Journal of Monetary Economics 22 (1988) 3-42. North-Holland

ON THE MECHANICS OF ECONOMIC DEVELOPMENT*

Robert E. LUCAS, Jr.
University of Chicago, Chicago, 1L 60637, USA

Received August 1987, final version received February 1988
This paper considers the prospects for constructing a neoclassical theory of growth and international trade that is consistent with some of the main features of economic development. Threemodels are considered and compared to evidence: a model emphasizing physical capital accumulation and technological change, a model emphasizing human capital accumulation through schooling. and a model emphasizing specialized human capital accumulation through learning-by-doing.

1. Introduction

By the problem of economic development I mean simply the problem ofaccounting for the observed pattern, across countries and across time, in levels
and rates of growth of per capita income. This may seem too narrow adefinition, and perhaps it is, but thinking about income patterns will necessarily involve us in thinking about many other aspects of societies too. so I
would suggest that we withhold judgment on the scope of this definition until
we have a clearer idea of where it leads us.
The main features of levels and rates of growth of national incomes are wellenough known to all of us, but I want to begin with a few numbers, so as toset a quantitative tone and to keep us from getting mired in the wrong kind ofdetails. Unless I say otherwise, all figures are from the World Bank's World
Development Report of 1983.
The diversity across countries in measured per capita income levels is
literally too great to be believed. Compared to the 1980 average for what the
WorId Bank calls the 'industrial market economies' (Ireland up throughSwitzerland) of U.S. $10,000, India's per capita income is $240, Haiti's is $270,*This paper was originally written for the Marshall Lectures, given at Cambridge University in
1985. ! am very grateful to the Cambridge faculty for this honor, and also for the invitatiou's longlead time, which gave me the opportunity to think through a new topic with the stimulus of sodistinguished an audience in prospect. Since then, versions of this lecture have been given as theDavid Horowitz Lectures in Israel, the W.A. Mackintosh Lecture at Queens University, the Carl
Snyder Memorial Lecture at the University of California at Santa Barbara, the Chung-Hua
Lecture in Taipei. the Nancy Schwartz Lecture at Northwestern University, and the Lionel
McKenzie Lecture at the University of Rochester. I have also based several seminars on various
parts of this material.
0304-3932j88j$3.50©1988, Elsevier Science Publishers B.V. (North-Holland)

4

R. E. Lucas, Jr., On the mechanics of economic development

and so on for the rest of the very poorest countries. This is a difference of afactor of 40 in living standards! These latter figures are too low to sustain lifein, say, England or the United States, so they cannot be taken at face value
and I will avoid hanging too much on their exact magnitudes. But I do notthink anyone will argue that there is not enormous diversity in living standards. I
Rates of growth of real per capita GNP are also diverse, even over sustained
periods. For 1960-80 we observe, for example: India, 1.4% per year; Egypt,
3.4%; South Korea, 7.0%; Japan, 7.1 %; the United States, 2.3%; the industrial
economies averaged 3.6%. To obtain from growth rates the number of years it
takes for incomes to double, divide these numbers into 69 (the log of 2 times
100). Then Indian incomes will double every 50 years; Korean every 10. An
Indian will, on average, be twice as well off as his grandfather; a Korean 32
times. These differences are at least as striking as differences in income levels,and in some respects more trustworthy, since within-country income comparisons are easier to draw than across-country comparisons.
I have not calculated a correlation across countries between income levels
and rates of growth, but it would not be far from zero. (The poorest countries
tend to have the lowest growth; the wealthiest next; the 'middle-income'countries highest.) The generalizations that strike the eye have to do withvariability within these broad groups: the rich countries show little diversity(Japan excepted - else it would not have been classed as a rich country in1980 at all). Within the poor countries (low and middle income) there isenormous variability. 2
Within the advanced countries, growth rates tend to be very stable over long
periods of time, provided one averages over periods long enough to eliminate
business-cycle effects (or corrects for short-term fluctuations in some otherway). For poorer countries, however, there are many examples of sudden, largechanges in growth rates, both up and down. Some of these changes are no
doubt due to political or military disruption: Angola's total GDP growth fell
from 4.8 in the 60s to - 9.2 in the 70s; Iran's fell from 11.3 to 2.5, comparing
the same two periods. I do not think we need to look to economic theory foran account of either of these declines. There are also some striking examples
1 The income estimates reported in Summers and Heston (1984) are more satisfactory than thosein the World Development Reports. In 1975 U.S. dollars, these authors estimate 1980 U.S. real
GDP per capita at $8000, and for the industrialized economies as a group, $5900. The comparable
figures for India and Haiti are $460 and $500, respectively. Income differences of a factor of 16 arecertainly smaJler, and J think more accurate, than a factor of 40, but I think they are still fairly
described as exhibiting 'enormous diversity'.
2 Baumol (1986) summarizes evidence, mainly from Maddison (1982) indicating apparent
convergence during this century to a common path of the income levels of the wealthiest
countries. But De Long (1987) shows that this effect is entirely due to 'selection bias': If one
examines the countries with the highest income levels at the beginning of the century (as opposed
to currently, as in Maddison's 'sample') the data show apparent divergence!

R.E. Lucas. Jr., On the mechanics of economic development

5of sharp increases in growth rates. The four East Asian 'miracles' of South
Korea, Taiwan, Hong Kong and Singapore are the most familiar: for the
1960-80 period, per capita income in these economies grew at rates of 7.0, 6.5,
6.8 and 7.5, respectively, compared to much lower rates in the 1950's andearlier. 3,4 Between the 60s and the 70s, Indonesia's GDP growth increased
from 3.9 to 7.5; Syria's from 4.6 to 10.0.
I do not see how one can look at figures like these without seeing them as
representing possibilities. Is there some action a government of India could
take that would lead the Indian economy to grow like Indonesia's I)r Egypt's?
If so, what, exactly? If not, what is it about the' nature of India' that makes it
so? The consequences for human welfare involved in questions like these aresimply staggering: Once one starts to think about them, it is hard to think
about anything else.
This is what we need a theory of economic development for: to provide
some kind of framework for organizing facts like these, for judging which
represent opportunities and which necessities. But the term' theory' is used inso many different ways, even within economics, that if I do not clarify what I
mean by it early on, the gap between what I think I am saying and what you
think you are hearing will grow too wide for us to have a serious discussion. I
prefer to use the term' theory' in a very narrow sense, to refer to an explicit
dynamic system, something that can be put on a computer and run. This iswhat I mean by the' mechanics' of economic development - the constructionof a mechanical, artificial world, populated by the interacting robots that
economics typically studies, that is capable of exhibiting behavior the grossfeatures of which resemble those of the actual world that I have just described.
My lectures will be occupied with one such construction, and it will take somework: It is easy to set out models of economic growth based on reasonablelooking axioms that predict the cessation of growth in a few decades, or thatpredict the rapid convergence of the living standards of different economies to
a common level, or that otherwise produce logically possible outcomes thatbear no resemblance to the outcomes produced by actual economic systems.
On the other hand, there is no doubt that there must be mechanics other thanthe ones I will describe that would fit the facts about as well as mine. This is
why I have titled the lectures 'On the Mechanics ... ' rather than simply 'The
Mechanics of Economic Development'. At some point, then, the study ofdevelopment will need to involve working out the implications of competingtheories for data other than those they were constructed to fit, and testingthese implications against observation. But this is getting far ahead of the
3The World Bank no longer transmits data for Taiwan. The figure 6.5 in the text is from
Harberger (1984, table 1, p. 9).
4According to Heston and Summers (1984), Taiwan's per-capita GDP growth rate in the 1950s
was 3.6. South Korea's was 1.7 from 1953 to 1960.

6

R.E. Lucas. Jr., On the mechanics of economic development

story I have to tell, which will involve leaving many important questions open
even at the purely theoretical level and will touch upon questions of empiricaltesting hardly at all.
My plan is as follows. I will begin with an application of a now-standard
neoclassical model to the study of twentieth century U.S. growth, closely
following the work of Robert Solow, Edward Denison and many others. I willthen ask, somewhat unfairly, whether this model as it stands is an adequate
model of economic development, concluding that it is not. Next, I willconsider two adaptations of this standard model to include the effects ofhuman capital accumulation. The first retains the one-sector character of theoriginal model and focuses on the interaction of physical and human capital
accumulation. The second examines a two-good system that admits specialized
human capital of different kinds and offers interesting possibilities for theinteraction of trade and development. Finally, I will turn to a discussion ofwhat has been arrived at and of what is yet to be done.
In general, I will be focusing on various aspects of what economists, using
the term very broadly, call the' technology'. I will be abstracting altogether
from the economics of demography, taking population growth as a given
throughout. This is a serious omission, for which I can only offer the excuse
that a serious discussion of demographic issues would be at least as difficult as
the issues I will be discussing and I have neither the time nor the knowledge to
do both. I hope the interactions between these topics are not such that theycannot usefully be considered separately, at least in a preliminary way. 5
I will also be abstracting from all monetary matters, treating all exchange as
though it involved goods-for-goods. In general, I believe that the importanceof financial matters is very badly over-stressed in popular and even muchprofessional discussion and so am not inclined to be apologetic for going tothe other extreme. Yet insofar as the development of financial institutions is alimiting factor in development more generally conceived I will be falsifying thepicture, and I have no clear idea as to how badly. But one cannot theorize
about everything at once. I had better get on with what I do have to say.
2. Neoclassical growth theory: Review
The example, or model, of a successful theory that I will try to build on is
the theory of economic growth that Robert Solow and Edward Denison
developed and applied to twentieth century U.S. experience. This theory willserve as a basis for further discussion in three ways: as an example of the form
that I believe useful aggregative theories must take, as an opportunity to
5Becker and Barro (1985) is the first attempt known to me to analyze fertility and capital
accumulation decisions simultaneously within a general equilibrium framework. Tamura (1986)
contains further results along this line.

