MACROECONOMICS I UPF
Transcript of MACROECONOMICS I UPF
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 1
MACROECONOMICS IUPF
LECTURE SLIDES SET 4Professor Antonio Ciccone
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 2
3. Applications of the Ramsey-Cass-Koopmans (RCK) model
3.1 Government spending, consumption, and interest rates
3.2 Bond versus tax financed government spending
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 3
3.1 Government spending, consumption, and interest rates
- Comparative “dynamics” in the RCK model
- Permanent, surprise drop in output
- Temporary, surprise drop in output
- Wars, government expenditures and interest rates
- The role of expectations- Permanent, anticipated drop in output
- Temporary, anticipated drop in output
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 4
k
c
k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
The RCK model
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 5
k
c
k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 6
k
c
NEW k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Permanent, surprise fall in output for given k
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 7
timePermanent, surprise fall in output
Evolution of consumption
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 8
timePermanent, surprise fall in output
Evolution of capital intensity
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 9
-- consumption can JUMP at the time newinformation arrives
-- but consumption must be smooth (follow thefirst-order condition) from than onward:
There CANNOT BE an ANTICIPATED jump in consumption
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 10
k
c
NEW k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Temporary, surprise fall in output for given k: PART I
k-ISOCLINE: NO CAPITAL GROWTH
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 11
k
c
k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Temporary, surprise fall in output for given k: PART II
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 12
k
c
NEW k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Temporary,surprise fall in output: Equilibrium response
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 13
k
c
k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Temporary,surprise fall in output: Equilibrium response
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 14
timeSTART of Tempfall in output
END of Tempfall in output
Evolution of the capital intensity
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 15
timeSTART of Tempfall in output
END of Tempfall in output
Evolution of real interest rate
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 16
timeSTART of Tempfall in output
Evolution of consumption
END of Tempfall in output
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 17
Wars and real interest rates
-- Suppose government expenditures associated withwars are surprise, temporary events
-- Study the dynamic response of: capital, interest rates, and consumption to wars
-- Government expenditures associated with warsdecrease output available for consumption andinvestment
( , )F K L G C I− = +
INCREASE G Same effect as temporary fall in output
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 18
timeSTART of War END of War
Evolution of real interest rate
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 19
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 20
- The role of expectations
- Permanent, anticipated drop in output
- Temporary, anticipated drop in output
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 21
k
c
k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Permanent, anticipated fall in output: PART I
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 22
k
c
NEW k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Permanent, anticipated fall in output: PART II
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 23
k
c
NEW k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Permanent, anticipated fall in output: Equilibrium response
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 24
timeINFO of permanent FUTUREfall in output
Evolution of capital intensity
Output actually falls
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 25
timeINFO of permanent FUTUREfall in output
Evolution of consumption
Output actually falls
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 26
- The role of expectations
- Permanent, anticipated drop in output
- Temporary, anticipated drop in output
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 27
k
c
k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Temporary, anticipated fall in output for given k: PART I
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 28
k
c
NEW k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Temporary, anticipated fall in output for given k: PART II
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 29
k
c
k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Temporary, anticipated fall in output for given k: PART III
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 30
k
c
k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Temporary, anticipated fall in output: Equilibrium response
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 31
k
c
k-ISOCLINE: NO CAPITAL GROWTH
c-ISOCLINE: NO CONSUMPTION GROWTH
k*0
Temporary, anticipated fall in output: Equilibrium response
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 32
timeINFO of FUTURETemp fall in output
END of Tempfall in output
Evolution of the capital intensity
START of FUTURETemp fall in output
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 33
time
Evolution of consumption
INFO of FUTURETemp fall in output
END of Tempfall in output
START of FUTURETemp fall in output
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 34
3. Application of the Ramsey-Cass-Koopmans (RCK) model
3.1 Government spending, consumption, and interest rates
3.2 Bond versus tax financed government spending
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 35
Government expenditures and taxes
t t tGDEFICIT G T= −
Government intertemporal budget constraint
0 00 0
t t t t tPV T dt GWEALTH PV G dt∞ ∞
+ =∫ ∫
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 36
-- Suppose that households believe in government budgetconstraint
-- The government cut taxes at time t
-- But there is no indication that the government cutsexpenditures
00
t tPV T dt∞
∫
-- WHAT HAPPENS TO DISCOUNTED FLOW OF TAXES?
