1
1
Growth Conicts
Jayasri Dutta
Department of Economics
University of Birmingham
[email protected]
November 2000
1I
would like to thank Toke Aidt, Rob Becker, Stan Engerman, Stephen Morris
and Paul Seabright for detailed comments on earlier versions, and the ESRC for
research support.
Abstract
Economic history provides many examples of situation where workers resist
the adoption of new technologies, but also of situations where expansion is
resisted by entrepreneurs. This paper starts with the hypothesis that this
resistance is a rational response to anticipated eects on the distribution of
incomes.
The basic construct is that of an economy where access to credit is
restricted to a subset of the population. It shows that changes in technology and institutions are of three kinds. Increases in the productivity
of capital are Pareto-improving; increases in the productivity of labour increase prots but lower wages, and market liberalization does the reverse.
It also shows that the implied inequality trap is temporary: the adoption of
pareto-improving technologies eventually reverses the distributional impact
of growth.
\ To found a great empire for the sole purpose of raising up a people
of customers may, at rst sight, appear a project only for a nation
of shopkeepers; but extremely t for a nation whose government is
inuenced by shopkeepers."
Adam Smith: The Wealth of Nations, 1776
It seems to me quite certain that, if for four centuries there had been a
very widely extended franchise and a very large electoral body in this
country, ... the threshing-machine, the power-loom, the spinning-jenny,
and possibly the steam-engine, would have been prohibited"
Sir Henry Sumner Maine: Popular Government, 1886
1
1
Introduction
Does growth make everybody better o? If not, would groups in society
attempt to block some forms of progress? This paper sets out a small model
to explore some of these questions.
We normally associate economic growth with technological progress,
which expands production possibilities. If an economy is able to produce
more from the same resources, it can surely aord to make every participant better o. One would imagine, then, that true technological progress
would be welcomed by all participants in an economy, precisely because all
resistance can be bought o. In fact, quite a substantial body of evidence
suggests episodes of resistance to progress, at dierent times in dierent
societies. It is likely, then, that these were responses to evidence, or anticipation, of inequalizing growth. At the same, we should not get carried
away by this evidence on episodes; the last 150 years provide evidence of
very widespread technical progress. To put it mildly, not all progress was
successfully resisted everywhere. The model studied in this paper attempts
to understand why some kinds of growth generate conicts, and others not;
and why these conicts are likely to vary across societies, and over time.
1.1 The evidence
The theory is built to explain facts from very dierent societies, and sources.
It is useful to review a selection here.
1. Productivity in the textile industries varied dramatically across countries at the turn of the century, as reported in Clark (1989). The major
dierence, in operational terms, was in terms of looms operated per
worker, which varied from 1 in India, 2 in Russia, 3 in Mexico, 4 in the
UK, 5 in Canada and 6 in Massachusetts. Perhaps more interestingly,
there is evidence for each country suggesting that employers wanted to
achieve increases in the number of looms per worker (typically, from
n to n + 1). Workers resisted this change with varying degrees of success. The hypothesis, then, is that resistance was successful in blocking productivity growth at dierent levels in each country. Woolcott
(1994) folows up this type of investigation by comparing productivity
increases in textiles in Japan and India between the wars. Japanese
textile industries typically employed illiterate young girls saving up for
their dowry : presumably, they had shorter horizons as far as wages
or working conditions were concerned. Indian workers were typically
2
adult males expecting to work for substantially longer periods. The
rate of growth of labour productivity dierred by a factor of 3 { being
2% per annum in India and 6% in Japan. The explanation suggested
is that Japanese workers had fewer reasons to resist progress, because
of demographic factors.
2. Prescott (1997) examines labour productivity in post-war US coalmining, which increased three-fold in the period 1950-70. The situation was reversed after the oil-price shocks; productivity fell by 50%
in the period 1970-80. This a very rare observation of \technological
regress"; Prescott sugests that it is evidence about the ability, rather
than willingness, to resist, or reverse progress. Deep shaft mining was
heavily unionized before, and during this episode. Competition with
cheap gas in the early years made productivity growth necessary to
the survival of the industry. The oil-price shocks raised the demand
for coal, which allowing unions to get away with greater demands for
work-sharing, or restrictions on working hours and workloads. The
ability to resist progress declined more or less in tandem with the decline in oil prices and the development of strip-mines for lower grade
coal in Arizona. As a consequence, we observe fairly continuous productivity growth since 1980.
3. 18th and 19th Century Britain saw several episodes of resistance to
change, including the Lancaster riots of 1799 and the Luddite revolt
(1811-13), which gives its name to all \resistance to progress'. The
govenment used enormous resources, including the army, to put down
these revolts. Mokyr (1990) suggests that the government became
more tolerant of resistance over time, and permitted rules and regulations which were inimical to progress, but likely to protect small
entrepreneurs rather than workers.