R.E. Lucas, Jr., On the mechanics of economic development

7

explain exactly what theories of this form can tell us that other kinds oftheories cannot, and as a possible theory of economic development. In thisthird capacity, the theory will be seen to fail badly, but also suggestively.
Following up on these suggestions will occupy the remainder of the lectures.
Both Solow and Denison were attempting to account for the main featuresof U.S. economic growth, not to provide a theory of economic development,
and their work was directed at a very different set of observations from thecross-country comparisons I cited in my introduction. The most usefulsummary is provided in Denison's 1961 monograph, The Sources of Economic
Growth in the United States. Unless otherwise mentioned, this is the source forthe figures I will cite next.
During the 1909-57 period covered in Denison's study, U.S. real output
grew at an annual rate of 2.9%, employed manhours at 1.3%, and capital stockat 2.4%. The remarkable feature of these figures, as compared to those citedearlier, is their stability over time. Even if one takes as a starting point thetrough of the Great Depression (1933) output growth to 1957 averages only
5%. If business-cycle effects are removed in any reasonable way (say, by using
peak-to-peak growth rates) U.S. output growth is within half a percentage
point of 3% annually for any sizeable subperiod for which we have data.
Solow (1956) was able to account for this stability, and also for some of therelative magnitudes of these growth rates, with a very simple but also easily
refineable model. 6 There are many variations of this model in print. I will set
out a particularly simple one that is chosen also to serve some later purposes. I
will do so without much comment on its assumed structure: There is no pointin arguing over a model's assumptions until one is clear on what questions it
will be used to answer.
We consider a closed economy with competitive markets, with identical,
rational agents and a constant returns technology. At date t there are N( t)persons or, equivalently, manhours devoted to production. The exogenously
given rate of growth of N( t) is A. Real, per-capita consumption is a streamc(t), t ~ 0, of units of a single good. Preferences over (per-capita) consumption
streams are given byooioe-pt_l_[c(t)l-o-I]N(t)dt,
I-a

(1)

6 Solow's 1956 paper stimulated a vast literature in the 1960s, exploring many variations on theoriginal one-sector structure. See Burmeister and Dobell (1970) for an excellent introduction andsurvey. By putting a relatively simple version to empirical use, as I shall shortly do, I do notintend a negative comment on this body of research. On the contrary, it is exactly this kind oftheoretical experimentation with alternative assumptions that is needed to give one the confidence
that working with a particular, simple parameterization may, for the specific purpose at hand, be
adequate.

R.E. Lucas, Jr., On the mechanics of economic development

8

where the discount rate p and the coefficient of (relative) risk aversion 0 are
both positive. 7
Production per capita of the one good is divided into consumption c( t) andcapital accumulation. If we let K(t) denote the total .stock of cal?ital, andK(t) its rate of change, then total output is N(t)c(t) + K(t). [Here K(t) is net
investment and total output N(t)c(t) + K(t) is identified with net national
product.] Production is assumed to depend on the levels of capital and labor
inpu ts and on the level A ( t) of the 'technology', according to(2)where 0 < f3 < 1 and where the exogenously given rate of technical change,

A/A, is p. > O.
The resource allocation problem faced by this simple economy is simply tochoose a time path c( t) for per-capita consumption. Given a path c(t) and an
initial capital stock K(O), the technology (2) then implies a time path K( t) for
capital. The paths A(t) and N(t) are given exogenously. One way to thinkabou t this allocation problem is to think of choosing c(t) at each date, given
the values of K(t), A(t) and N(t) that have been attained by that date.
Evidently, it will not be optimal to choose c( t) to maximize current-period
utility, N(t)[1j(1 - o)][c(t) - 1]1-0, for the choice that achieves this is to set
net investment K(t) equal to zero (or, if feasible, negative): One needs to set
some value or price on increments to capital. A central construct in the studyof optimal allocations, allocations that maximize utility (1) subject to thetechnology (2), is the current-value Hamiltonian H defined by
N
H(K, 8, c, t) = -1-[c 1- O -1] + 8[AK.8N 1-.8 - Nc],-0which is just the sum of current-period utility and [from (2)] the rate ofincrease of capital, the latter valued at the' price' 8( t). An optimal allocationmust maximize the expression H at each date t, provided the price O( t) iscorrectly chosen.
The first-order condition for maximizing H with respect to c is(3)
which is to say that goods must be so allocated at each date as to be equallyvaluable, on the margin, used either as consumption or as investment. It is
7The inverse a -I of the coefficient of risk aversion is sometimes called the intertemporalelasticity of substitution. Since all the models considered in this paper are deterministic, this latter
terminology may be more suitable.

R.E. Lucas, Jr., On the mechanics 0/ economic development

9known that the price 8( t) must satisfy.

a8(t) = p8(t) - aKH(K(t),8(t),c(t), t)=[p - f3A ( t ) N ( t )1-f3 K ( t ) f3 - 1] 8( t ) ,(4)

at each date t if the solution c(t) to (3) is to yield an optimal path (c(t»~=o.
Now if (3) is used to express c(t) as a function 8(1), and this function 8- 1/
is substituted in place of c(t) in (2) and (4), these two equations are a pair offirst-order differential equations in K (t) and its 'price' 8(1). Solving thissystem, there will be a one-parameter family of paths (K (t), 8( t», satisfying
the given initial condition on K(O). The unique member of this family thatsatisfies the transversality condition:0

lim e- pt8(t)K(t) = 0(5)t-+ 00is the optimal path. I am hoping that this application of Pontryagin's Maximum Principle, essentially taken from David Cass (1961), is familiar to mostof you. I will be applying these same ideas repeatedly in what follows.
For this particular model, with convex preferences and technology and withno external effects of any kind, it is also known and not at all surprising thatthe optimal program characterized by (2), (3), (4) and (5) is also the uniquecompetitive equilibrium program, provided either that all trading is consummated in advance, Arrow-Debreu style, or (and this is the interpretation I
favor) that consumers and firms have rational expectations about future prices.
In this deterministic context, rational expectations just means perfect foresight. For my purposes, it is this equilibrium interpretation that is mostinteresting: I intend to use the model as a positive theory of U.S. economic
growth.
In order to do this, we will need to work out the predictions of the model inmore detail, which involves solving the differential equation system so we cansee what the equilibrium time paths look like and compare them to observations like Denison's. Rather than carry this analysis through to completion, I
will work out the properties of a particular solution to the system and thenjust indicate briefly how the rest of the answer can be found in Cass's paper.
Let us construct from (2), (3) and (4) the system's balanced growth path: theparticular solution (K(t), 8(1), c(t» such that the rates of growth of each ofthese variables is constant. (I have never been sure exactly what it is that is'balanced' along such a path, but we need a term for solutions with thisconstant growth rate property and this is as good as any.) Let K denote therate of growth of per-capita consumption, c(t)jc(t), on a balanced growthR.E. Lucas, Jr., On the mechanics of economic development

10

path. Then from (3), we have 8(t)/8(t) = -al(. Then from (4), we must havef3A ( t ) N ( t ) 1 - fJ K ( t ) fJ - 1 = P + aI( .

(6)That is, along the balanced path, the marginal product of capital must equal
the constant value p + al(. With this Cobb-Douglas technology, the marginal
product of capital is proportional to the average product, so that dividing (2)through by K( t) and applying (6) we obtain
N(t)c(t)K(t) =A( )K( )fJ-11t.T( )l- fJ = p+al(
K(t) + K(t)
t
t
iV t
13'

(7)

By definition of a balanced path, K(t)/K(t) is constant so (7) implies thatN( t )c(t)/K( t) is constant or, differentiating, that
K(t)

N(t)

c(t)

K(t)

N(t)

c(t)

--=--+--=I(+A.

(8)

Thus per-capita consumption and per-capita capital grow at the common
rate 1(. To solve for this common rate, differentiate either (6) or (7) to obtainp.

(9)

1(= - - .

1-13

Then (7) may be solved to obtain the constant, balanced consumption-capitalratio N(t)c(t)/K(t) or, which is equivalent and slightly easier to interpret, theconstant, balanced net savings rate s defined bys=K(t)N(t)c(t)+K(t)f3(I(+A)=---

p+al('(10)

Hence along a balanced path, the rate of growth of per-capita magnitudes is
simply proportional to the given rate of technical change, p., where theconstant of proportionality is the inverse of labor's share, 1 - 13. The rate oftime preference p and the degree of risk aversion a have no bearing on thislong-run growth rate. Low time preference p and low risk aversion a induce ahigh savings rate s, and high savings is, in turn, associated with relatively highoutput levels on a balanced path. A thrifty society will, in the long run, be
wealthier than an impatient one, but it will not grow faster.
In order that the balanced path characterized by (9) and (10) satisfy thetransversality condition (5), it is necessary that p + al( > I( + A. [From (10), one
sees that this is the same as requiring the savings rate to be less than capital's

R.E. Lucas, Jr., On the mechanics of economic development

11

share.] Under this condition, an economy that begins on the balanced pathwill find it optimal to stay there. What of economies that begin off thebalanced path - surely the normal case? Cass showed - and this is exactly
why the balanced path is interesting to us - that for any initial capital
K(O) > 0, the optimal capital-consumption path (K(t), c(t» will converge tothe balanced path asymptotically. That is, the balanced path will be a good
approximation to any actual path 'most' of the time.
Now given the taste and technology parameters (p, 0, X, f3 and JL) (9) and(10) can be solved for the asymptotic growth rate K of capital, consumption
and real output, and the savings rate s that they imply. Moreover, it would bestraightforward to calculate numerically the approach to the balanced pathfrom any initial capital level K (0). This is the exercise that an idealizedplanner would go through.
Our interest in the model is positive, not normative, so we want to go in the
opposite direction and try to infer the underlying preferences and technology
from what we can observe. I will outline this, taking the balanced path as themodel's prediction for the behavior of the U.S. economy during the entire(1909-57) period covered by Denison's study.8 From this point of view,
Denison's estimates provide a value of 0.013 for X, and two values, 0.029 and0.024 for K + X, depending on whether we use output or capital growth rates(which the model predicts to be equal). In the tradition of statistical inference,
let us average to get K + X = 0.027. The theory predicts that 1 - f3 should
equal labor's share in national income, about 0.75 in the U.S., averaging overthe entire 1909-57 period. The savings rate (net investment over NNP) is
fairly constant at 0.10. Then (9) implies an estimate of 0.0105 for JL. Eq. (10)implies that the preference parameters p and 0 satisfy
p + (0.014)0 = 0.0675.

(The parameters p and 0 are not separately identified along a smoothconsumption path, so this is as far as we can go with the sample averages I
have provided.)
These are the parameter values that give the theoretical model its best fit to
the U.S. data. How good a fit is it? Either output growth is underpredicted orcapital growth overpredicted, as remarked earlier (and in the theory of growth,a half a percentage point is a large discrepancy). There are interesting secularchanges in manhours per household that the model assumes away, and labor's
share is secularly rising (in all growing economies), not constant as assumed.
There is, in short, much room for improvement, even in accounting for thesecular changes the model was designed to fit, and indeed, a fuller review of
8With the parameter values described in this paragraph, the half-life of the approximate linear
system associated with this model is about eleven years.

