Transcript Neoclassical theory (continue) - TMyPF-UNAM

The aim of this presentation is to outline an
analytical framework that makes it possible to
compare alternative theories of distribution.
The theories of distribution are described and
compared by using the work procedures
presented in the previous lecture.
We argue that, through some simplifications,
it is possible to have a common analytical
framework for all theories of distribution.
This framework is summarised by the first
three equations of the models we construct to
present these theories.
The differences among them are described by
the remaining equation(s).
We also argue that it is possible to divide the
theories of distribution in two groups on the
basis of the question “what is the role of the
material elements and of the historically
prevailing institutional organization in the
determination of the distributive variables”.
All theories recognise that the material elements (i.e.
technological knowledge and the availability of
resources) affect the relation among distributive
variables.
Yet, some theories state that the material elements
affect the relation among distributive variables, but
not their levels.
Other theories instead state that the material
elements affect both the relation among distributive
variables and their levels.
For the first group of theories the material elements
determine the relation among distributive variable,
while the historically prevailing institutional
organization determines their levels.
The political agreements among the parts conflicting
over the division of the income produced contribute
to the formation of the “conventions” as to what is
normal or fair to pay for the working activity and for
the use of capital and of other resources.
The second group of theories state instead that the
material elements affect both the relation among
distributive variables and their levels.
These theories deny the utility of (or consider
damaging) the political agreements among the parts
conflicting over the division of the national product.
The material and natural elements determine what is
fair to pay for the working activity, the use of capital
and of the other resources.
1. Institutional and accounting framework
The analysis assumes a close economy, no payment of rents,
simple production and n commodities, where n can be equal
to 1 (if we consider a one-commodity world) or greater than 1
(if we consider a more-than-one commodities world).
2. Equilibrium equation
The net output of the economy is equal to total wages plus
total profit:
Y=W+
Y = px = pω L + r pk
where:
p is a line vector representing the relative prices of the n
commodities produced
x is a row vector of the net output of the n commodities
produced
ω is a row vector of the commodities representing the real
wage rate
L is the amount of labour employed in the whole economy
r is the rate of profit
k is a row vector representing the amounts of the n
commodities used as circulating capital in the whole
economy.
We also have:
y = w + rk
and
w = y – rk
where:
w = pω
K = pk
y = Y/L
k = K/L
(1)
3. Specification of the behavioral equations
Let’s start from the equations relative to the
behaviour of y and k.
We must study some technical elements relative to
the choice of technique.
Let’s start with the assumption that producers know
just one technique of production.
In this case, if p is a constant function of r, Y and K are also
constant functions of r and (w = y – rk) is linear.
Figure 1
w
r
If p is not a constant function of r, Y and K are not constant
functions of r and (w = y – rk) is non-linear.
Figure 2
w
r
p is a constant function of r when:
• n=1
• n >1 and we use the “standard commodity” as numeraire.
Notice that if the techniques of production used to produce
the n commodities change, the “standard commodity”
varies
Thus we cannot derive linear w-r relations for different
techniques of production by using one “standard
commodity” as numeraire.
Let’s assume n=1 (i.e., a one-commodity world) to analyse
the properties of the w-r relation describing the use of one
technique of production:
Figure 3
In a one commodity world we have a different linear w-r
relation, with a given y (i.e., a given “average productivity of
labour”) and a given k (i.e., a given “capital-labour ratio” or
“organic composition of capital”), for each technique of
production.
Notice that Rmax, which is the maximum rate of profit, is
equal to the “average productivity of capital” and to the
inverse of the capital-output ratio.
Notice too that y and k are data describing the technical
characteristic of the technique of production considered.
In a one commodity world where producers only
know one technique of production, the behavioural
equations for y and k can be written as follows:
y = y*
(2)
k = k*
(3)
Assume now that we have two techniques of production (call
them A and B) to produce the existing commodity.
From the 2 w-r functions, corresponding to the 2 techniques,
we can derive the “envelope” of the techniques chosen by the
profit-maximising producer at different values of w and r.
In Figure 4 below we have that:
w* is the switch point
yA>yB and kA>kB
for w>w*, technique A is dominant
for w<w*, technique B is dominant
Figure 4
From 2 to m > 2 techniques of production:
Notice that as w decreases, r increases and we can have that the dominant
technique changes, bringing about a lower y and a lower k
Figure 5
If we assume complete (continuous) substitutability among
inputs (factors) of production, the external “envelope”
derived from the dominant techniques is a continuous curve.
Behind each point of the “envelope” there is a technique,
which can be represented by a straight line, with a different y
and a different k.
As we move downwards along the “envelope”, w diminishes,
r increases, and y and k decrease.
We can thus derive the following bijective functions:
1.
2.
3.
4.