4. Quite a good illustration of the previous claim comes from Harris
(1997), describing the repeal of the \Bubble Act" in 1825. The Act,
put in place in 1725, prevented the free and spontaneous formation of
joint-stock companies in England, and made specic state authorization necessary. The Act was a response to the South Sea Bubble of
1720; and a political movement calling for its repeal took almost 20
years to convince parliament. Much of the opposition came from Businesssmen and entrepreneurs; contemporary accounts seem convinced
of the legitimate role of their vested interests.
3
5. Very similar stories arise in other times and places. Diamond (1998)
documents the arrival of gunpowder in 18th Century Japan. A series of regulations successfully suppressed their production and use for
100 years; the Samurai, who controlled the pre-Restoration state, had
monopoly skills invested in swordplay, and wanted to restrict the right
to bear arms by the rest of the population. Olson (1982) provides a
very large number of examples of resistance to progress by coalitions,
sometimes of entrepreneurs and sometimes of workers. Among them,
Chinese merchant guilds in the 17th Century who were recorded to
have used cannibalism to enforce size restrictions on individual rms,
and the invention of apartheid by South African trade unions to restrict labour supply.
6. Parente and Prescott (1994) simulate and calibrate an aggregate model
of \barriers to technology adoption", parametrized by an exogenous
cost of adoption. Their ndings suggest that the implied cost of adoption increased substantially in Europe and Japan in the 1970's, and
decreased in Korea and Taiwan somewhat earlier. Costs of adoption
reect the extent of successful resistance to progress: and the question
raised by this exercise relates to the timing of these changes.
1.2 Sources of resistance
These episodes suggest that not all progress is universally desirable. They
are instances of resistance by identiable groups in society, who stood to
lose in relative, and possibly absolute terms. The changes contemplated {
in technology, or in institutional structures { are imagined to be conducive
to growth. On many occasions, there is suÆcient evidence after the fact to
conrm the hypotheses that it could generate more for all.
Why were they perceived to be harmful to sub-groups? These could
be attributed to all sorts of reasons: failure of rational expectations where
workers imagine that productivity growth will reduce the number of jobs,
failing to visualize that there will be just as many jobs, and higher wages, at
equilibrium; short-termism, especially if the costs of change are up-front, but
benets arrive over time (notice that the Woolcott(1994) ndings suggest
quite the reverse; or assignment failures, where existing institutions may fail
to assign the shares of an increasing pie appropriately. If progress requires
agent L to take an action, it should be the case that her own income does
not decline when progress occurs.
4
The model which follows is a relatively simple theory of why \assignment
failures" may happen at competitive equilibria of borrowing constrained
economies. Very briey, at any point of time, there are workers, and shopkeepers: the choice of occupation is endogenous, subject to borrowing constraints. Total output is aected by the level of technology , and by the
degree of liberalization , which represnts the proportion of the population who have the right to borrow. Output is x(; ), increasing in both.
At equilibrium, workers earn wages w(; ) and shopkeepers earn prots
v(; ). Growth can come from technology, , or institutional change, .
The important point is that both are likely to be contested; prots decrease
with , while wages may decrease with some increases in . In addition,
the level of is an important determinant of the likelihood of resistance to
technology: resistance is much more likely if is low. There are no Luddites
if opportunities are equally distributed. Resistance to institutional change
is likely to arise always and everywhere; resistance to technology is likely to
decrease as growth progresses.
The quote from Maine makes a particularly strong claim, quite the contrary of \textbook" growth models: that all progress harms somebody.
2
The Model
The model here borrows from Lucas (1978), with some drastic simplications. 1 Changes in technology and institutions take place over time. Generations overlap, and successive generations must decide whether to adopt
newly available technologies, and whether to change institutional structures.
Time is discrete, indexed by t. A continuum of individuals are born every
period, and live for two periods. They work when young, and consume when
old. Every individual has one unit of labour when young, and none when
old, and derive no utility from leisure. They do choose their occupation,
deciding whether to become workers, or shopkeepers. Shops produce and sell
an undierentiated consumption good. Production requires labour, capital,
and supervision. A shopkeeper must borrow money to set up shop, and
then supervise it. All of this takes place in a small open economy, which
faces interest rates rt in international capital markets. Capital is mobile,
but labour remains in the country. Real wage rates wt adjust to clear the
domestic labour market at each time t. The measure of the population, and
1
I assume that individuals do not dier in ability, which trivializes the size distribution
of rms, the main objective of Lucas' model.
5
the aggregate supply of labour, is normalized to be 1 every period.