12

R.E. Lucas, Jr., On the mechanics of economic development

the literature would reveal interesting progress on these and many otherfronts. 9 A model as explicit as this one, by the very nakedness of its simplifying assumptions, invites criticism and suggests refinements to itself. This isexactly why we prefer explicitness, or why I think we ought to.
Even granted its limitations, the simple neoclassical model has made basic
contributions to our thinking about economic growth. Qualitatively, it emphasizes a distinction between 'growth effects' - changes in parameters that alter
growth rates along balanced paths - and 'level effects' - changes that raise or
lower balanced growth paths without affecting their slope - that is fundamental in thinking about policy changes. Solow's 1956 conclusion that changes insavings rates are level effects (which transposes in the present context to theconclusion that changes in the discount rate, P, are level effects) was startlingat the time, and remains widely and very unfortunately neglected today. The
influential idea that changes in the tax structure that make savings more
attractive can have large, sustained effects on an economy's growth ratesounds so reasonable, and it may even be true, but it is a clear implication of
the theory we have that it is not.
Even sophisticated discussions of economic growth can often be confusing
as to what are thought to be level effects and what growth effects. Thus
Krueger (1983) and Harberger (1984), in their recent, very useful surveys ofthe growth experiences of poor countries, both identify inefficient barriers totrade as a limitation on growth, and their removal as a key explanation ofseveral rapid growth episodes. The facts Krueger and Harberger summarize
are not in dispute, but under the neoclassical model just reviewed one would
not expect the removal of inefficient trade barriers to induce sustained
increases in growth rates. Removal of trade barriers is, on this theory, a level
effect, analogous to the one-time shifting upward in production possibilities,
and not a growth effect. Of course, level effects can be drawn out through timethrough adjustment costs of various kinds, but not so as to produce increases
in growth rates that are both large and sustained. Thus the removal of an
inefficiency that reduced output by five percent (an enormous effect) spreadout over ten years in simply a one-half of one percent annual growth rate
stimulus. Inefficiencies are important and their removal certainly desirable, but
the familiar ones are level effects, not growth effects. (This is exactly why it is
not paradoxical that centrally planned economies, with allocative inefficienciesof legendary proportions, grow about as fast as market economies.) The
empirical connections between trade policies and economic growth that
9In particular, there is much evidence that capital stock growth, as measured by Denison,
understates true capital growth due to the failure to correct price deflators for quality improvements. See, for example, Griliches and Jorgenson (1967) or Gordon (1971). These errors may wellaccount for all of the 0.005 discrepancy noted in the text (or more!).
Boxall (1986) develops a modification of the Solow-Cass model in which labor supply isvariable, and which has the potential (at least) to account for long-run changes in manhours.

R. E. Lucas, Jr., On the mechanics of economic development

13

Krueger and Harberger document are of evident importance, but they seem to
me to pose a real paradox to the neoclassical theory we have, not a confirmation of it.
The main contributions of the neoclassical framework, far more important
than its contributions to the clarity of purely qualitative discussions, stemfrom its ability to quantify the effects of various influences on growth.
Denison's monograph lists dozens of policy changes, some fanciful and manyothers seriously proposed at the time he wrote, associating with each of themrough upper bounds on their likely effects on U.S. growth. 1o In the main, thetheory adds little to what common sense would tell us about the direction ofeach effect - it is easy enough to guess which changes stimulate production,
hence savings, and hence (at least for a time) economic growth. Yet most suchchanges, quantified, have trivial effects: The growth rate of an entire economy
is not an easy thing to move around.
Economic growth, being a summary measure of all of the activities of an
entire society, necessarily depends, in some way, on everything that goes on ina society. Societies differ in many easily observed ways, and it is easy toidentify various economic and cultural peculiarities and imagine that they are
keys to growth performance. For this, as Jacobs (1984) rightly observes, we do
not need economic theory: 'Perceptive tourists will do as well.' The role oftheory is not to catalogue the obvious, but to help us to sort out effects thatare crucial, quantitatively, from those that can be set aside. Solow andDenison's work shows how this can be done in studying the growth of the U.S.
economy, and of other advanced economies as well. I take success at this level
to be a worthy objective for the theory of economic development.
3. Neoclassical growth theory: Assessment
It seems to be universally agreed that the model I have just reviewed is not atheory of economic development. Indeed, I suppose this is why we think of'growth' and 'development' as distinct fields, with growth theory defined as
those aspects of economic growth we have some understanding of, anddevelopment defined as those we don't. I do not disagree with this judgment,
but a more specific idea of exactly where the model falls short will be useful inthinking about alternatives.
If we were to attempt to use the Solow-Denison framework to account forthe diversity in income levels and rates of growth we observe in the world
today, we would begin, theoretically, by imagining a world consisting of many
10 Denison (1961, ch. 24). My favorite example is number 4 in this' menu of choices available toincrease the growth rate': '0.03 points [i.e., 0.03 of one percentage point) maximum potential ...
Eliminate all crime and rehabilitate all criminals.' This example and many others in this chapter
are pointed rebukes to those in the 1960s who tried to advance their favorite (and often worthy)
causes by claiming ties to economic growth.

14

R. E. Lucas, Jr., On the mechanics of economic development

economies of the sort we have just described, assuming something about theway they interact, working out the dynamics of this new model, and comparing them to observations. This is actually much easier than it sounds (there
isn't much to the theory of international trade when everyone produces thesame, single good!), so let us think it through.
The key assumptions involve factor mobility: Are people and capital free tomove? It is easiest to start with the assumption of no mobility, since then we
can treat each country as an isolated system, just like the one we have justworked out. In this case, the model predicts that countries with the same
preferences and technology will converge to identical levels of income andasymptotic rates of growth. Since this prediction does not accord at all wellwith what we observe, if we want to fit the theory to observed cross-country
variations, we will need to postulate appropriate variations in the parameters(p, a, A, {3 and JL) and/or assume that countries differ according to theirinitial technology levels, A(O). Or we can obtain additional theoretical flexibility by treating countries as differently situated relative to their steady-statepaths. Let me review these possibilities briefly.
Population growth, A, and income shares going to labor, 1 - {3, do of course
differ across countries, but neither varies in such a way as to provide an
account of income differentials. Countries with rapid population growth are
not systematically poorer than countries with slow-growing populations, as thetheory predicts, either cross-sectionally today or historically. There are, certainly, interesting empirical connections between economic variables (narrowly
defined) and birth and death rates, but I am fully persuaded by the work of
Becker (1981) and others that these connections are best understood as arisingfrom the way decisions to maintain life and to initiate it respond to economic
conditions. Similarly, poor countries have lower labor shares than wealthy
countries, indicating to me that elasticities of substitution in production are
below unity (contrary to the Cobb-Douglas assumption I am using in theseexamples), but the prediction (9) that poorer countries should therefore growmore rapidly is not confirmed by experience.
The parameters p and a are, as observed earlier, not separately identified,
but if their joint values differed over countries in such a way as to account forincome differences, poor countries would have systematically much higher(risk-corrected) interest rates than rich countries. Even if this were true, I
would be inclined to seek other explanations. Looking ahead, we would likealso to be able to account for sudden large changes in growth rates ofindividual countries. Do we want a theory that focuses attention on spontaneous shifts in people's discount rates or degree of risk aversion? Such theories
are hard to refute, but I will leave it to others to work this side of the street.
Consideration of off-steady-state behavior would open up some new possibilities, possibly bringing the theory into better conformity with observation,
but I do not view this route as at all promising. Off steady states, (9) need not
hold and capital and output growth rates need not be either equal or constant,

R.E. Lucas. Jr., On the mechanics of economic development

15

but it still follows from the technology (2) that output growth (gyP say) andcapital growth (gkP say), both per capita, obey

But gyt and gkt can both be measured, and it is well established that for novalue of f3 that is close to observed capital shares is it the case that gyt - f3gkt
is even approximately uniform across countries. Here 'Denison's Law' works
against us: the insensitivity of growth rates to variations in the model'sunderlying parameters, as reviewed earlier, makes it hard to use the theory to
account for large variations across countries or across time. To conclude thateven large changes in 'thriftiness' would not induce large changes in U.S.
growth rates is really the same as concluding that differences in Japanese andU.S. thriftiness cannot account for much of the difference in these two
economies' growth rates. By assigning so great a role to 'technology' as asource of growth, the theory is obliged to assign correspondingly minor roles
to everything else, and so has very little ability to account for the wide
diversity in growth rates that we observe.
Consider, then, variations across countries in 'technology' - its level andrate of change. This seems to me to be the one factor isolated by theneoclassical model that has the potential to account for wide differences inincome levels and growth rates. This point of departure certainly does accord
with everyday usage. We say that Japan is technologically more advanced thanChina, or that Korea is undergoing unusually rapid technical change, and suchstatements seem to mean something (and I think they do). But they cannot
mean that the 'stock of useful knowledge' [in Kuznets's (1959) terminology] ishigher in Japan than in China, or that it is growing more rapidly in Korea
than elsewhere. 'Human knowledge' is just human, not Japanese or Chinese or
Korean. I think when we talk in this way about differences in 'technology'
across countries we are not talking about 'knowledge' in general, but about
the knowledge of particular people, or perhaps particular subcultures ofpeople. If so, then while it is not exactly wrong to describe these differences byan exogenous, exponential term like A(t) neither is it useful to do so. We want
a formalism that leads us to think about individual decisions to acquire
knowledge, and about the consequences of these decisions for productivity.
The body of theory that does this is called the theory of 'human capital', and I
am going to draw extensively on this theory in the remainder of these lectures.
For the moment, however, I simply want to impose the terminological convention that 'technology' - its level and rate of change - will be used to refer tosomething common to all countries, something 'pure' or 'disembodied', something whose determinants are outside the bounds of our current inquiry.
In the absence of differences in pure technology then, and under theassumption of no factor mobility, the neoclassical model predicts a strong
tendency to income equality and equality in growth rates, tendencies we can

