Economics and Finance, 2014-15
Lecture 3: Consumption and Investment decisions under perfect capital
markets
Luca Deidda
UNISS, DiSEA
October 2014
Luca Deidda (UNISS, DiSEA)
EF
October 2014
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Plan
I
Introduction
I
The economy under perfect capital markets and no production
I
The economy under perfect capital markets and production
I
Separation theorem(s)
Luca Deidda (UNISS, DiSEA)
EF
October 2014
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Introduction
Introduction
I
In the previous lecture we analyzed the case of of financial autarky,
showing that individual preferences over current and future consumption
affect investment decisions
I
Now we want to analyze if the presence of a perfect market for financial
resources makes a difference
Luca Deidda (UNISS, DiSEA)
EF
October 2014
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The economy under perfect capital markets and no production
The economy under perfect capital markets and no
production
I
Let us assume now, that individuals can lend/borrow at an interest rate r
I
For instance, we can assume that there is costless financial
intermediation by competitive banks that issues deposits and supplies
loans at the interest rate r
Luca Deidda (UNISS, DiSEA)
EF
October 2014
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The economy under perfect capital markets and no production
Budget constraint and consumption possibilities
I
The possibility to borrow/lend in the capital markets implies the following
budget constraint:
c2 ≤ (y1 − c1 )(1 + r ) + y2
(1)
I
The above constraint says that the value of consumption in period 2
cannot exceed the value of income at time 2 plus the overall return of
financial investment (lending), (y1 − c1 )(1 + r )
I
Non-satiation implies that any optimal choice of c1 and c2 satisfies the
above constraint as strict equality
Luca Deidda (UNISS, DiSEA)
EF
October 2014
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The economy under perfect capital markets and no production
Optimal saving (financial investment) decision
I
The individual will choose how much to consume in the two periods, and
hence how much to invest in the capital market in the first period, so to
maximize u(c1 , c2 ) subject to: c2 = (y1 − c1 )(1 + r ) + y2
I
Unless financial constrained he will invest up to the point that
SMSc1∗ ,c2∗ = 1 + r ⇒ 1 + r =
∂U
∂c1∗
∂U
∂c2∗
(2)
So that the two conditions that are simultaneously satisfied by the optimal
solution are
Luca Deidda (UNISS, DiSEA)
1+r
=
c2∗
=
∂U
∂c1∗
∂U
∂c2∗
(3)
(y1 − c1∗ )(1 + r ) + y2
EF
(4)
October 2014
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The economy under perfect capital markets and no production
Optimal saving (financial investment): comment
gives the graphical representation of the optimal decision
I
Figure
I
The existence of a capital market, allows to transfer financial resources
to/from period 2
I
Endowments do not matter for optimal consumption-saving decision
Figure 1
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EF
October 2014
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The economy with real investment decisions under perfect capital markets
The economy with real investment decisions under
perfect capital markets
I
Let us assume now that individuals can borrow/lend at the interest rate r ,
and
I
They also have access to the real investment opportunity that generates
a real return R(I) given a level of investment I, as analyzed before
I
We recall that, given the properties of R(I), real investment opportunities
give rise to the consumption possibilities frontier shaped according to
Figure 2
Luca Deidda (UNISS, DiSEA)
EF
October 2014
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The economy with real investment decisions under perfect capital markets
Optimal real investment decision
Let us consider various alternative choices:
A1: No investment: Utility equals u(y1 , y2 )
A2: Optimal real investment without using the capital market
A3: Optimal real investment and financial operations in the capital market
I
The various alternatives are represented in
Luca Deidda (UNISS, DiSEA)
EF
Figure 3
October 2014
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The economy with real investment decisions under perfect capital markets
The stages of the optimal decision
I
Real investment decision
I
Financial decision
I
Note that the two decisions are independent one from the other
(Separation theorem)
Luca Deidda (UNISS, DiSEA)
EF
October 2014
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Separation theorem
Individual preferences and investment decisions:
Separation theorem
Theorem (Fisher separation theorem)
With perfect capital markets, the production decision is governed solely by the
objective market criterion of wealth maximisation without regard to individuals’
subjective preferences that enter into their consumption decisionsÓ
For a graphical representation, see
Luca Deidda (UNISS, DiSEA)
Figure 4
EF
October 2014
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Separation theorem
Corollary
I
Separation between ownership and control is irrelevant (and costless)
I
Production/investment decisions can be delegated at no cost
I
Independently of the subjective preferences of the decision maker, the
investment decision will be efficient: it will maximize the Net present
value (NPV) of the project
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EF
October 2014
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Separation theorem
Optimal Choice under perfect capital markets and no
real investment
C2
W2
€
€
C2*
€
C1*
Luca Deidda (UNISS, DiSEA)
W1
EF
C1
October 2014
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Separation theorem
Figure 2: Production possibilities frontier
c2
€
0
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c1
EF
October 2014
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€
€
Separation theorem
Figure 3: Optimal choice with Financial markets and
production
C2
y 2p
y2
y1p
Luca Deidda (UNISS, DiSEA)
y1
EF
C1
October 2014
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Separation theorem
Figure 4: Optimal choice with Financial markets and
production
C2
€
y2
y1
C1
€
Luca Deidda (UNISS, DiSEA)
EF
€
October 2014
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