Not everyone has access to capital markets. All individuals can lend,
or save, at the interest rate rt . Some have the right to borrow at this
rate. This a privilege available to a proportion t of the population at time
t. Privilege can correspond to quite dierent characteristics of societies
and their institutions: access to family resources, being connected to those
who manage nancial institutions, living in cities where debt monitoring
and repayment are monitored at low cost, being part of an ethnic group
or caste with well-developed credit networks and enforcement mechanisms,
or inheriting businesses with a good reputation. For our purposes, it is
important to note that possible distributions of privilege are predetermined
and commonly known to be so. It is easiest to think of this as a directory
of names, ordered such that for every , the right to borrow is extended to
those with names in the range [0; ].
The combination of privilege and occupational choice determines the
number of enterprises in the economy. Clearly, restrictions on are likely to
imply a restriction on the entry of new rms. For this reason, it is useful to
think of as the degree of liberalization. The model identies this closely
with nancial liberalization, but its conclusions extend to other forms of
entry-prevention aided by the state, such as industrial licensing or costly
bureaucratic procedures which discourage startups of new enterprises.
2.1 Technology: the shop
Shopkeepers own and supervise shops, which produce a single consumer
good x. Production is in two phases: a sweat-shop, which combines labour,
`, and capital, k, to produce an intermediate good y, and nishing, which
uses supevision a and y to produce x. As a useful mnemonic, think of
k as looms and y as yards of textiles, while x refers to nished cloth on
the storeshelf. The production technology for y has xed coeÆcients, with
productivity t = (kt ; `t) > 0. Technology implies
y = min[k k; ` `]:
We note that any increase in represents technological progress: higher
k corresponds to faster looms, and higher ` to improvements in working
methods which allows a worker to operate more looms at the same time.
The production of x has a stationary technology
x = a 1 y ; 0 < < 1:
6
Supervision, or entrepreneurial input, is necessary to convert raw output
into marketable consumer goods. Note that supervision, a, has diminishing marginal productivity, reecting limitations on the managers' span of
control.
Clearly, we can combine these to write the production function, with
three inputs and a single output:
x = F (a; k; `; t ) = a1 (min[kt k; `t `]) :
(1)
We note that F has constant returns to scale in inputs (a; k; `); diminishing
marginal productivity of each input; and is strictly increasing in the technology vector t. Equation (1) is a special case of the class of production
functions set out in Lucas (1978). The intermediate input y indexes the size
of operations.
The cost of production is as follows. A shopkeeper has to rent capital
at rental rate r, and hire workers at wage w per hour. A unit of y needs
k(y) = y=k units of capital and `(y) = y=` units of labour. The cost of
producing y is C (y), with constant unit costs c(w; r; ):
r w
C (y) = y( + ) yc(w; r; ):
k
`
The shopkeeper must provide the supervisory input himself, and keeps all
residual prots.
A prot-maximizing shop will choose its size y in the usual manner:
(S) max
V (a; y) = a1 y C (y; w; r; );
y
given a,,w and r, these choices imply:
1
(S:1) y^ = a( r + w ) 1 k
`
y
^
(S:2) k^ =
(S:3) `^ =
(S:4) x^ =
k
y^
`
a( r
)1 :
+
k
w
`
We note, further, that prots are
V (a) = a(1 )( r w ) 1 av(w; r; ):
k + `
7
(2)
We note that v(w; r) is the reward to supervision per hour. This is constant
because the technology displays constant returns to scale.
2.2 Occupations: rms and the labour market
Individuals have one unit of labour when young, which they suply inelastically. This can be allocated to work or to supervision:
`h + ah 1:
Individuals choose ah; `h, to maximize their income, subject to the time and
borrowing constraints. Capital and supervision are complementary inputs:
individuals who cannot borrow cannot set up shop. Incomes are vah + w`h if
0 h t, and w`h otherwise. Obviously, those who do not have borrowing
privileges have no choice, and work at the going wage rate. Privileged
individuals will choose to set up shop only if it pays at least as well as the
going wage rate. It follows that
Z t
ahdF (h) > 0 ) v (w; r) w:
0
Let nt be the supply of entrepreneurship, i.e. nt = R0t ahdF . By construction, ah 1, implying nt t ; those without the right to borrow cannot set
up their own business. Some privileged individuals may choose to become
workers, despite having the right to borrow. This is true only when the two
occupations yield the same incomes:
nt < t ) v(wt ; rt ; t ) = wt :
Together, the number of shops, nt satises the complementary slackness
condition
(N) :Either
N:1 : [v(wt ; rt ; t ) = wt ; nt < t ]
or
N:2 : [v(wt ; rt ; t ) wt ; nt = t ]:
Each shop has the same technology of production and faces the same
price on goods, labour and capital markets. The aggregate demand for
labour is
1
n
Lt = t ( r wt ) 1 nt `t (wt ; rt ):
(3)
`t kt + `t
The supply of labour is 1 nt . Wages adjust to clear labour markets every
period:
(L) L = 1 n ) ` (w ; r ) = 1 nt :
t
t
t
8
t
t
nt
2.3 Equilibrium Paths
At any time, t, the economy has technology t, liberalization level t , and
must pay the rental rate rt determined in international markets. The state
of the economy, at time t, is summarized as
st = [t ; t ; rt ]; kt > 0; `t > 0; 0 t 1; rt > 0:
The full history of exogenous variables is the state process fst gt = 01.