16

R. E. Lucas, Jr., On the mechanics of economic development

observe within countries and, perhaps, within the wealthiest countries taken asa group, but which simply cannot be seen in the world at large. When factor
mobility is permitted, this prediction is very powerfully reinforced. Factors of
production, capital or labor or both, will flow to the highest returns, which is
to say where each is relatively scarce. Capital-labor ratios will move rapidly toequality, and with them factor prices. Indeed, these predictions survive differences in preference parameters and population growth rates. In the model asstated, it makes no difference whether labor moves to join capital or the otherway around. (Indeed, we know that with a many-good technology, factor priceequalization can be achieved without mobility in either factor of production.)
The eighteenth and nineteenth century histories of the Americas, Australia
and South and East Africa provide illustrations of the strength of these forces
for equality, and of the ability of even simple neo-classical models to accountfor important economic events. If we replace the labor-capital technology of
the Solow model with a land-labor technology of the same form, and treat
labor as the mobile factor and land as the immobile, we obtain a model thatpredicts exactly the immigration flows that occurred and for exactly thereason - factor price differentials - that motivated these historical flows.
Though this simple deterministic model abstracts from considerations of risk
and many other elements that surely played a role in actual migration
decisions, this abstraction is evidently not a fatal one.
In the present century, of course, immigration has been largely shut off, so it
is not surprising that this land-labor model, with labor mobile, no longer gives
an adequate account of actual movements in factors and factor prices. What issurprising, it seems to me, is that capital movements do not perform the samefunctions. Within the United States, for example, we have seen southern labor
move north to produce automobiles. We have also seen textile mills move from
New England south (to 'move' a factory, one lets it run down and builds its
replacement somewhere else: it takes some time, but then, so does moving
families) to achieve this same end of combining capital with relatively low
wage labor. Economically, it makes no difference which factor is mobile, solong as one is.
Why, then, should the closing down of international labor mobility haveslowed down, or even have much affected, the tendencies toward factor priceequalization predicted by neoclassical theory, tendencies that have proved tobe so powerful historically? If it is profitable to move a textile mill from New
England to South Carolina, why is it not more profitable still to move it to
Mexico? The fact that we do see some capital movement toward low-income
countries is not an adequate answer to this question, for the theory predicts
that all new investment should be so located until such time as return and real
wage differentials are erased. Indeed, why did these capital movements nottake place during the colonial age, under political and military arrangementsthat eliminated (or long postponed) the 'political risk' that is so frequently

R.E. Lucas, Jr., On the mechanics of economic development

17

cited as a factor working against capital mobility? I do not have a satisfactory
answer to this question, but it seems to me a major - perhaps the major - discrepancy between the predictions of neoclassical theory and the patterns oftrade we observe. Dealing with this issue is surely a minimal requirement for atheory of economic development.
4. Human capital and growth
To this point, I have reviewed an example of the neoclassical model ofgrowth, compared it to certain facts of U.S. economic history, and indicated
why I want to use this theory as a kind of model, or image, of what I think ispossible and useful for a theory of economic development. I have also
described what seem to me two central reasons why this theory is not, as it
stands, a useful theory of economic development: its apparent inability to
account for observed diversity across countries and its strong and evidently
counterfactual prediction that international trade should induce rapid movement toward equality in capital-labor ratios and factor prices. These observations set the stage for what I would like to do in the rest of the lectures.
Rather than take on both problems at once, I will begin by considering analternative, or at least a complementary, engine of growth to the' technologicalchange' that serves this purpose in the Solow model, retaining for the moment
the other features of that model (in particular, its closed character). I will dothis by adding what Schultz (1963) and Becker (1964) call 'human capital' tothe model, doing so in a way that is very close technically lo similarly
motivated models of Arrow (1962), Uzawa (1965)and Romer (1986).
By an individual's 'human capital' I will mean, for the purposes of thissection, simply his general skill level, so that a worker with human capital h(t)is the productive equivalent of two workers with ~h(t) each, or a half-timeworker with 2h(t). The theory of human capital focuses on the fact that theway an individual allocates his time over various activities in the current
period affects his productivity, or his h(t) level, in future periods. Introducing
human capital into the model, then, involves spelling out both the way humancapital levels affect current production and the way the current time allocation
affects the accumulation of human capital. Depending on one's objectives,
there are many ways to formulate both these aspects of the 'technology'. Let
us begin with the following, simple assumptions.
Suppose there are N workers in total, with skill levels h ranging from 0 to
infinity. Let there be N(h) workers with skill level h, so that N = f 000 N ( h) d h.
Suppose a worker with skill h devotes the fraction u( h) of his non-leisure time
to current production, and the remaining 1 - u( h) to human capital accumulation. Then the effective workforce in production - the analogue to N(t) in(2) - is the sum N C = foOOu(h)N(h )hdh of the skill-weighted manhours devoted to current production. Thus if output as a function of total capital K

R.E. Lucas, Jr., On the mechanics of economic development

18

and effective labor N e is F(K, N e ), the hourly wage of a worker at skill h is
FN(K, Ne)h and his total earnings are FN(K, Ne)hu(h).
In addition to the effects of an individual's human capital on his own
productivity - what I will call the internal effect of human capital - I want toconsider an external effect. Specifically, let the average level of skill or humancapital, defined byl°O hN(h)dh
h a = -1:"""0OO"""'N-(-h-)d-h- ,also contribute to the productivity of all factors of production (in a way that I
will spell out shortly). I call this h a effect external, because though all benefit
from it, no individual human capital accumulation decision can have anappreciable effect on h a' so no one will take it into account in deciding how toallocate his time.
Now it will simplify the analysis considerably to follow the preceding
analysis and treat all workers in the economy as being identical. In this case, if
all workers have skill level h and all choose the time allocation u, the effective
workforce is just N e = uhN, and the average skill level h a is just h. Even so, I
will continue to use the notation h a for the latter, to emphasize the distinction
between internal and external effects. Then the description (2) of the technology of goods production is replaced byN(t)c(t) + K(t) =AK(t),8[u(t)h(t)N(t)P-,Bh a (t)'f,(11)

where the term h a (t)Y is intended to capture the external effects of humancapital, and where the technology level A is now assumed to be constant.
To complete the model, the effort 1 - u(t) devoted to the accumulation ofhuman capital must be linked to the rate of change in its level, h (t).
Everything hinges on exactly how this is done. Let us begin by postulating atechnology relating the growth of human capital, h(t), to the level alreadyattained and the effort devoted to acquiring more, say:h(t) =h(t)fG (l-u(t»,(12)

where G is increasing, with G(O) = O. Now if we take t < 1 in this formulation,
so that there is diminishing returns to the accumulation of human capital, it iseasy to see that human capital cannot serVe as an alternative engine of growth
to the technology term A(t). To see this, note that, since u(t):2 0, (12) implies
that

h(t)

h(t) ~h(t)

f-l

G(l),

R.E. Lucas, Jr., On the mechanics of economic development

19

so that h(t)/h(t) must eventually tend to zero as h(t) grows no matter how
much effort is devoted to accumulating it. This formulation would simply
complicate the original Solow model without offering any genuinely new
possibilities.
Uzawa (1965) worked out a model very similar to this one [he assumed
y = 0 and U( c) = c] under the assumption that the right-hand side of (12) islinear in u( t) (~ = 1). The striking feature of his solution, and the feature thatrecommends his formulation to us, is that it exhibits sustained per-capita
income growth from endogenous human capital accumulation alone: noexternal 'engine of growth' is required.
Uzawa's linearity assumption might appear to be a dead-end (for ourpresent purposes) because we seem to see diminishing returns in observed.
individual patterns of human capital accumulation: people accumulate it
rapidly early in life, then less rapidly, then not at all - as though each
additional percentage increment were harder to gain than the preceding one.
But an alternative explanation for this observation is simply that an individual's lifetime is finite, so that the return to increments falls with time. Rosen(1976) showed that a technology like (12), with ~ = 1, is consistent with theevidence we have on individual earnings. I will adapt the Uzawa-Rosen
formulation here, assuming for simplicity that the function G is linear:h(t) = h(t)8[1- u(t)].

(13)

According to (13), if no effort is devoted to human capital accumulation,[u( t) = 1], then none accumulates. If all effort is devoted to this purpose[u( t) = 0], h (t) grows at its maximal rate 8. In between these extremes, there
are no diminishing returns to the stock h(t): A given percentage increase inh (t) requires the same effort, no matter what level of h (t) has already been
attained.
It is a digression I will not pursue, but it would take some work to go from ahuman capital technology of the form (13), applied to each finite-lived
individual (as in Rosen's theory), to this same technology applied to an entire
infinitely-lived typical household or family. For example, if each individualacquired human capital as in Rosen's model but if none of this capital werepassed on to younger generations, the' household's' stock would (with a fixeddemography) stay constant. To obtain (13) for a family, one needs to assume
both that each individual's capital follows this equation and that the initiallevel each new member begins with is proportional to (not equal to!) the levelalready attained by older members of the family. This is simply one instanceof a general fact that I will emphasize again and again: that human capital
accumulation is a social activity, involving groups of people in a way that has
no counterpart in the accumulation of physical capital.
Aside from these changes in the technology, expressed in (11) and (13) toincorporate human capital and its accumulation, the model to be discussed is

20

R.E. Lucas, Jr., On the mechanics of economic development

identical to the Solow model. The system is closed, population grows at the
fixed rate A, and the typical household has the preferences (1). Let us proceed
to the analysis of this new model. ll
In the presence of the external effect ha(t)", it will not be the case that
optimal growth paths and competitive equilibrium paths coincide. Hence wecannot construct the equilibrium by studying the same hypothetical planningproblem used to study Solow's model. But by following Romer's analysis of avery similar model, we can obtain the optimal and equilibrium paths separately, and compare them. This is what I will now do.
By an optimal path, I will mean a choice of K(t), h(t), Ha(t), c(t) and u(t)that maximizes utility (1) subject to (11) and (13), and subject to theconstraint h(t) = ha(t) for all t. This is a problem similar in general structure
to the one we reviewed in section 2, and I will turn to it in a moment.
By an equilibrium path, I mean something more complicated. First, take apath h a(t), t ~ 0, to be given, like the exogenous technology path A (t) in the
Solow model. Given ha(t), consider the problem the private sector, consistingof atomistic households and firms, would solve if each agent expected theaverage level of human capital to follow the path h a(t). That is, consider the
problem of choosing h(t), k(t), c(t) and u(t) so as to maximize (1) subject to(11) and (13), taking ha(t) as exogenously determined. When the solution pathh (t) for this problem coincides with the given path h a (t) - so that actual andexpected behavior are the same - we say that the system is in equilibrium. 12
The current-value Hamiltonian for the optimal problem, with 'prices' 01(t)and 02(t) used to value increments to physical and human capital respectively,IS

H(K, h,=°°1,

2 , c, u,t)N
1 _ (J (c 1- a -1) + 01[ AKP(uNh)I- Phy - Nc]

In this model, there are two decision variables - consumption, c( t), and thetime devoted to production, u(t) - and these are (in an optimal program)
11 The model discussed in this section (in contrast to the model of section 2) has not been fully
analyzed in the literature. The text gives a self-contained derivation of the main features ofbalanced paths. The treatment of behavior off balanced paths is largely conjecture, based onparallels with Uzawa (1965) and Romer (1986).
12 This formulation of equilibrium behavior in the presence of external effects is taken fromArrow (1962) and Romer (1986). Romer actually carries out the study of the fixed-point problem
in a space of h ( t), t ~ 0, paths. Here I follow Arrow and confine explicit analysis to balanced
paths only.