5.
a monotonically decreasing relation between w and r
a monotonically increasing relation between w and y
a monotonically increasing relation between w and k
a monotonically decreasing relation between r and y
a monotonically decreasing relation between r and k
Figure 6
To sum up, if we assume that in the economy there is one
commodity and that there is continuous substitutability
between capital and labour, the behavioural equations of y
and k take the form:
y = y(r)
(2)
k = k(r)
(3)
With
0 ≤ r ≤ Rmax
r k(r) < y
Rmax k(Rmax) = y
if
0 ≤ r < Rmax
Notice that if we abandon the assumption of a onecommodity world, p is not a constant function of r
anymore and the monotonic relations (bijective
functions) between w and y, w and k, r and y, r and
k, do not hold anymore.
If p is not a constant function of r, the non-linear w-r
relation representing one technique of production
used can be described by Figure 7 below:
Notice that when the pair (w, r) change, k varies even if the
same technique of production is used.
Figure 7
In a more-than-one commodity world, if we have
more than one techniques of production, it can
happen that a technique that is dominant at high
values of w (low values of r), becomes nondominant as w diminishes (r rises), but then becomes
dominant again when w diminishes (r rises) further.
This phenomenon is known as “re-switching of
techniques”.
Figure 8
It may also occurred that at high values of w (low values of r)
k diminishes as w diminishes (r rises), as it happens in a onecommodity world, but then k increases as w diminishes (r
rises) further.
This phenomenon is known as “reverse capital deepening”.
The monotonic feature of the relations between w and y, w
and k, r and y, and r and k does not hold anymore.
When we assume the existence of more than one commodity
and complete (continuous) substitution among inputs (factors)
of production, the occurrence of the “reverse capital
deepening” phenomenon must be considered the general case.
This implies that in general, as we move downwards along
the “w-r envelope”, w diminishes and r rises, but k can either
decrease or increase.
A given value of k does not univocally identify a point of the
“w-r envelope”. It can identify more than one points of the
“envelope”.
The occurrence of the “reverse capital deepening” creates
problems to the neoclassical theories of growth and
distribution.
Alternative theories of distribution
4. The last behavioural equation(s)
Since in equations (1-3) we have 4 unknowns, we
must introduce at least another behavioural equation
to complete the presentation of the theories of
distribution and to make a comparison among them
Let’s start this part of the study by assuming a onecommodity world and continuous substitution among
inputs of production.
We can so derive a “w-r envelope”, which
enjoys the property that each one of its points
identifies one pair (w, r) and one value of k.
Moreover, each value of k identifies one point
of the “envelope” and one pair (w, r).
Figure 9
Through the use of the “w-r envelope”, which
summarises the previous equations (1-3), and
the introduction of another equation (or of
other equations) we can represent and
compare the different theories of distribution.
Ricardo’s theory
Ricardo took the real wage rate as given at its
“historically subsistence” level, call it w*.
w = w*
(4)
Given the level of w* we can derive the rate of
profit, r*, through the “envelope”.
In a one-commodity world, the use of “contained
labour” as numeraire is satisfactory.
Ricardo’s theory (continue)
Ricardo’s theory of distribution was conceived to offer (and is
compatible with) a conflictual interpretation of the relations
between social groups (classes).
He focussed on the conflicts between “rentiers” and “profit
earners” and considered the interests of the capitalist class as
coincident with those of the whole society as far as
improvements in the standard of life were concerned.
Capitalists’ savings (and related accumulation) favour growth
and raise the income of the whole economy.
Marx’s theory
The real wage rate is taken as given and the rate of profit is
derived through the “w-r envelope”.
Historical, social, political and economic factors affect the
level of these variables.
A historical and conventional theory of distribution is put
forward.
The material conditions of production constrain the relation
between distributive variables, not their levels.
Marx’s theory (continue)
The theory proposes a conflictual interpretation of the
economic and social processes that affect income distribution
and is compatible with the idea of “exploitation”.
The labour theory of value holds in this one-commodity
world and the emergence of “exploitation” in the production
process is neatly described.
Marx focussed on the conflicts between capitalists and
workers and played down the positive role that Smith and
Ricardo attributed to the capitalist class.
Other classical theories
For some authors of the British classical tradition (Joplin,
Gilbart, Tooke, J.S. Mill), but also in some works of Ricardo
and Marx, we can find the idea that the rate of profit can be
taken as an exogenously determined variable, influenced by
the prevailing level of the interest rate, while the real wage
rate can be derived through the “w-r envelope”.
r = r*
(4)
r = r(i)
i = i*
(4)
(5)
Other classical theories (continue)
These positions emerge when the so-called “financial
revolution” and its developments clarify the relevant and
expanding role of the financial sector in the economy and the
possibility of persistent variations in the interest rate, which
were independent of the prevailing level of the rate of profit.
Historians indicate 1830 as a reference date for the “financial
revolution”.
In 1830 a Parliament Act allowed joint-stock ownership in
banking and a “clearing house” in the Bank of England,
setting up the first official payment system in history.
