PowerPointPrsentation

1
More AboutPresent Values
Theoretical Foundations Fisher Separation
2
Fisher - SeparationNeanderthalian Consumption
Patterns

• Some people prefer to consume now, some to invest
  now and consume later. Without /saving
  in-vestment opportuni-ties, consumers can only
  decide whether to consume now or later.

3
Fisher - SeparationConsumption Patterns and
Financial Markets
If there were financial investment
opportuni-ties, a household can decide to lend a
part of his income to financial markets. At an
interest rate of i.e. 20 p.a. and a consumption
pattern of (4060), the household will then enjoy
72 in t 1. Financial markets increase wealth.
4
Fisher - SeparationConsumption and Real Asset
Investments
To invest always means a decision between
consumption (V0A) and investment (a0A). What you
invest in to, you will earn one period later.
(b1A). Given an income (Y0), the graph shows
all possible combinations of consumption and
investment-plans). This transformation -
function is convex shaped, because of the
generally declining marginal prod-uctivity of
real - asset investments. From Y0 each unit of
invested money will first lead to a relatively
higher future income, later (when investing your
money in less profitable projects) it will lead
to a lower future income.
5
Fisher SeparationConsumption and Real Investments
The individual combination of consumption/investme
nt depends on the individual utility
function. The utility - function UA describes all
combinations, providing the same utility to a
specific individual. The optimum consumption/
investment-pattern is then given at (PA), where
the utility function becomes tangent to the the
transfor-mation function.
6
Fisher Separation Consumption and Real Investments
The figure shows the investment (a0) and
consumption-budgets (V0) of two investors (A und
B). Investor A plans to invest (a0A) more than
he wants to spend on immediate consumption (V0A).
From his investment he can expect a future income
of b1a. Investor B prefers to consume (V0B) and
to invest less (a0B). From his investment he can
expect to get b1B. His future consumption budget
may then be lower than that of Investor A.
7
Fisher Separation Consumption, Financial and
Real Asset Investments
Real investments compete with financial
investments. This compe-tition is shown by the
combination of the two transformation
functions. The slope of the financial market line
is determined by the interest rate, given by
(1i), i.e. each currency unit invested in
financial assets (f0A) leads to a future income
of f0A (1i). Where the functions become tangent
(that is PA), the profitability of real asset
investments equal the profits from financial
asset investments. Below PA, real asset
investements are more attractive (i.e.PAI) ,
above PA financial assets become superior (i.e.
PAF).
8
Fisher Separation Consumption, Financial and
Real Asset Investments
The optimal real-investment pro-gramme is given
at P. At an avai-lable income of Y0 and a given
consumption plan of V0 without financial markets
only a proportion of r0 would be invested,
generating an income of e1 in t1. The economy
would be underinvested. As financial markets
exist, it would be possible to borrow F0 to
realize the optimal investment programme a0. This
programme will generate a future income of b1 in
t1. Subtrac-ting a1 (interest and repayment) the
reamaining income in t1 will be higher than in a
world without financial market.
r0
F0
9
Fisher Separation Separabilityof Consumption and
Investment
The graph shows the theoretical independency of
consumption and investment plans under ideal
financial market conditions. Two investors, A and
B, can realize the same programme a0 despite of
their different consumption plans VOA resp. VOB.
While B has to borrow (F0B), A can realize the
real-investment programme a0 and will invest a
part (F0A) of her income at an interest rate of i
in financial assets.