21

R.E. Lucas, Jr., On the mechanics of economic development

selected so as to maximize H. The first-order conditions for this problem are
thus:
(14)

and
(15)
On the margin, goods must be equally valuable in their two uses - consumption and capital accumulation [eq. (14)] - and time must be equally valuable
in its two uses - production and human capital accumulation [eq. (15)].
The rates of change of the prices 1 and 2 of the two kinds of capital are
given by° °81 = pOl - 0t/3AKfl- 1(uNh)1- fl hy ,(16)°(1- +(17)

82 = p02 -1

f3Y)AKfl(uN)l- fl h- fl + Y - O2<5(1 - u).

Then eqs. (11) and (13) and (14)-(17), together with two transversality
conditions that I will not state here, implicitly describe the optimal evolutionof K(t) and h(t) from any initial mix of these two kinds of capital.
In the equilibrium, the private sector 'solves' a control problem of essentiallythis same form, but with the term h a(t)Y in (11) taken as given. Market
clearing then requires that h a(t) = h(t) for all t, so that (11), (13), (14), (15)and (16) are necessary conditions for equilibrium as well as for optimal paths.
But eq. (17) no longer holds: It is precisely in the valuation of human capitalthat optimal and equilibrium allocations differ. For the private sector, inequilibrium, (17) is replaced bySince market clearing implies (h(t) = ha(t) for all t, this can be written as

Note that, if y = 0, (17) and (18) are the same. It is the presence of theexternal effect y > 0 that creates a divergence between the 'social' valuation
formula (17) and the private valuation (18).
As with the simpler Solow model, the easiest way to characterize both
optimal and equilibrium paths is to begin by seeking balanced growth solutions of both systems: solutions on which consumption and both kinds ofcapital are growing at constant percentage rates, the prices of the two kinds of

R.E. Lucas, Jr., On the mechanics of economic development

22

capital are declining at constant rates, and the time allocation variable u( t) isconstant. Let us start by considering features that optimal and equilibrium
paths have in common [by setting aside (17) and (18)].
Let K denote c(t)/c(t), as before, so that (14) and (16) again imply themarginal productivity of capital condition:

f3A K ( t ) P- 1( U ( t ) h ( t ) N ( t ) ) 1 - Ph ( t ) Y = P + a K ,(19)which is the analogue to condition (6). As in the earlier model, it is easy toverify that K(t) must grow at the rate K + A and that the savings rate s isconstant, on a balanced path, at the value given by (10). For the derivation ofthese facts concerning physical capital accumulation, it is immaterial whether
h (t) is a matter of choice or an exogenous force as was technological change inthe earlier model.
Now if we let" = h(t)/h(t) on a balanced path, it is clear from (13) that,,=8(1-u),(20)

and from differentiating (19) that K, the common growth rate of consumption
and per-capita capital is

K=

(l-

f3

Y

+ )".

1-13

(21)

Thus with h(t) growing at the fixed rate ", (1 - 13 + Y)" plays the role of theexogenous rate of technological change JL in the earlier model.
Turning to the determinants of the rate of growth " of human capital, one
sees from differentiating both first-order conditions (14) and (15) and substituting for 0l/()l that(22)

At this point, the analyses of the efficient and equilibrium paths diverge.
Focusing first on the efficient path, use (17) and (15) to obtain

Oz

Y

()z

1 - 13- =p-s- --Suo(23)

Now substitute for u from (20), eliminate Oz/()z between (22) and (23), andsolve for" in terms of K. Then eliminating K between this equation and (21)

R. E. Lucas, Jr., On the mechanics of economic development

23

gives the solution for the efficient rate of human capital growth, which I willcall v*:v* =0-1[~ _ 1- {3l-{3+y

(p -

A)].

(24)

Along an equilibrium balanced path (18) holds in place of (17) so that inplace of (23) we have
(25)
Then by the same procedure used to derive the efficient growth rate v* from(23), we can obtain from (25) the equilibrium growth rate v:

v = [0(1- {3 + y) - y] -1[(1_ {3)(~ - (p - A»].

(26)

[For the formulas (24) and (26) to apply, the rates v and v* must not exceed
the maximum feasible rate ~. This restriction can be seen to require1-{3 p-A
0>1-l-{3+y ~(27)

so the model cannot apply at levels of risk aversion that are too low (that is, if
the intertemporal substitutability of consumption is too high).13 When (27)holds with equality, v = v* =~; when the inequality is strict, v* > v, as one
would expect.]Eqs. (24) and (26) give, respectively, the efficient and the competitive
equilibrium growth rates of human capital along a balanced path. In either
case, this growth increases with the effectiveness ~ of investment in humancapital and declines with increases in the discount rate p. (Here at last is aconnection between 'thriftiness' and growth!) In either case, (21) gives thecorresponding rate of growth of physical capital, per capita. Notice that thetheory predicts sustained growth whether or not the external effect y is
positive. If y = 0, K = v, while if y > 0, K > v, so that the external effect induces
more rapid physical than human capital growth.
For the case 0 = 1, the difference between efficient and equilibrium humancapital growth rates is, subtracting (26) from (24),yv* - v = l-{3+y(P-A).
l31f utility is too nearly linear (a is too near zero) and if ~ is high enough, consumers will keep
postponing consumption forever. [This does not occur in Uzawa's model, even though he assumes
a = 0, because he introduces diminishing returns to 1 - u(t) in his version of (13).)

24

R.E. Lucas, Jr., On the mechanics of economic del'elopmellt

Fig. 1Thus the inefficiency is small when either the external effect is small (y ~ 0) or
the discount rate is low (p - A= 0).
Eqs. (21), (24) and (26) describe the asymptotic rates of change of bothkinds of capital, under both efficient and equilibrium regimes. What can besaid about the levels of these variables? As in the original model, thisinformation is implicit in the marginal productivity condition for capital,eq. (19). In the original model, this condition - or rather its analogue,eq. (6) - determined a unique long-run value of the normalized variablez(t) = e-(K+Jo..)tK(t). In the present, two-capital model, this condition defines acurve linking the two normalized variables ZI(t) = e-(K+A)tK(t) and Z2(t) =e-Jlth(t). Inserting these variables into (19) in place of K(t) and h(t) andapplying the formula (21) for /C, we obtain(28)
It is a fact that all pairs (ZI' Z2) satisfying (28) correspond to balanced paths.

Let us ask first what this locus of (normalized) capital combinations looks like,and second what this means for the dynamics of the system.
Fig. 1 shows the curve defined by (28). With no external effect (y = 0) it is astraight line through the origin; otherwise (y > 0) it is convex. The position of

R. E. Lucas, Jr., On the mechanics of economic development25

the curve depends on u and K, which from (20) and (21) can be expressed asfunctions of P. Using this fact one can see that increases in p shift the curve tothe right. Thus an efficient economy, on a balanced path, will have a higher
level of human capital (z2) for any given level of physical capital (Zl)' sincep* > P.

The dynamics of this system are not as well understood as those of the
one-good model, but I would conjecture that for any initial configuration(K(O), h(O)) of the two kinds of capital, the solution paths (of either theefficient or the equilibrium system) (Zl(t), z2(t)) will converge to some pointon the curve in fig. 1, but that this asymptotic position will depend on theinitial position. The arrows in fig. 1 illustrate some possible trajectories. Under
these dynamics, then, an economy beginning with low levels of human andphysical capital will remain permanently below an initially better endowed
economy.
The curve in fig. 1 is defined as the locus of long-run capital pairs (K, h)such that the marginal product of capital has the common value p + OK givenby the right side of (19). Along this curve, then, returns to capital are constantand also constant over time even though capital stocks of both kinds are
growing. In the absence of the external effect y, it will also be true that the real
wage rate for labor of a given skill level (the marginal product of labor) isconstant along the curve in fig. 1. This may be verified simply by calculating
the marginal product of labor from (11) and making the appropriate substitutions.
In the general case, where y ~ 0, the real wage increases as one moves up
the curve in fig. 1. Along this curve, we have the elasticity formula
K 8w
--=

w 8K

(1 + {3)yl-{3+y'so that wealthier countries have higher wages than poorer ones for labor ofany given skill. (Of course, workers in wealthy countries are typically also
more skilled than workers in poor countries.) In all countries, wages at eachskill level grow at the rateyw= - - P .
1-{3Then taking skill growth into account as well, wages grow at
w+p=l-{3+y1- {3P=K,or at a rate equal to the growth rate in the per-capita stock of physical capital.

26

R.E. LuclJS, Jr., On the mechanics of economic development

The version of the model I propose to fit to, or estimate from, U.S. timeseries is the equilibrium solution (21), (26) and (10). As in the discussion of
Solow's version A, K, /3 and s are estimated, from Denison (1961), at 0.013,
0.014, 0.25 and 0.1, respectively. Denison also provides an estimate of 0.009
for the annual growth rate of human capital over his period, an estimate based
mainly on the changing composition of the workforce by levels of educationand on observations on the relative earnings of differently schooled workers. I
will use this 0.009 figure as an estimate of P, which amounts to assuming thathuman capital is accumulated to the point where its private return equals its
social (and private) cost. (Since schooling is heavily subsidized in the U.S., thisassumption may seem way off, but surely most of the subsidy is directed atearly schooling that would be acquired by virtually everyone anyway, and sodoes not affect the margins relevant for my calculations.) Then the idea is touse (10), (21) and (26) to estimate p, 0', Y and ~.
As was the case in the Solow model, p and 0' cannot separately be identified
along steady-state paths, but eq. (10) (which can be derived for this model inexactly the same way as I derived it for the model of section 2) implies
p + O'K = 0.0675. Eq. (21) implies y = 0.417. Combining eqs. (21) and (26)yields a relationship involving y, P, /3, ~, A and p + O'K, but not p or 0'
separately. This relationship yields an estimate for ~ of 0.05. The implied
fraction of time devoted to goods production is then, from (20), U = 0.82.
Given these parameter estimates, the efficient rate of human capital growth
can be calculated, as a function of 0, from (24). It is: .,,* = 0.009 + 0.0146/0.
Table 1 gives some values of this function and the associated values of u* andK* = (1.556)v*. Under log utility (a = 1), then, the U.S. economy 'ought' to
devote nearly three times as much effort to human capital accumulations as it
does, and 'ought' to enjoy growth in per-capita consumption about two fullpercentage points higher than it has had in the past.
One could as easily fit trus model to U.S. data under the assumption that all
returns to human capital are internal, or that y = O. In this case P, .,,* and K
have the common value, from (21), (24) and (26), O'-l[~ - (p - A»), and theratio of physical to human capital will converge to a value that is independentof initial conditions (the curve in fig. 1 will be a straight line). Identifying thiscommon growth rate with Denison's 0.014 estimate for K implies a u value of
0.72, or that 28% of effective workers' time is spent in human capital

Table 1
C1

)I.

u·

".