Sraffa’s monetary theory of distribution
In his reconstruction of the theories of the classical political
economists Sraffa hinted at the possibility of taking r, rather
than w, as an independent variable determined by the level of
the interest rates.
Sraffa claimed that in modern society, where workers
partecipate in the division of the surplus produced in the
economy, this choice is the most appropriate way of closing
the model describing the price system.
Sraffa’s theory too considers income distribution as a
conflictual process.
Sraffa’s monetary theory of distribution (continue)
The material conditions of production constrain the relation
between distributive variables, as described by the “w-r
envelope”.
Yet, they do not fix the level of these variables.
Historical and conventional elements enter the determination
of their level.
Monetary policy decisions affect the level of the interest rate,
as long as they are compatible with the expectations and the
interests of the financial sector.
Sraffa’s monetary theory of distribution (continue)
The dominant level of the interest rate tends to affect the rate
of profit and to constrain the real wage rate.
Workers’ reactions and “real wage resistance” may set in
motion conflictual processes, in which phenomena like
unemployment and inflation can play a relevant role.
The historical evolution of these processes eventually
generates levels of distributive variables compatible with the
constraints imposed by the material conditions of production,
which are described by the “w-r envelope”.
Postkeynesian theories of growth and distribution
(Kaldor, Pasinetti)
These theories take the investment decisions and the propensity to
save of the capitalist class (or of the profit-earners, or of the firm
sector of the economy) as exogenously given.
On this basis they determine the rate of profit through the
Cambridge (or Pasinetti) equation, where g is the rate of capital
accumulation and sc is the propensity to save of the capitalists.
r = g / sc
(4)
The real wage rate is determined as the residual variable through
the “w-r envelope”.
Postkeynesian theories of growth and distribution
(Kaldor, Pasinetti) - continue
A recent debate on the role of the Government sector has
clarified that these theories can be made compatible with
Sraffa’s monetary theory of distribution.
Monetary policy decisions can determine the interest rate and
affect the rate of profit.
The “w-r envelope” determine the real wage rate as a
residual variable.
The Cambridge equation, revised to consider the Government
sector, allows one to identify the fiscal policy to be pursued to
keep the economy along a pre-defined growth path.
Kalekian theories of distribution
These theories too determine the rate of profit exogenously.
It depends on the “degree of monopoly” enjoyed by
producers.
The “degree of monopoly” can impose an extra-charge over
the rate of profit established by the prevailing interest rate.
The real wage rate is seen as a residual variable.
Neoclassical theory
In this theory the level of both distributive variables (w and r)
is determined through the “w-r envelope”, taking k as given.
k = k*
(4)
The value of k taken as given is that fixed by the available
quantity of capital and labour existing in the economy.
In a one-commodity world for each value of k we can
identify, through the “w-r envelope”, one pair of these
distributive variables.
Neoclassical theory (continue)
The material conditions of production and the availability of
resources thus constrain both the relation between distributive
variables and their level.
The conflictual interpretation of the distributive processes
turns out to be false since competitive market forces are able
to guarantee satisfactory results in terms of efficiency and
social justice.
The social and political factors, acting over a certain historical
period, interfere with the operation of market forces and
negatively affect efficiency and social justice.
Neoclassical theory (continue)
When more than one commodities are produced, the neat
results of the “w-r envelope” derived for a one-commodity
world disappear.
The value of k identifying the available quantities of capital
and labour existing in the economy is not associated anymore
with one point of the “envelop” and one pair (w, r).
Under these conditions k can still be seen as an indicator of
the relative scarcity of the factors of production characterising
the economy, but the level of distributive variables cannot be
considered anymore as reflecting this relative scarcity.
Neoclassical theory (continue)
The marginal productivities of the factors of production
cannot be assumed anymore as monotonically decreasing.
They can either increase or decrease with the more intense
use of the factor, reflecting the “reverse capital deepening”
phenomenon.
As a consequence they cannot be taken as an alternative
indicator of the relative scarcity of the factors of production.
Neoclassical theory (continue)
The demand functions for capital and for labour cannot be
taken as monotonically decreasing anymore.
They too can either decrease or increase when their rates of
remuneration diminish.
The demand function for investment too cannot be taken as
monotonically decreasing.
Neoclassical theory (continue)
These results cause serious problems to the neoclassical
approach.
The neoclassical version of Say’s Law loses strength because
the variations of the interest rate may not be able to restore
the equibrium between saving and investment decisions.
Moreover, in Solow’s theory of growth problems of
instability may come about and convergence towards the
natural rate of growth and among different economies may be
problematic.
Neoclassical theory (continue)
“Reverse capital deepening” can be seen as the most
important result of the 1960s debate on capital theory.
It clarifies that
1. multiple equilibria are the general case,
2. the level of the distributive variables cannot reflect the
relative scarcity of the factors of production
3. the neoclassical version of Say’s Law finds it difficult to
attribute an equilibrating role to the variations of the
interest rate
4. the neoclassical theory of growth and distribution suffers
from instability problems.