varian, 8
Problem Set 1
Thaler, 1 – 3
Buying & Selling
Varian, 9
Buying & Selling
Varian, 9
Intertemporal Choice
Varian, 10; Thaler, 8 – 9
Market Demand
Varian, 15
Equilibrium
Varian, 16
Problem Set 2
Asset Markets
Varian, 11
Uncertainty (Risk)
Varian, 12
Risky Assets
Varian, 13
Portfolio Theory
TBD
Loss Aversion, etc.
Thaler, 6 – 7
Capital Markets I
Thaler, 10 – 11
Capital Markets II
Thaler, 12 and 14
Problem Set 3
Technology
Varian, 18
Profit Maximization
Varian, 19
Exchange
Varian, 31
Welfare
Varian, 33
General Equilibrium
TBD
Problem Set 4
Auctions
Varian, 17
Auctions
Thaler, 5
Externalities
Varian, 34
Exam 1
Exam 3
Production
Varian, 32
Exam 4
Information
Varian, 35
Asymmetric Information Problem Set 5
Varian, 37
Thaler, 15
Exam 2
Exam 5
Intertemporal Trades
C2
(1 + r )m1 + m2
m2
•E
0
= {m1 , m2 }
A  c1 , c2 
•
c2
I0
 1  r 
m1
c1
Borrowing
in period 1
m2
m1 +
(1 + r )
C1
Intertemporal Trades
C2
C2
C1 = C2
C1 = C2
C1
C1
Patient preferences
Impatient preferences
(Negative time preference)
(Positive time preference)
Asset Markets: Debt
Asset Markets: Debt
Dow Jones Industrial Index
16,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
Jan-08
$0
Jan-07
$0
Jan-06
$100
Jan-05
$10
Jan-04
$20
Jan-03
$400
Jan-02
General Electric
Jan-01
$30
Jan-00
$500
Jan-99
$40
Jan-98
$50
Jan-97
Jan-08
Jan-07
Jan-06
Jan-05
Jan-04
Jan-03
Jan-02
Jan-01
Jan-00
Jan-99
Jan-98
Jan-97
Jan-96
$60
Jan-96
Jan-08
Jan-07
Jan-06
Jan-05
Jan-04
Jan-03
Jan-02
Jan-01
Jan-00
Jan-99
Jan-98
Jan-97
Jan-96
Asset Markets: Equity
Google
$800
$700
$600
$300
$200
S&P 500 Index
1,800
1,600
1,400
1,200
1,000
800
600
400
200
0
Asset Markets: Equity
Average Annual Returns*
GE Average
1982-2005
24%
100%
SP500 Average
1982-2005
12.3%
80%
60%
40%
20%
-40%
S&P 500 Index
*Calculated from a value-weighted index of all publicly traded stocks using CRSP data.
*Calculated as compounded annual return on average monthly returns from preceding 12 months.
General Electric
Jan-04
Jan-02
Jan-00
Jan-98
Jan-96
Jan-94
Jan-92
Jan-90
Jan-88
Jan-86
Jan-84
-20%
Jan-82
0%
Present Valuation Techniques and Asset Valuation

The present value (PV) of an amount to be received at time t (FV) when the perperiod discount rate is r:
PV 

FV
1  r t
The present value (PV) of a stream of future values, when the per-period discount
rate is r:
n
FV0
FVn
FVt
FV1
PV 





1  r 0 1  r 1
1  r n t 0 1  r t


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:

PVFirm 
t
 1  r 
t 0
t
Optimal Holding Period for an Asset
$350
24%
22%
$300
20%
FV t 
$250
18%
16%
$200
14%
12%
$150
10%
8%
$100
PV t 
$50
0
1
2
Time
3
4
5
6
7
8
t*
9
10
11
12
13
14
15
16
17
18
19
4%
2%
Rate of return from holding asset
$0
6%
0%
20
Risk and Uncertainty: “Contingent Consumption Plans”
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.
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.
$100
Lucky
day
Do not
purchase
Purchase
Do not
purchase
Lucky
day
$295
If
Pr(Lucky) = 0.025):
Purchase
$35,000
Outcome A:
E x   $34 ,900
 x  $995
Unlucky
day
$25,000
Lucky
day
$34,900
Outcome B:
E x   $100
 x  $31
Unlucky
day
$95
E x   $34 ,900
x  0
Unlucky
day
$34,900
Risk and Uncertainty: “Contingent Consumption Plans”
CGood
$35,000
Lucky
day
Do not
purchase
• E 
C g0 , Cb0
C g0  $35,000