An equilibrium path is a sequence fnt ; wt ; xt g1t=0 , with nt 2 [0; t ], wt; xt 0 such that every individual chooses their occupation subject to borrowing
constraints, enterpreneurs choose input and output levels to maximize profits, and labour markets clear at each t: in other words, (S.1)-(S.4), (N),
and (L) are satised at each t. Equilibria are stationary whenever outcomes nt; xt ; wt depend on the current state st, irrespective of history. or
expectations of future states.
Propositions 1 and 2 establish the existence, and characteristics of equilibria. It is convenient to dene the functions E (n); C (n) for each n 2 [0; 1]:
E (n) = (
and
n 1 1 n) ;
(4)
1 (1 )( 1 n ) :
)
(5)
1 n
n
We note that both functions are continuous and monotonically increasing
in n; and that E (0) = 0; A(0) = 1, and E (1) = C (1) = 1.
Proposition 1 Let st = [t ; t ; rt ] be the state of the economy at t. An
C (n) = (
n
equilibrium exists if, and only if
E (t ) 1 rt `;t
kt
at each t. This equilibrium is stationary, i.e. nt
x(st ) at each t and st .
(6)
= n(st); wt = w(st ); xt =
From condition (N), we note that an equilibrium at time t can be in one
of two regimes. At an unconstrained equilibrium, N.1 holds, and v(w; r) =
w. Individuals are indierent between occupations which earn the same
income per hour, and some individuals who are allowed to borrow will choose
to set up shop. Typically, in such a situation, n < , all individuals earn
9
the same income, and borrowing constraints do not bind. This is the type
of equilibrium examined in Lucas (1978). At a constrained equilibrium,
privilege commands rents: N.2 is true, and v(w; r) > w. In consequence,
all those who have the right to borrow and set up shop do so, and we have
n = . Borrowing constraints bind in the sense that the two occupations
earn dierent incomes. Proposition 2 sets out the conditions on the state st
which give rise to each type of equilibrium.
Proposition 2 Suppose (6) holds. Equilibrium outcomes at t satisfy (N.1),
vt = wt and nt < t if, and only if st satises
1 (C) C (t) > rt`t :
kt
Further, equilibrium outcomes satisfy (N.2) whenever st fails to satisfy (C).
2.3.1 Proof of Propositions 1 and 2
We drop the time subscript for convenience, to examine equilibria for a given
state s = (; ; r).
P.1 Dene c = w` + rk as the unit cost of production. (S.1) implies,
( y(a) )1 = :
a
c
The demand
for
labour
by
a
shop
with
a units of supervision is y(a` ) .
Let n = R0 ahdF (h) be the total supply of supervision. The aggregate
demand for labour is
n 1
Ld = ( ) 1 :
` c
The total supply of labour is 1 n; and labour market clearing, (L),
obtains whenever `
r`
n 1
w(n; s) = c`
=
` (
1 n)
k
r`
:
k
(7)
P.2 We note that the equation (7) summarizes the restrictions imposed
by individual optimization, (S), and labour market clearing, (L), irrespective of the incidence of borrowing constraints, (N), and must
hold at every t and st along an equilibrium path. We note, further,
that the right-hand side of the equation is monotonically increasing
in n, and that n in each state. Condition (6) of Proposition 1 is
necessary for this, and w, to be non-negative.
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P.3 From (N), we know that either v = w or n = must hold at equilibrium. From (S) and (7), we have
1 n ) :
v(n; s) = (1 ) (
(8)
L
n
P.4 Suppose, rst, that N.1 holds, and v = w. From (7), and (8), we
obtain
1
1 (1 )( n ) = r` q(s): (9)
)
1 n
1 n
k
The quantity q(s) is strictly positive; and C (n) is strictly increasing
with C (0) = 1, C (1) = 1. A unique solution to (9) exists. This solution satises the required restriction, n < , if, and only if, condition
(C) is satised.
P.5 Suppose condition (C) fails. By construction, C () < q(s). Let n = ,
folowing (N.2). This denes an equilibrium if, and only if, v(; s) w(; s) 0. We note that v(n; s) w(n; s) 0 whenever C (n) < q(s).
w(; s) 0 holds whenever (6) holds.