1
2
3

0.024
0.016
0.014

0.52
0.68
0.72

0.037
0.025
0.022

R.E. Lucas, Jr., On tht! mechanics of economic development

27

accumulation. Accepting Denison's estimate of a 0.009 growth rate of humancapital due to schooling, this would leave 0.005 to be attributed to other forms,
say on-the-job training that is distinct from productive activities.
What can be concluded from these exercises? Normatively, it seems to me,very little: The model I have just described has exactly the same ability to fit
U.S. data as does the Solow model, in which equilibrium and efficient growth
rates coincide. Moreover, it is clear that the two models can be merged [byre-introducing exogenous technical change into (11)] to yield a whole class ofintermediate models that also fit data in this same rough sense. I am simply
generating new possibilities, in the hope of obtaining a theoretical account ofcross-country differences in income levels and growth rates. Since the model
just examined is consistent with the permanent maintenance of per-capita
income differentials of any size (though not with differences in growth rates)
some progress toward this objective has been made. But before returning toempirical issues in more detail, I would like to generate another, quite
different, example of a system in which human capital plays a central role.
5. Leaming-by-doing and comparative advantage
The model I have just worked through treats the decision to accumulate
human capital as equivalent to a decision to withdraw effort fromproduction - to go to school, say. As many economists have observed, on-thejob-training or leaming-by-doing appear to be at least as important asschooling in the formation of human capital. It would not be difficult toincorporate such effects into the previous model, but it is easier to think about
one thing at a time so I will just set out an example of a system (again, for the
moment, closed) in which all human capital accumulation is learning-by-doing.
Doing this will involve thinking about economies with many consumption
goods, which will open up interesting new possibilities for interactions between international trade and economic growth. 14
Let there be two consumption goods, c 1 and c 2 , and no physical capital. For
simplicity, let population be constant. The ith good is produced with the
Ricardian technology:
i = 1,2,(29)

where hj(t) is human capital specialized to the production of good i and uj(t)is the fraction of the workforce devoted to producing good i (so u j ~ 0 and
u 1 + u 2 = 1). Of course, it would not be at all difficult to incorporate physicalcapital into this model, with (29) replaced by something like (11) for each goodi. Later on, I will conjecture the behavior of such a hybrid model, but it will be
simpler for now to abstract from capital.
14 The formulation of learning used in this section is taken from Krugman (1985).

28

R.E. Lucas, Jr., On the mechanics of economic development

In order to let hj(t) be interpreted as a result of learning-by-doing, assume
that the growth of h;(t) increases with the effort uj(t) devoted to producing
good i (as opposed to increasing with the effort withdrawn from production).
A simple way to do this is(30)

To be specific, assume that 81 > 82 , so that good 1 is taken to be the'high-technology' good. For the sake of discussion, assume at one extreme thatthe effects of hj(t) in (29) and (30) are entirely external: production and skill
accumulation for each good depend on the average skill level in that industry
only.
As was the case with (13), the equation for human capital accumulation in
the model discussed earlier, (30) seems to violate the diminishing returns weobserve in studies of productivity growth for particular products. Learningby-doing in any particular activity occurs rapidly at first, then more slowly,
then not at all. Yet as in the preceding discussion, if we simply incorporate
diminishing returns into (30), human capital will lose its status as an engine of
growth (and hence its interest for the present discussion). What I want (30) to'stand for', then, is an environment in which new goods are continually being
introduced, with diminishing returns to learning on each of them separately,
and with human capital specialized to old goods being 'inherited' in some way
by new goods. In other words, one would like to consider the inheritance ofhuman capital within 'families' of goods as well as within families of people. is
Under these assumptions of no physical capital accumulation and purely
external human capital accumulation, the individual consumer has no intertemporal tradeoffs to decide on, so all we need to know about his preferences
is his current-period utility function. I will assume a constant elasticity of
substitution form:(31)

where a j ~ 0, a 1 + a 2 = 1, p> -1, and (1 = 1/(1 + p) is the elasticity of
substitution between C 1 and c 2 • (Please note that the parameters p and (Jrepresent completely different aspects of preferences in this section from thosethey represented in sections 2-4.) With technology and preferences given by(29)-(31), I will first work out the equilibrium under autarchy and then turn tointernational trade considerations.
Take the first good as numeraire, and let (l,q) be the equilibrium prices in aclosed economy. Then q must equal the marginal rate of substitution in
15Stokey (1987) formulates a model of learning on an infinite family of produced andpotentially producible goods that captures exactly these features.

R.E. Lucas, Jr., On the mechanics of economic development

29

consumption, orSolving for the consumption ratio,(32)
Hence both goods will be produced, so that (29) plus profit maximization
implies that relative prices are dictated by the human capital endowments:
q = h IIh 2' Then (29) and (32) together give the equilibrium workforce allocation as a function of these endowments,

or(33)
The dynamics of this closed economy are then determined by inserting thisinformation into eq. (30). Solving first for the autarchy price path, q( t) =h 1(t)lh 2 (t), we have
1 dq
q

1 dh 1

1 dh 2dt = h; dt - h dt = ~IUl - ~2(1- u 1 ),
2

or
(34)
Solving this first-order equation for q(t) = h l (t)/h 2 (t), given the initial endowments hl(O) and h 2 (0), determines the workforce allocation at each date[from (33)] and hence, from (30), the paths of hl(t) and h 2(t) separately.
It will come as no surprise to trade theorists that the analysis of (34) breaks
down into three cases, depending on the elasticity of substitution (J between
the two goods. I will argue below, on the basis of trade considerations, that theinteresting case for us is when (J> 1, so that c1 and C2 are assumed to be goodR. E. Lucas, Jr., On the mechanics of economic development

30

1

q*

q

Fig. 2

substitutes. But in order to make this case, we need all three possibilities infront of us. Refer to fig. 2.
The figure is drawn for the case a> 1, in which case the function [1 +(a 2 ja 1)Oql-o]-1 has the depicted upward slope. To the left of q*, dqjdt < 0,so q(t) tends to O. To the right, dqjdt > 0, so q(t) grows without bound. Thus
the system in autarchy converges to specialization in one of the two goods[unless q(O) = q*]. The choice of which good to specialize in is dictated byinitial conditions. If we are initially good at producing C 1 [if q(O) > q*], we
produce a lot of it, get relatively better and better at producing more of it,
eventually, since c1 and C2 are good substitutes, producing vanishingly small
amounts of c 2 •If the goods are poor substitutes, (J < 1, the curve in fig. 2 slopes down andq* becomes a stable stationary point. At this point, the workforce is so
allocated as to equate 81u 1 and 82 u 2 •In the borderline case of a = 1, the curve is flat. The workforce is initiallyallocated as dictated by the demand weights, ui = ai' i = 1,2, and this allocation is maintained forever. The autarchy price grows (or shrinks) at theconstant rate (ljq)(dqjdt) = a 181 - a 282 forever.
As we learn how to produce computers more and more cheaply, then, we
can substitute in their favor and consume more calculations and fewer
potatoes, or we can use this benefit to release resources from computer
production so as to consume more potatoes as well. The choice we take, notsurprisingly, depends on whether these two goods are good substitutes or poorones.

R.E. Lucas, Jr., On [he mechanics of economic development

31

As was the case with the human capital model of the preceding section, it isobvious that the equilibrium paths we have just calculated will not be efficient.
Since learning effects are assumed to be external, agents do not take them into
account. If they did, they would allocate labor toward the 'high 8;' good,
relative to an equilibrium allocation, so as to take advantage of its higher
growth potential.
Thus, except for the absence of physical capital, this closed economy model
captures very much the same economics as does the preceding one. In bothcases, the accumulation of human capital involves a sacrifice of current utility.
In the first model, this sacrifice takes the form of a decrease in current
consumption. In the second, it takes the form of a less desirable mix of current
consumption goods than could be obtained with slower human capital growth.
In both models the equilibrium growth rate falls short of the efficient rate andyields lower welfare. A subsidy to schooling would improve matters in thefirst. In the second, in language that is current in the United States, an'industrial policy' focused on 'picking winners' (that is, subsidizing the production of high cx;8; goods) would be called for. In the model, 'picking
winners' is easy. If only it were so in reality!
The introduction of international trade into this second model leads topossibilities that I think are of real interest, though I have only begun to thinkthem through analytically. The simplest kind of world to think about is one
with perfectly free trade in the two final goods and with a continuum of small
countries, since in that case prices in all countries will equal world prices(1, p), say, and each country will take p as given. Fig. 3 gives a snapshot of
this world at a single point in time. The contour lines in this figure areintended to depict a joint distribution of countries by their initial humancapital endowments. A country is a point (h 1 ,h 2 ), and the distribution
indicates the concentration of countries at various endowment levels.
At a given world price p, countries above the indicated line are producers ofgood 2, since for them h1/h 2 < P and they maximize the value of theirproduction by specializing in this good. Countries below the line specialize inproducing good 1, for the same reason. Then for each p one can calculate
world supply of good 1 by summing (or integrating) the hi values below thisprice line, and the world supply of good 2 by summing the h 2 values above theline. Clearly, the supply of good 2 is an increasing function of p and of good 1
a decreasing function, so that the ratio cllC1 of total quantities supplied.
.
Increases as p Increases.
Now world relative demand, with identical homothetic preferences, is justthe same decreasing function of p that described each country's demand in theautarchic case: c2lc 1 = (a2lcxl)Op - 0 . Hence this static model determines theequilibrium world relative price p uniquely. Let us turn to the dynamics.
Those countries above the price line in fig. 3 are producing only good 2, so
their hi endowments remain fixed while their h 2 endowments grow at the rate
82 , Each country below the price line will produce only good 1, so that its h 2 is32

R.E. Lucas, Jr., On the mechanics of economic development

Fig. 3

constant while hI grows at the rate 81 , Thus each country's (h 1 ,h 2 ) coordinates are changing as indicated by the arrows in fig. 3, altering the distributionof endowments that determines goods supplies over time. These movements
obviously intensify the comparative advantages that led each country to
specialize in the first place. On the other hand, as the endowment distributionchanges, so does the equilibrium price p. Is it possible that these pricemovements will induce any country to switch its specialization from one goodto the other?
A little reflection suggest that if anyone switches, it will have to be a
producer of the high-8 good: good 1. The terms of trade are moving against
good 1 (in the absence of switching) since its supply is growing faster. The
issue again turns on the degree of substitutability between the two goods. If 0
is low, the terms of trade may deteriorate so fast that a marginal good 1
producer may switch to producing good 2: he is getting relatively better at
producing good 1, but not fast enough. The inequality that rules this possibility out is82