Purchase
Unlucky
day
Lucky
day
Unlucky
day
C 1g  $34 ,900
C
1
b
 C g0  K

A  C 1g , Cb1
•

$25,000
$34,900
$34,900

I0
 
 
 1 
Cb0  $25,000
C
0
b
 C g0  K

C
Cb1  $34,900
1
b
 Cb0  K  K




K = the “expected loss” ($10,000), and K is the insurance premium.
C Bad
Economic Treatment of Risk
The Meaning of Risk Aversion
1. Risk aversion is defined through peoples’ choices:
Given a choice between two options with equal expected values and
different standard deviations, a risk averse person will choose the option
with the lower standard deviation:
If EX1   EX 2  , and  1 
2
, then1  2
Given a choice between two options with equal standard deviations and
different expected values, a risk-averse person will choose the option
with the higher expected value:
If  1 
2
, and EX1   EX 2  , then1  2
2. Non-linearity in the utility of wealth.
Dealing With Risk: Insurance
$100,000
Pr(xA) = .990
E[X] = $99,500
 = $4,975
cv = 0.0500
Pr(xB) = .010
$50,000
Dealing With Risk: Insurance
Pr(xA) = .990
$100,000
$500
$99,500
E[X] = $99,500
 = $0
cv = 0
$100,000
Pr(xB) = .010
$100,000
$500
- $50,000
+ $50,000
$99,500
Dealing With Risk: Insurance
For a risk-averse person . . .
E[X] = $99,500
 = $0
cv = 0
Is
Preferable
to
E[X] = $99,500
 = $4,975
cv = 0.0500
Can we find another option, keeping  = $0, but with a lower
E[X], that will be considered equal to the original? For example,
suppose that for this risk-averse person . . .
E[X] = $99,415
 = $0
cv = 0
Is
Equivalent
to
E[X] = $99,500
 = $4,975
cv = 0.0500
Dealing With Risk: Insurance
If, for a risk-averse person . . .
$99,415
Is
Equivalent
to
E[X] = $99,500
 = $4,975
cv = 0.0500
Then $99,415 is called a certainty equivalent.
Furthermore, we will be able to sell an insurance policy to this
person for $585.
The $85 difference between the amount the person will pay and
the expected loss is called a risk premium.
Economic Treatment of Risk
Utility
The Meaning of Risk Aversion
A
l
U3
l
U2
U1
l
B
U($)
D
l
C
Risk Premium
$0
$99,415
$99,500
$100,000
$
$50,000
U 1  U $50,000 
U 2  U $99,415   EU 99,500 
U 3  U $100,000
Economic Treatment of Risk
Utility
Risk Aversion and Risk Neutrality
U($)
U($)
U($)
$
Economic Treatment of Risk
Utility
Risk Tolerance
U1($)
U2($)
Risk Premium 1
Risk Premium 2
$
Risk Premium 1 > Risk Premium 2 :
Agent 1 is more risk averse than Agent 2
Agent 2 is more risk tolerant than Agent 1
Modeling Risk and Expected Utility in Insurance Problems
Expected Utility:
E Utility 
 pr( x ) * x
n
n
n
If n  2, E U   pr x1 *U x1   pr x2 *U x2 
Certainty Equivalent:
U CE   EU 
Risk Premium:
RP  Ex  CE
Dealing With Risk: Diversification (Portfolio Theory)
Expected Return of a Portfolio (2 investments):
 
E r1,2
 
 E r1,2  Expected return of a portfolio comprised of investments 1 and 2

 w1E r1   w2 E r2 , where 
wi  Weight of investment i in the portfolio

E ri   Expected return of investment i

Expected Variance of a Portfolio (2 investments):
12,2

12,2  Variance of the portfolio

w  Weight of investment i in the porfolio
 w1212  w22 22  2w1w21,2 , where  i
 i2  Variance of investment i