P.6 By construction, equilibrium outcomes n; w and hence x are stationary.
This proves the required results.
C (n) = (
n
2.4 Comments
This section sets out the model of a dynamic open economy where
participation in capital markets is restricted. The level of technology,
and the extent of restrictions on borrowing , as well as the international
interest rate, may vary over time. We found stationary spot-market
equilibria, where individuals choose occupations, and the number of
rms, wages, and national income are endogenous, and determined
as functions of the current state of the economy. Call these n(s),
w(s), and x(s) respectively. The main interest here is to examine
the equilibrium eects of technological progress, and the extent to
which these increase the propensity to disgree and to resist changes in
technology or in institutions.
We want to consider the role of alternative factors inuencing growth,
and the extent to which they are contested. The natural question,
then, is how conicts are resolved. There is more than one way, and
11
the outcomes depend on the mechanisms of social and political negotiation. The purpose here is to study the underlying economic mechanism, and the extent to which dierences in the economic environment
inuence the incentives to either promote or resist progress. Thus, the
model is \partial" equilibrium: partial in the sense that politicluences,
and the equilibria of conict resolution methods and political bargains
are not modelled. The eect of policies can be studied precisely because the economy is fully specied. The provenance of policy is not
explored for the moment.
The model is simple, and allows for stationary solutions. Obviously,
if technology, institutions, and international prices were to remain the
same over time, these outcomes would dene characteristics of steadystate paths. Stationarity is useful for the present purpose, as it allows
us to evaluate policy eects in terms of comparative statics of these
time-invariant equilibrium maps. There are some natural extensions,
which can lead to richer dynamical systems, with quite important economic implications, which I explore briey in the next few paragraphs.
The rst, and most natural extension, is to heterogeneous abilities, following Lucas (1978) more directly. Briey, imagine that individuals
dier in ability ah; and that ability matters in supervision, and not
when working for someone else. This introduces a non-trivial occupational choice for those with the right to borrow, who will choose to set
up a business only if v(s)ah w(s) ) ah a(s). It becomes important, then, to evaluate whether privilege is correlated with intrinsic
ability. If it is, the bite of borrowing constraints is that much smaller,
because most individuals who should be entrepreneurs are likely to
have the right to borrow. If they are independent, we obtain equilibria
which are very similar to the ones studied here, with an important difference in observable implications. Liberalization may actually reduce
the number of rms, but increase their eÆciency, because the entry of
higher-ability entrepeneurs can drive up productivity and wages suÆciently to increase the entry threshold a(s). The sort of result derived
here carries through for nt, interpreted as the quality-weighted supply
of entrepreneurship.
A second extension, familiar from Galor & Zeira (1993), as well as
Banerjee & Newman (1993), has to do with inheritance of wealth, and
not merely privilege. This provides a natural route for undrstanding
12
the dynamics of t . Imagine that individuals leave bequests because
they value the welfare or consumption of their children. If borrowing
constraints take the form of dierential borrowing and lending rates,
this leads to a determination of t as follows. Individuals who inherit
suÆcient wealth choose to become entrepreneurs, which yields a better return on their savings than the available lending rates. Borrowing
rates may be high enough to prohibit entrepreneurship among those
who inherit smaller amounts, leading to the phenomenon that a low
t implies large rents from entrepreneurship, which leads to large bequests to their ospring who are alos likely to set up their own shops.
In an otherwise stationary model, this explains the steady-state value
of , typically decreasing in the wedge between borrowing and lending
rates. In non-stationary environments, as we consider, the co-evolution
of t and t are likely to exhibit important characteristics of interest.
Finally, the assumption that the economy is open disables the natural dynamics familiar in overlapping generations economies since Diamond (1969), corresponding to the determination of interest rates.
In a closed economy of this type, interest rates preserve memory because they depend on the supply of savings and hence, past states.
The major results here are likely to be preserved in situtations where
intertemporal substitution elasticities are relatively high.
13
3
Growth and Distribution: comparative statics
At any point of time, the technology and institutions are given; and equilibrium in goods and labour markets detrmines the number of enterprises,
total employment, output, wages, and prots. Growth refers to an increase
in per capita output, which can arise in response to changes in any of the elements of st: technical progress, liberalzation, or movements in international
prices. These changes are likely to aect the distribution of incomes incomes
between wages and prots, as well as the proportion of population earning
these incomes. Some sources of growth are more equalizing than others. For
the remainder, I consider rt to be stationary and equal to r every period.
The output and distributional eects of changes in interest rates are very
similar to that of (reciprocal) changes in kt, as evident from conditions (S):
note, too, that condition (6) holds for r small enough relative to all other
parameters. We can now write equilibria as functions of the restricted state
variable (; ). This Section evaluates the comparative statics of stationary
equilibria, with the purpose of isolating circumstances where growth gives
rise to conicts.