0 >1-8'1(35)

R.E. Lucas, Jr., On the mechanics of economic development

33

I have already said that I think 0> 1 is the interesting case, so I want toaccept (35) for the rest of the discussion.
Under (35) - that is, with no producer switching - we can read the dynamics of prices right off the relative demand schedule:
1 dp~1 - ~2--P dt0(36)With relative price movements determined, the growth rates of real output
in all countries is also determined. Measured in units of good 1, output of
the good 1 producers grows at the rate ~1' Output of the good 2 producers,
also measured in units of good 1, grows at the rate ~2 + (ljp)(dpjdt) = ~2 +(<'>1 - <'>2)/0. In general, then countries in equilibrium will undergo constantbut not equal growth rates of real output.
Which countries will grow fastest? The condition that producers of thehigh-~ good, good 1, will have faster real growth is just
~1 > ~2 +~1 - ~2o,which is equivalent to the condition: 0 > 1. That is, producing (having acomparative advantage in) high-learning goods will lead to higher-than-average real growth only if the two goods are good substitutes. Since it is exactly
this possibility that the model is designed to capture, the case 0> 1 seems tome the only one of potential interest. If the terms-of-trade effects of technological change dominated the direct effects on productivity (which would be
the case if 0 < 1), those countries with rapid technological change would enjoy
the slowest real income growth. There may be instances of such 'immiserizing
growth', but if so they are surely the exceptions, not the rule. (These are the'trade considerations' I mentioned earlier.)This simple model shares with the model of section 4 the prediction of
constant, endogenously determined real growth rates. In addition, it offers thepossibility of different growth rates across countries, though differences thatare not systematically related to income levels. In the equilibrium of themodel, production patterns are dictated by comparative advantage: Eachcountry produces goods for which its human capital endowment suits it. Givena learning technology like (30), countries accumulate skills by doing what they
are already good at doing, intensifying whatever comparative advantage they
begin with. This aspect of the theory will tend to lock in place an initialpattern of production, with rates of output growth variable across countries
but stable within each country. There is no doubt that we observe forces forstability of this type, but there seem to be offsetting forces in reality that thismodel does not capture.

R.E. Lucas, Jr., On the mechanics of economic development

34

One of these has to do with the composition of demand. With homothetic
utility the composition of world demand will remain fixed as income grows. In
fact, we know that income elasticities for important classes of goods differ
significantly from unity (contrary to the assumption of homotheticity). (Weknow, for example, that demand shifts systematically away from food consumption as income grows.) This force will 'create' comparative advantages in
the production of other goods as time passes, altering world production
patterns and growth rates as it does.
Another, I would guess more important, force has to do with the continual
introduction of new goods and the fall-off of learning rates on old goods. By
modeling learning as occuring at fixed rates on a fixed set of goods, I have here
abstracted from important sources of change in world trade patterns. Modifying the model to incorporate possibilities of these two types is an entirely
practical idea, given current theoretical technology, but the general equilibrium possibilities for such a modified system have not as yet been worked
OUt.

16

The present model provides a simple context for discussing two popular'strategies' for economic development: 'import substitution' and 'export promotion'. Consider first a country with q = h 1/h 2 currently to the right of q* in
fig. 2, but with (h 1,h 2 ) lying above the equilibrium world price price line in fig.
3. Under free trade, this country will specialize in the production of good 2
forever. Under autarchy (which is just the extreme version of an importsubstitution policy) this country will specialize in producing good 1. Eventually its expertise in this protected industry will grow to the point where it will
have a comparative advantage in good 1 under free trade, and the maintenance of autarchy will no longer serve any purpose, but this need not be sofrom the beginning.
I hasten to add that this is only one theoretical possibility among many.
Another possibility is an initial q value below q* in fig. 2. In this case,autarchy will not provide nurture for the infant industry, but will rather
permanently cut off the country from consuming the high-learning good.
Within the context of this model, then, there is no substance-free way todeduce useful guides for trade and development policies. One needs to know
something about the actual technological possibilities for producing different
goods in different places in order to arrive at definite conclusions.
I take an 'export promotion' strategy to mean something slightly different:
the manipulation through taxes and subsidies of the terms of trade p faced bya country's producers. With this kind of flexibility, one need not simply choose
between world price p and autarchy price q, but can rather set any production
incentives and hence choose any growth rate between the two extremes in thefree trade equilibrium. Obviously, even with this flexibility it does not follow
16Again. see Stokey (1987).

R.E. Lucas, Jr., On the mechanics of economic development

35

that 'growth-increasing' and 'welfare-improving' policies will necessarily
coincide, but they certainly might.
My objective in this section has been to offer one example of a theoreticalmodel in which rates of growth differ across countries, and not to offer policy
advice. The case for infant industry protection based on external effects that
this model formalizes is the classic one, and it does not become either more orless valid, empirically, by being embedded in a slightly new framework. But isit possible, I wonder, to account for the large cross-country differences ingrowth rates that we observe in a theoretical model that does not involve
external effects of the sort I have postulated here? I have not seen it done.
6. Cities and growth

My concern to this point has been almost exclusively with the aggregate
mechanics of economic development, and I am afraid the discussion in theselectures will not get much beyond these mechanics. But I believe a successful
theory of development (or of anything else) has to involve more than aggregative modeling, and I would like both to explain what I mean by this and toindicate where one might look to extend the analysis to a deeper and moreproductive level.
The engine of growth in the models of sections 4 and 5 is human capital.
Within the context of these two models, human capital is simply an unobservable magnitude or force, with certain assumed properties, that I havepostulated in order to account for some observed features of aggregative
behavior. If these features of behavior were all of the observable consequencesof the idea of human capital, then I think it would make little difference if we
simply re-named this force, say, the Protestant ethic or the Spirit of History or
just 'factor X'. After all, we can no more directly measure the amount of
human capital a society has, or the rate at which it is growing, than we canmeasure the degree to which a society is imbued with the Protestant ethic.
But this is not all we know about human capital. This same force, admittedly unobservable, has also been used to account for a vast number ofphenomena involving the way people allocate their time, the way individuals'
earnings evolve over their lifetimes, aspects of the formation, maintenance anddissolution of relationships within families, firms and other organizations, andso on. The idea of human capital may have seemed ethereal when it was first
introduced - at least, it did to me - but after two decades of research applications of human capital theory we have learned to 'see' it in a wide variety ofphenomena, just as meteorology has taught us to 'see' the advent of a warm
front in a bank of clouds or 'feel' it in the mugginess of the air.
Indeed, for me the development of the theory of human capital has verymuch altered the way I think about physical capital. We can, after all, no more
directly measure a society's holdings of physical capital than we can its human

36

R.E. Lucas. Jr., On the mechanics of economic development

capital. The fiction of 'counting machines' is helpful in certain abstract
contexts but not at all operational or useful in actual economies - evenprimitive ones. If this was the issue in the famous 'two Cambridges' controversy, then it has long since been resolved in favor of this side of theAtlanticP Physical capital, too, is best viewed as a force, not directly
observable, that we postulate in order to account in a unified way for certain
things we can observe: that goods are produced that yield no immediate
benefit to consumers, that the production of these goods enhances laborproductivity in future periods, and so on.
The fact that the postulates of both human and physical capital have manyobservable implications outside the contexts of aggregate models is importantin specific, quantitative ways, in addition to simply giving aggregative theorists
a sense of having 'microeconomic foundations'. For example, in my application of a human capital model to U.S. aggregative figures, I matched the U.S.
observations to the predictions of a competitive model (as opposed to an
efficient one) in spite of the fact that education, in the U.S., involves vast
government intervention and is obviously not a competitive industry in any
descriptive sense. Why not instead identify the observed paths with themodel's efficient trajectories? The aggregative data have no ability to discriminate between these two hypotheses, so this choice would have yielded as
good a 'fit' as the one I made. At this point, I appealed to the observation thatmost education subsidies are infra-marginal from the individual's point ofview. This observation could stand considerable refinement before it could
really settle this particular issue, but the point is that aggregate models basedon constructs that have implications for data other than aggregates - models
with'microeconomic foundations' if you like - permit us to bring evidence tobear on questions of aggregative importance that cannot be resolved withaggregate theory and observations alone. Without the ability to do this, we cando little more than extrapolate past trends into the future, and then be caught
by surprise every time one of these trends changes.
The particular aggregate models I have set out utilize the idea of humancapital quite centrally, but assign a central role as well to what I have beencalling the external effects of human capital. This latter force is, it seems tome, on a quite different footing from the idea of human capital generally: The
twenty years of research I have referred to earlier is almost exclusively
concerned with the internal effects of human capital, or with investments inhuman capital the returns to which accrue to the individual (or his immediatefamily). If it is this research that permits us to 'see' human capital, then theexternal effects of this capital must be viewed as remaining largely invisible, orvisible at the aggregative level only. For example, in section 4 I arrived at an
estimate of y = 0.4 for the elasticity of U.S. output with respect to the external
effects of human capital on production. Does this seem a plausible number?
17That is. the English side.

R.E. Lucas, Jr., On the mechanics of economic development

37

Or, putting the question in a better way: Is 'Y = 0.4 consistent with otherevidence? But what other evidence? I do not know the answer to this question,
but it is so central that I want to spend some time thinking about where theanswer may be found. In doing so, I will be following very closely the lead ofJane Jacobs, whose remarkable book The Economy of Cities (1969) seems tome mainly and convincingly concerned (though she does not use this terminology) with the external effects of human capital.
I have been concerned with modeling the economic growth of nations,considered either singly or as linked through trade. In part, this was a responseto the form of the observations I cited at the beginning: Most of our data
come in the form of national time series, so 'fitting the facts' is taken to mean
fitting national summary facts. For considering effects of changes in policies
the nation is again the natural unit, for the most important fiscal andcommercial policies are national and affect national economies in a uniform
way. But from the viewpoint of a technology - like (11) - through which theaverage skill level of a group of people is assumed to affect the productivity ofeach individual within the group, a national economy is a completely arbitrary
unit to consider. Surely if Puerto Rico were to become the fifty-first state thiswould not, by itself, alter the productivity of the people now located in Puerto
Rico, even though it would sharply increase the average level of human capitalof those politically defined as their fellow citizens. The external effects that theterm h~ in (11) is intended to capture have to do with the influences people
have on the productivity of others, so the scope of such effects must have to dowith the ways various groups of people interact, which may be affected bypolitical boundaries but are certainly an entirely different matter conceptually.
Once this question of the scope of external effects is raised, it is clear that it
cannot have a single correct answer. Many such effects can be internalized
within small groups of people - firms or families. By dealing with an infinitely-lived family as a typical agent, I have assumed that such effects aredealt with at the non-market level and so create no gap between private andsocial returns. At the other extreme, basic discoveries that immediately become common property - the development of a new mathematical resultsay - are human capital in the sense that they arise from resources allocatedto such discoveries that could instead have been used to produce current
consumption, but to most countries as well as to most individual agents they
appear 'exogenous' and would be better modelled as A(t) in section 2 than as
h aCt) in section 4.
If it were easy to classify most external productivity effects as either global
in scope or as so localized as to be internalizable at the level of the family or
the firm, then I think a model that incorporated internal human capital effects
only plus other effects treated as exogenous technical change would be
adequate. Such a model would fit time series from advanced countries about aswell as any I have advanced, being an intermediate model to those I discussed
in sections 2 and 4, which were in turn not distinguishable on such data alone.