   Covariance of investments 1 and 2
 1,2
Dealing With Risk: Diversification (Portfolio Theory)
Portfolio Example
Weight:
Pr(•)
0.200
0.200
0.200
0.200
0.200
State
1
2
3
4
5
0.5
x
11.00%
9.00%
25.00%
7.00%
-2.00%
0.5
y
-3.00%
15.00%
2.00%
20.00%
6.00%
10.00%
0.76%
8.72%
0.87
8.00%
0.71%
8.41%
1.05
x,y
4.00%
12.00%
13.50%
13.50%
2.00%
.
E[i]
Var(i)
(i)
c.v.
Cov(x,y)
Var(x,y)
(x,y)
c.v.
9.00%
 

 E rx, y  wx Erx   wy E ry
-0.24%
2
0.25%   x, y
4.97%
0.55

 wx2 x2  w2y y2  2wx wy cov rx , ry


where : cov rx , ry   x, y x y

Capital Asset Pricing Model
Capital Market Line
Security Market Line
r = E[return of a portfolio ]
r = E[return of a security ]
rx = rf +
rm - rf
m
rm
X
(
)
ri = rf + ri - rf  i
rm
rx
rm - rf
rf
rm - r f
m
rf
x
m

cov(rx , rm )
Beta,  ≡
var (rm )
1
i
Capital Asset Pricing Model
25
Returns
20
15
10
5
0
0.0
0.2
0.4
Mutual Fund Name
American Century Heritage A
Fidelity Advisor Equity Growth T
Fidelity Magellan
Putnam International Growth & Income
Fidelity Diversified International
Templeton Growth A
Vanguard 500 Index
Vanguard Total Stock Market Index
Vanguard PRIMECAP
Janis Growth & Income
Dreyfus Premier Balanced B
Dreyfus Founders Balanced A
0.6
Symbol
ATHAX
FAEGX
FMAGX
PNGAX
FDIVX
TEPLX
VFINX
VTSMX
VPMCX
JAGIX
PRBBX
FRIDX
0.8
Beta
1.0
1.2
1.4
1.6
3-Year
5-Year
10-Year
Beta
Returns Beta
Returns Beta
Returns
1.44
20.50
1.17
19.26
0.96
8.42
1.18
8.31
1.16
11.20
1.16
3.34
1.33
6.88
1.03
10.42
1.04
3.53
1.07
12.55
1.03
20.56
0.96
6.90
1.08
14.57
1.02
22.18
0.96
10.85
0.77
5.78
0.85
14.81
0.80
7.01
1.00
5.72
1.00
11.18
1.00
3.43
1.04
6.19
1.04
12.27
1.01
3.89
1.01
9.63
1.06
15.78
1.08
8.50
1.13
6.69
1.05
11.22
0.98
5.84
0.98
4.05
0.90
6.59
0.87
1.43
0.98
3.71
0.88
7.21
Capital Asset Pricing Model
cov(rx , rm )
Beta,  ≡
var (rm )
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
GOOG
2.01
Intel
INTC
1.72
J.P. Morgan Chase
JPM
0.68
Microsoft
MSFT
1.61
Nordstrom Inc.
JWN
1.51
PF
0.75
Wal-Mart Stores
WMT
-0.18
Wellpoint Inc.
WLP
0.61
Wells Fargo
WFC
0.32
Google
Pfizer
Economic Analysis of Market Opportunities
Efficient Markets and Economic Profits –
Total Market Returns, Selected Time Periods
Monthly:
Value-Weighted Equal-Weighted
Index
Index
Annual:
Value-Weighted Equal-Weighted
Index
Index
1/80 to 12/02:
AVG
STDEV
0.0108
0.0464
0.0202
0.0548
0.1370
0.7234
0.2708
0.8974
1/97 to 12/99:
AVG
STDEV
0.0208
0.0501
0.0250
0.0579
0.2805
0.7981
0.3450
0.9643
1/00 to 12/02:
AVG
STDEV
-0.0115
0.0564
0.0109
0.0778
-0.1298
0.9319
0.1385
1.4576
1/97 to 12/01:
AVG
STDEV
0.0046
0.0554
0.0179
0.0685
0.0572
0.9103
0.2378
1.2135
1980s:
AVG
STDEV
0.0139
0.0482
0.0152
0.0530
0.1798
0.7591
0.1986
0.8585
1990s:
AVG
STDEV
0.0143
0.0393
0.0279
0.0474
0.1859
0.5883
0.3916
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.
“Most respondents in a sample of undergraduates refused to stake $10 on
the toss of a coin if they stood to win less than $30.”
Value = V($)
+v
- $10
+ (Loss)
+ $30
-v
+ (Gain)