3.1 Sources of Growth
Proposition 3 (Technical progress) 1. An increase in labour productivity, ` , increases aggregate output x.
2. An increase in capital productivity, k , increases aggregate output, x
whenever (C) holds. It has no impact on x otherwise.
Proposition 3 demonstrates, formally, that technology improvements
must result in growth, irrespective of the degree of liberalization. This, one
might say, is perfectly intuitive: the only statement which needs explanation
is that k may be growth-neutral. This arises at low levels of liberalization,
which imply the failure of condition (C). If access to borrowing is severely
restricted, the number of enterprises is constrained at its maximal value,
, as is the pool of workers available. Capital is complementary to labour,
and an increase in its productivity simply reduces the demand for capital.
In this situation, the inelastic supply of entrepreneurship is a binding constraint. We note that condition (C) can be understood as a situation where
the economy is suÆciently liberalized, and there is no shortage of entreprise
at equilibrium.
14
The next Proposition evaluates the eects of technical progress on entrepreneurship: this is meaningful only if is suÆciently large.
Proposition 4 (Progress and Entrepreneurship)
Suppose = 1. The
R1 h
supply of entrepreneurship, n = 0 a dF (h) is greater than 1 . n
increases with labour productivity, `, and decreases with capital productivity,
k .
An increase in labour productivity frees up more worker-hours, and increases the supply of enterprise in an unconstrained world. Increases in capital productivity have the opposite eect, because the demand for workers
per rm increases, driving up equilibrium wages which draws more prospective shop-keepers to the labour market. Proposition 4 suggests that we
are unlikely to observe a systematic correlation between technical progress
and the size distribution of rms, because the eects of dierent forms of
technical change are quite dissimilar.
Proposition 5 (Liberalization) Liberalization rst increases, and then
decreases, aggregate output. Specically,
@x
0 < (1 ) ) @
0;
< 0;
(1 ) < < n ) @x
@
@x
n < 1 )
= 0:
@
n is the supply of entrepreneurship, and n < , (C).
Financial liberalization does have growth eects, but these eects can
be paradoxical, as we see in Proposition 5. The intuition for this result is as
follows: for low levels of (indeed, for n), the number of enterprises
is equal to . At the same time, the number of workers is (1 ). The
production of output requires both labour and supervision, and = 1 achieves the output-maximizing proportion of entrepreneurship. This is not
the division which would be achieved at an unconstrained equilibrium. At
the output-maximizing , prots are excessive, and the equilibrium level n
must exceed the output-maximizing level 1 .
Proposition 5 raises a natural question: we know that restricting access
to capital markets will \work". It suÆces to set = (1 ). Borrowing
constraints bind (because 1 < n), and the number of enterprises is
15
precisely 1 . This maximizes output, which comes with some degree of
inequality because prots exceed wages and privilege continues to earn rents.
The diÆculty comes from the conict between growth and distribution: a
change in is not a Pareto improvement.
3.2 Distributional Eects
We saw, in Propositions 3 and 5, that technology and liberalization are both
potential sources of growth. We now turn to the question of who benets
from growth. The answer depends critically on the source.
Are there circumstances when growth is necessarily Pareto-improving?
Proposition 6 (Consensus) All growth is Pareto-improving if condition
(C) holds.
Recall that condition (C) implies that borrowing restrictions do not bind
at equilibrium: it is certainly true if = 1. If is suÆciently high, growth
can only come from improvements in technology. The claim of the Proposition is that all individuals gain from technical progress at an unconstrained
equilibrium.
Things are quite dierent in economies where is low, and the supply of
entrepreneurship is constrained. Indeed, as we see, condition (C) is virtually
necessary for Pareto-improving growth. For the next proposition, we need
to dene the function R(n) for each n 2 [0; 1]:
R(n) = 2 (
n
1 (10)
1 n ) = E (n):
We note that R(n) is continuous and monotonically increasing, with R(0) =
0 and R(1) = 1. Further, R(n) < E (n) as < 1; and R(n) > C (n)
whenever n < 1+1 .
Proposition 7 (Agreeable technical change) 1. An increase in capital productivity, k increases wages, w and prots, v:
@w
@v
0;
0:
@k
@k
2. An increase in labour productivity, ` increases prots:
@v
> 0:
@`
16
It decreases wages, i.e.
@w
@`
< 0, whenever s satises
1
(R) max[R(); C ()] < r` :
k
The eect on wages is positive,
@w
@`
> 0 if (R) fails.
Proposition 7 establishes that better looms are always agreeable, but
improvements which allow workers to operate more looms may not be. It
is probably important to understand the underlying story. Imagine that is low, and the supply of entrepreneurship constrained by borrowing. The
number of enterprises is xed and cannot respond to technical progress.