38

R.E. Lucas, Jr., On the mechanics of economic del'elopment

Such a model would, I think, have difficulty reconciling observed pressures for
immigration with the absence of equivalent capital flows, but perhaps thisanomaly could be accounted for in some other way.
But we know from ordinary experience that there are group interactions thatare central to individual productivity and that involve groups larger than theimmediate family and smaller than the human race as a whole. Most of what
we know we learn from other people. We pay tuition to a few of theseteachers, either directly or indirectly by accepting lower pay so we can handaround them, but most of it we get for free, and often in ways that are
mutual - without a distinction between student and teacher. Certainly in ourown profession, the benefits of colleagues from whom we hope to learn are
tangible enough to lead us to spend a considerable fraction of our timefighting over who they shall be, and another fraction travelling to talk withthose we wish we could have as colleagues but cannot. We know this kind of
external effect is common to all the arts and sciences - the 'creative professions'. All of intellectual history is the history of such effects.
But, as Jacobs has rightly emphasized and illustrated with hundreds ofconcrete examples, much of economic life is 'creative' in much the same way
as is 'art' and 'science'. New York City's garment district, financial district,diamond district, advertising district and many more are as much intellectual
centers as is Columbia or New York University. The specific ideas exchangedin these centers differ, of course, from those exchanged in academic circles, but
the process is much the same. To an outsider, it even looks the same: Acollection of people doing pretty much the same thing, each emphasizing his
own originality and uniqueness.
Considerations such as these may convince one of the existence of external
human capital, and even that it is an important element in the growth ofknowledge. But they do not easily lend themselves to quantification. Hereagain I find Jacobs's work highly suggestive. Her emphasis on the role of cities
in economic growth stems from the observation that a city, economically, islike the nucleus of an atom: If we postulate only the usual list of economic
forces, cities should fly apart. The theory of production contains nothing tohold a city together. A city is simply a collection of factors of production capital, people and land - and land is always far cheaper outside cities thaninside. Why don't capital and people move outside, combining themselves withcheaper land and thereby increasing profits? Of course, people like to live near
shopping and shops need to be located near their customers,. but circularconsiderations of this kind explain only shopping centers, not cities. Cities are
centered on wholesale trade and primary producers, and a theory that accounts
for their existence has to explain why these producers are apparently choosing
high rather than low cost modes of operation.
It seems to me that the 'force' we need to postulate account for the central
role of cities in economic life is of exactly the same character as the 'external
human capital' I have postulated as a force to account for certain features of

R.E. Lucas, Jr., On the mechanics of economic development

39

aggregative development. If so, then land rents should provide an indirect
measure of this force, in much the same way that schooling-induced earnings
differentials provide a measure of the productive effects of internal humancapital. It would require a much more detailed theory of the external effects ofhuman capital than anything I have provided to make use of the informationin urban land rents (just as one needs a more detailed theory of human capitalthan that in section 4 to utilize the information in earnings data), but thegeneral logic is the same in the two cases. What can people be paying
Manhattan or downtown Chicago rents for, if not for being near other people?

7. Conclusions
My aim, as I said at the beginning of these lectures, has been to try to findwhat I called 'mechanics' suitable for the study of economic development:that is, a system of differential equations the solution to which imitates someof the main features of the economic behavior we observe in the world
economy. This enterprise has been taken about as far as I am able to take it, atpresent, so I will stop and try to sum up what the main features of thesemechanics are and the sense in which they conform to what we observe.
The model that I think is central was developed in section 4. It is a systemwith a given rate of population growth but which is acted on by no otheroutside or exogenous forces. There are two kinds of capital, or state variables,in the system: physical capital that is accumulated and utilized in production
under a familiar neoclassical technology, and human capital that enhances the
productivity or both labor and physical capital, and that is accumulated
according to a 'law' having the crucial property that a constant level of effort
produces a constant growth rate of the stock, independent of the level alreadyattained.
The dynamics of this system, viewed as a single, closed economy, are as
follows. Asymptotically, the marginal product of physical capital tends to a
constant, given essentially by the rate of time preference. This fact, which withone kind of capital defines the long-run stock of that capital, in the two-capitalmodel of section 4 defines a curve in the 'physical capital-human capital
plane'. The system will converge to this curve from any initial configuration ofcapital stocks, but the particular point to which it converges will depend on
initial conditions. Economies that are initially poor will remain poor, relatively, though their long-run rate of income growth will be the same as that of
initially (and permanently) wealthier economies. A world consisting of sucheconomies, then, each operating autarchically, would exhibit uniform rates ofgrowth across countries and would maintain a perfectly stable distribution ofincome and wealth over time.
If trade in capital goods is introduced into this model world economy, withlabor assumed immobile, there will be no tendency to trade, which is to say no

40

R.E. Lucas, Jr., On the mechanics of economic development

systematic tendency for borrowing and lending relationships to emerge between rich and poor countries. Put another way, the long-run relationshipbetween the two kinds of capital that holds in each country implies the same
marginal productivity of physical capital, no matter what the level of capitalthat has been accumulated. The picture I have given for a world of closed
economies thus carries over without change to a world with free trade incapital goods.
If labor mobility is introduced, everything hinges on whether the effects ofhuman capital are internal - affecting the productivity of its 'owner' only - orwhether they have external benefits that spill over from one person to another.
In the latter case, and only in the latter case, the wage rate of labor at any
given skill level will increase with the wealth of the country in which he isemployed. Then if labor can move, it will move, flowing in general from poor
countries to wealthy ones.
The model I have described fits the evidence of the last century for the u.s.
economy as well as the now standard neoclassical model of Solow andDenison, which is to say, remarkably well. This is of course no accident, forthe mechanics I have been developing have been modeled as closely as
possible on theirs. It also fits, about as well, what seem to me the main featuresof the world economy: very wide diversity in income levels across countries,
sustained growth in per-capita incomes at all income levels (though not, ofcourse, in each country at each income level), and the absence of any marked
tendency for growth rates to differ systematically at different levels of income.
The model is also consistent with the enormous pressures for immigration that
we observe in the world, even with its extreme assumptions that assign noimportance to differences in endowments of natural resources and that permit
perfectly free trade in capital and consumption goods. As long as people ateach skill level are more productive in high human capital environments, suchpressures are predicted to exist and nothing but the movement of people canrelieve them.
Though the model of section 4 seems capable of accounting for average
rates of growth, it contains no forces to account for diversity over countries orover time within a country (except for arbitrary shifts in tastes or technology).
Section 5 develops a two-commodity elaboration of this model that offers
more possibilities. In this set-up, human capital accumulation is taken to be
specific to the production of particular goods, and is acquired on-the-job or
through learning-by-doing. If different goods are taken to have different
potentials for human capital growth, then the same considerations of comparative advantage that determine which goods get produced where will also
dictate each country's rate of human capital growth. The model thus admits
the possibility of wide and sustained differences in growth rates acrosscountries, differences that one would not expect to be systematically linked toeach country's initial capital levels.

R.E. Lucas, Jr., On the mechanics of economic development

41

With a fixed set of goods, which was the only case I considered, this accountof cross-country differences does not leave room for within-country changes ingrowth rates. The comparative advantages that dictate a country's initial
production mix will simply be intensified over time by human capital accumulation. But I conjecture that a more satisfactory treatment of product-specificlearning would involve modeling the continuous introduction of new goods,
with learning potentials on any particular good declining with the amountproduced. There is no doubt that we observe this kind of effect occuring inreality on particular product lines. If it could be captured in a tractable
aggregative model, this would introduce a factor continuously shaking up an
existing pattern of comparative advantages, and offer some interesting possibilities for shifts over time in a country's growth rate, within the same generalequilibrium framework used in section 5.
If such an analysis of trade-related shifts in growth rates should turn out topossible, this would be interesting, because the dramatic recent development
success stories, the 'growth miracles' of Korea, Taiwan, Hong Kong andSingapore (not to mention the ongoing miracle of Japan) have all been
associated with increases in exports, and more suggestively still, with exportsof goods not formerly produced in these countries. There is surely no strain inthinking that a model stressing the effects of learning-by-doing is likely to shedlight on these events.
A successful theory of economic development clearly needs, in the firstplace, mechanics that are consistent with sustained growth and with sustained
diversity in income levels. This was the objective of section 4. But there is no
one pattern of growth to which all economies conform, so a useful theory
needs also to capture some forces for change in these patterns, and amechanics that permits these forces to operate. This is a harder task, certainly
not carried out in the analysis I have worked through, but I think the analysisof section 5 is a promising beginning.

Acknowledgements
The fact that a fairly well known economist is willing to speak so broadly on
a topic of such enormous importance, about which he obviously knows very
little, has proved a great stimulus to discussion whenever these lectures havebeen given. I have received many more interesting reactions than I will ever beable to follow up on, or even to acknowledge. But I would like to thank Nancy
Stokey for her criticism of preliminary drafts, Arnold Harberger, Jane Jacobs,
Akiva Offenbacher, Theodore Schultz and Robert Solow for their comments,
Richard Manning for his very able assistance, and Edward Prescott and
Sherwin Rosen for stimulating discussions of all aspects of economic development over many years before and after these lectures were first given.

42

R.E. Lucas, Jr., On the mechanics of economic development

Finally, I would like to thank Robert King and Charles Plosser for encouraging the publication of this awkwardly-sized (too long for an article, too shortfor a book) paper. In response to their suggestions, I have retained the lecture
style in this version, making for the most part only minimal changes. (Section
5 is the only exception: I found a much better framework than the one used in
the original, and so have replaced much of the original text.) Their hope, andmine, is that without being definitive on any aspect of the problem we may be
productively provocative on many.
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