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 37
Nothing, because:
0 00 0
t t t t tPV T dt PV G dt GWEALTH∞ ∞
= −∫ ∫
and the right-hand side of this equation has not changed.
Government will have to compensate current tax cut by taxincrease sometime in the future.
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 38
Now let’s look at household intertemporal budget constraint:
0 00 0
0 00
t t t t
t t
PV C dt PV T dt
PV w Ldt Q
∞ ∞
∞
+
= +
∫ ∫
∫
-- current tax cut does NOT affect this constraint at all as onlythe DISCOUNTERD PRESENT VALUE OF TAXES MATTERS
-- and present value of taxes remains constant if expendituresdo not change
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 39
-- TAX CUT DOES NOT CHANGE HH CONSUMPTION
-- AS A RESULT IT DOES NOT CHANGE THE NATIONALSAVINGS RATE:
t t t tS Y C G= − −
-- DOES NOT AFFECT:- INVESTMENT(!) - AND INTEREST RATES (!)
-- HH SAVINGS INCREASES, BUT IS OFFSET BY AN INCREASE IN GOVERNMENT DEFICIT:
( ) ( )t t t t t tS Y T C T G= − − + −
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 40
Hence, government cuts taxes
Has to issue debt (government bonds)Government ensures that real interest rate on bond mimics
market interest rate (before issue of new bonds)Households buy these new bonds with their tax savings
Hence,Household use to buy government bonds what they “save”
in current taxes
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 41
3. The Diamond model
1. Overlapping generations models2 Setup of the Diamond model1. Technology2. Household behavior3. Dynamic equilibrium system
3. Equilibrium growth and optimality4. Applications of the Diamond model1. Government spending, consumption, and interest rates2. Bond versus tax financed government spending
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 42
-- Discrete time model-- Households live for two periods, and only work in the first
1. Overlapping Generations models
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 43
Time 3 Time 4Time 2Time 1
Generation 1
YOUNG:Workand
Consume
RETIRED:Consume
THE LIFE CYCLE OF A SINGLE GENERATION
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 44
TIMING
Time 3 Time 4Time 2Time 1
Generation 1
Generation 2
Generation 3
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 45
2. Setup of the Diamond model
1. Technology2. Household behavior3. Dynamic equilibrium system
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 46
1. Technology
( )1 t t t tY K A L αα −=
Owned/Supplied by RETIRED Supplied by YOUNG
Capital fully depreciates during production: 1δ =
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 47
time
t t+1
Born -Earn Wage-Consume-Save
- Earn Interest- Consume
2. Household behavior
GENERATION tProduction usesgeneration t labor
Production usesgeneration t capital
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 48
UTILITY of GENERATION t
MAXIMIZATION WITH DISCOUNTING&INTEREST
with respect to C
subject to INTERTEMPORAL BUDGET CONSTRAINT
11
tt t
t
cc wr++ =+
1max ( ) (1 ) ( )t tU c U cβ ++ −
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 49
FIRST-ORDER CONDITIONS FOR GENERATION t
1'( ) (1 )(1 ) '( )t tU c r U cβ += − +
“EFFECTIVE TIME DISCOUNTING”
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 50
Take the following CES utility function:
with
CONSUMPTION PROFILE BECOMES
[ ]1 (1 )(1 )tt
t
c rc
σβ+ = − +