A single enterprise, when faced with improvements in labour productivity,
responds by hiring fewer workers at the going rate. The shift in labour
demand reduces equilibrium wage rates. If is high, close to one, say, the
number of enterprises responds to the increase in prots, and this reduces
the supply of labour simultaneously. The overall eect on wages is positive.
Workers, as a group, may resist productivity improvements, in anticipation
of their general equilibrium eects.
Technical progress enhances the total amount a society can produce with
its resources: it need not be redistributive, because there is simply more for
all. Propositions 6 and 7 underline the importance of institutional structures
in actually achieving consensus. If privilege is suÆciently widely distributed
{ at the limit, = 1 represents perfect equality of opportunity { this statement is true at equilibrium outcomes.
Proposition 8 (Liberalization conicts) Wages increase, and prots decrease with the degree of liberalization:
@w
@
@v
0; @
0:
There may be consensus on technical progress. There can never be any
agreement on the right degree of liberalization, because it is, of necessity,
redistributive. An increase in erodes the value of privilege, and lowers
prots. A decrease in restricts the formation of new enterprises, lowering
the potential demand for labour and the equilibrium wage level.
17
3.3 Proof of Propositions 3-8
P.8 Let E (n) = ( 1 nn )1 ; C (n) = E (n) (1 )( 1 nn ) ; and R(n) =
E (n) for each n 2 [0; 1]. By construction, E (n) C (n), and C (n) 1 R(n) whenever n 1+1 . Dene q() = r`k .
P.9 Let n be the solution to C (n) = q(). Note that C (n) is monotonically increasing, and that C (1 ) = 0 < q() and c(1) = 1 > q(),
implying (1 ) < n < 1. Condition (C) holds whenever < n.
P.10 Let n(; ); x(; ); w(; ), and v(; ) be equilibrium outcomes for
each state (; ). From (N), (7), (8), and Proposition 2, these satisfy;
n(; ) = min[; n ];
(11)
1 x(; ) = ` n (1 n) ;
(12)
n 1 r`
w(; ) = ` (
;
(13)
1 n)
k
1 n ) :
v(; ) = (1 ) (
(14)
`
P.11
P.12
P.13
P.14
n
We write ni ; n, etc. for partial derivatives of these functions.
n is monotonically increasing in q(), implying
n` 0; nk 0; n 0:
From (12), xn 0 if, and only if < (1 ). From [P.9], n > (1 ).
Thus, n = whenever < (1 ). Thus,
0 1 ) x 0;
1 < < n ) x < 0;
> n ) x = 0:
From (13, 14),
< n ) w > 0; v < 0;
> n ) w = 0; v = 0:
From (12), [P.11] and [P.12], we have
n ) xk = 0;
< n ) xk > 0:
18
P.15 Let b = `(1n n) . The dening equation C (n) = q() implies
(1 ) b = r
(15)
`
k
which implies b` < 0 and bk < 0. Further, x = nb whenever > n.
From (12), x` > 0 whenever < n. Thus,
x` > 0;
and
n ) xk = 0;
> n ) xk > 0:
P.16 From (14),v = 1b whenever > n, and v = (1 )` ( 1 ) otherwise. We obtain
v` > 0; vk 0:
P.17 From (N), n ) w = v; from (13), < n ) w` = 11 [R()
`
q]. hence,
max[C (); R()] q ) w` 0;
max[C (); R()] < q ) w` < 0:
b1
4
On Technology Adoption
So far, we know the eects of changes in any of the state variables on growth,
and on the distribution of income generated by a competitive equilibrium;
all dynamics is subsumed in the temporal evolution of the state variable st.
Growth from one source or another may generate conicts; it is likely that
these conicts slow down the process of growth itself. In this Section, I set
out a relatively simple feedback mechanism, corresponding to an extremal
method of conict resolution. All change requires unanimity, and changes
which are contested are not made. In reality, societies use quite dierent
methods of resolving conicts, including voting, or bargaining, or outright
bribery. Obviously, dierent mechanisms for choosing policy are likely to
generate quite distinct patterns of growth and distribution.
Imagine that r and are stationary over time, and that < 1 .
Technological progress occurs, exogenously, which increases the productivity
of labour, or capital, in the best available frontier technology. These are
f^ t = (^kt ; ^`t)g1t=0 :
19
Technical knowledge accumulates over time, increasing ^ t. For the present
illustration, I assume balanced growth in the frontier technology:
^kt+1 = (1 + g)^kt ; ^`t+1 = (1 + g)^`t :
Firms, and workers must decide whether to adopt a newly arrived productivity improvement, and can choose to adopt ^kt, or ^`t, or both. Let
it 2 f0; 1g be the adoption decisions at t, with i = k; `. The evolution of
technology is
it = it ^it + (1 it )i;t 1 ; i = k; `:
In the following, I assume that a technology is only adopted if, and only if,
there is unanimous agreement: in other words, only Pareto-improvements
are implemented.
Will all improvements in technology be adopted? To see this, dene the
indices
r^1 r1 q^t = ^`t ; qt = `t :
kt
kt
Proposition 9 (Resistance to Change) All improvents in capital productivity are adopted:
kt = ^kt :
Improvements in labour productivity are adopted if, and only if
q^t R():
The proposition is a fairly straightforward application of Proposition 7.
Increases in k are always Pareto-improving; an increase in ` is Paretoimproving only if condition (R) holds. As < 1 < 1+1 by assumption,
this requires R() > q^t. As the contemplated change is non-marginal, the
inequality must hold at the updated value q^.
The index q^ controls the clock of conict: new technologies are resisted
if q^ is large enough. Resistance to change ebbs as q^ falls; and fall it must,
as technology progresses.
Proposition 10 (Growth erodes resistance) For each > 0, there exists a time, T (), such that all technologies are adopted from T () on:
t = ^ t whenever t T ():
T ()is strictly decreasing, with T (1) = 0 and T (0) = 1
20
To see this, we note, rst, that
1 ) q^ < q^ :
(1 + g) t+1 t
Suppose q^0 > R(). Dene by the equation
q^t+1 = q^t
(1 + g) = Rq(0) ;
and T () the smallest integer exceeding . R() is monotonically increasing:
, and hence T (), increases with . By construction, q^T ()+i < R() for
each i. We note that R(0) = 0, and R(1) = 1, implying T (0) = 1 and
T (1) = 0.
Imagine a society which starts from large inequalities of opportunity,
represented by a low . Workers will resist technology improvements in
early stages, because real wages are likely to fall at early stages of growth.
If successful at this resistance, as I assume here, generations of technical improvements will not be adopted. Technical progress hurts in the beginning;
and that may slow down growth in early stages. Eventually, and this is the
content of Proposition 10, it must be universally desirable. Transitions to
Pareto-superior growth take time: how long it takes depends on how unequal
the society is.
Two further points. Notice that resistance is likely when q^t is large; and
that an increase in the cost of capital, r, increases q^. Thus, an exogenous
increase in the cost of non-labour inputs ( e.g. an oil price shock) increases
workers' resistance to technological progress, which may be a factor relevant
to \productivity slowdowns" recorded in the 1980's. Second, I have explored
the role of technology adoption; in this world, liberalization will necessarily
be resisted by the privileged. In situations where (R) holds, it is possible to
nd Pareto-improving agreements on (; ), where technical change should
be accompanied by an apropriate degree of liberalization.
21
References
1. Banerjee, A.V. and A. Newman (1993) \Occupational Choice and Economic Development", Journal of Political Economy,..
2. G. Clark (1989) \Why isn't the whole world developed? Lessons from
the Cotton Mills ", Journal of Economic History , 48, 141-173
3. Jared Diamond (1998) Guns, Germs, and Steel,..
4. P. A. Diamond (1967) \ National debt in the Neoclassical Growth
Mode", American Economic Review,55, 1l25-1150.
5. O. Galor and J. Zeira (1993) \Income distribution and macroeconomics", Review of Economic Studies,..
6. O. Galor and D. Tsiddon (1997) \ Technical progress and the Distribution of Income", American Economic Review,.
7. R. Harris (1997) \Political economy, interest groups, and the repeal of
the Bubble Act", economic History Review, L-4:674-696.
8. P. Krusell and J-V Rios-Rull (1996) \Vested interests in a positive
theory of stagnation and growth", Review of Economic Studies, ..
9. R.E. Lucas (1978) \On the size distribution of business rms", Bell
Journal of Economics and Management Science, 9, 508-23.
10. J. Mokyr (1990) The Lever of Riches, Oxford University Press
11. M. Olson (1982) The rise and decline of nations, Yale University Press
12. S. Parente (1994) \Technology adoption, learning by doing, and economic growth", Journal of Economic Theory, 63, 346-69
13. S. Parente and E. Prescott (1994) \Barriers to technology adoption
and development", Journal of Political Economy, 102, 298-321
14. E.C. Prescott (1997)\ Barriers to Riches", Lawrence R. Klein Memorial Lectures, University of Pennsylvania
15. E.C. Prescott (1998) \ Needed: A theory of productivity", International Economic Review,..
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16. S. Woolcott (1994) \The perils of lifetime employment systems: productivity advance in the Indian and Japanese textile industries", Journal of Economic History, 54: 306-324
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