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 51
11
tt t
t
cc wr++ =+
[ ](1 )(1 )1
t tt t
t
c rc w
r
σβ− ++ =
+
( )11 (1 ) (1 )t t tc r wσ σβ −+ − + =
11 (1 ) (1 )t
tt
wcrσ σβ −=
+ − +
Consumption profile intoBudget constraint
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 52
11 (1 ) (1 )t
tt
wcrσ σβ −=
+ − +
11 (1 ) (1 )t
t t t tt
ws w c wrσ σβ −= − = −
+ − +
1
1(1 ) (1 )
1 (1 ) (1 )t
t tt
rs wr
σ σ
σ σββ
−
−− +
=+ − +
Consumption and savings of generation t (when young)
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 53
s
r
(1 )1 (1 )t ts w
σ
σββ
−=
+ −
0
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 54
s
r
(1 )1 (1 )t ts w
σ
σββ
−=
+ − t ts w=
0
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 55
s
r
(1 )1 (1 )t ts w
σ
σββ
−=
+ −
0
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 56
11
1(1 ) (1 )
1 (1 ) (1 )
t t t t
tt t
t
K I L s
rL wr
σ σ
σ σββ
+−
−
= =
− +=
+ − +
3. Dynamic equilibrium system
Savings per young person
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 57
( )1(1 )t t t t tw MPL K A L ααα −= = −
( )111 1t t t t tr MPK K A L ααα −−= − = −
( )1 t t t tY K A L αα −=
Financed by SAVINGSof the now RETIRED
Supplied by YOUNG
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 58
( )
11
11
(1 ) (1 )(1 )1 (1 ) (1 )
t t t t
tt t t
t
K I L s
rK A Lr
σ σαα
σ σβαβ
+−
−−
= =
− += −
+ − +
( )11 1t t t tr K A L ααα −−= −
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 59
( )
1
1 11 1
11 1
(1 ) (1 )1 (1 ) (1 )
t
t t
t t tt t t
t t t t t
KL A
K A LL A rL A L A r
αα σ σ
σ σββ
+
+ +− −
−+ +
=
− +=
+ − +
( )11 1t t t tr K A L ααα −−= −
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 60
11
1(1 ) (1 )1
(1 )(1 ) 1 (1 ) (1 )
t
tt
t
k
rkn a r
σ σα
σ σββ
+−
−
=
− +=
+ + + − +
%
%
1 1t tr kαα −= −%
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 61
3. Equilibrium growth and optimality
1
1 (1 )(1 )(1 ) 1 (1 )
t
t
k
kn a
σα
σββ
+ =
−=
+ + + −
%
%
1σ =
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 62
0
1tk +%
0k%
1t tk bkα+ =% %
tk%1k% BGP
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 63
Optimality
• How to weight different generationsunclear.
• Is the allocation at least Pareto efficient?
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 64
Dynamic Inefficiency
• A situation where the allocation is not evenPareto efficient
• I.e. we can increase consumption of atleast one generation without decreasingconsumption of all others
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 65
Consider case without technological progress a=0.
How much do we need to invest per person at time tto keep capital intensity constant?
11
1 1 1t t t t
tt t
K L i ikL L n
++
+ += = =
+
1t tk k+ = (1 )t ti k n= +
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 66
0 GoldRulek
( )t ty f k=
tk
(1 )tk n+
Consumption per capita
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 67
0
tkGoldRulek
Consumption per capita
1MPK n= +
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 68
11 (1 )
(1 ) 1 (1 )t tk kn
σα
σββ+
−=
+ + −
1 (1 )(1 ) 1 (1 )
k kn
σα
σββ
−=
+ + −
111 (1 )
(1 )1 (1 )BGPk
n
σ α
σββ
−⎛ ⎞−= ⎜ ⎟+ + −⎝ ⎠
BGP
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UPF Macroeconomics I, 2008-09 SLIDE SET 4 SLIDE 69
11 (1 )(1 )
(1 )1 (1 )BGPMPK
n
σ
σβαβ
−⎛ ⎞−
= − ⎜ ⎟+ + −⎝ ⎠
1(1 )MPK kαα −= −
1 (1 )(1 ) (1 )(1 )
BGPMPK nσ
σβα
β⎛ ⎞+ −
= − +⎜ ⎟−⎝ ⎠