The dominant model (i.e. explanation) of economic growth is the Solow model. To many it represents a powerful and flexible tool. Whatever its merits as a basic framework for analysis, many have sought to introduce modifications necessary to bring Solow closer to reality. My own view is that among the least acceptable assumptions in Solow is that there are neither costs nor benefits to be associated with increased population density. This assumption – as I shall argue implicit in the model and which I will refer to as the assumption of density neutrality – stands in the way of its being of much use in either historical analysis (the model, because of density neutrality, is ahistorical) or in an ecologically informed discussion of modern economic development and growth.
In what follows I will compare Solow to the much richer and nuanced model of economic growth developed by Ester Boserup in her 1981 book Population and Technological Change. Boserup argues that density plays a central role in economic growth and development. Its role being a positive or a negative one depending on the relative size of costs and benefits of increased density.
A brief proof of the density neutrality of Solow
The following presumes a certain degree of familiarity with the Solow model. In Solow, once an economy’s “steady state” level of real per capita income is reached, given its state of technology, the depreciation rate, the investment ratio and the rate of population growth, this level of real per income and the capita-labor ratio implied by the production function will remain in equilibrium at these levels. Of course, continuous population growth within a given area means increasing levels of population density yet, by assumption, this does not impact steady state equilibrium.
For this to be true one of the following must also be true:
(1) that there are neither costs nor benefits to be associated with increasing population within an area.
(2) that, following a neoclassical environmental view, the rate of technological progress is positive and just happens to be sufficient to offset the costs of increased density
(3) that the benefits of increased density are just enough to offset its increased costs
(4) that as population grows, new territory is opened up
The fourth assumption listed has merit if one is thinking of hunter-gatherers or long-fallow agriculturalists. With relatively little capital per worker needed to sustain a tolerable standard of living, with scarce labor, and with leisure highly valued if land is relatively abundant some will strike off into new territory once the costs of increased density, here increased pressure on the natural resource base, begin to be felt. The term noncircumscribed has been applied to describe the tendency of hunter-gatherers and slash and burn agriculturalists to open new territories rather than adapt more labor or capital intension technologies. I will reject the first assumption listed out of hand. There are obviously, given the stock of natural resources, very real costs to increased density as the exploited stock of renewable resources are used at levels that are not sustainable and as the stock of exhaustible resources are depleted. This leaves the second,third, and fourth assumptions still to be considered. Because Boserup has much to say about these matters, especially about the benefits of increased density, I would like to first discuss her model.
A brief summary of Boserup: "to starve or not to starve: that is the question".
Boserup begins by flatly rejecting the Malthusian notion that growing numbers press against an economy’s natural resources without society fighting against this. In the struggle for survival, we have repeatedly risen to the challenge by inventively squeezing more from the resources we have. Plows replace hoes, seed-drills replace broadcast seeding, land is worked annually or even more often, it is weeded and fertilized, meat dairy and wool are replaced by cotton and fish. In general more capital and labor intensive techniques are employed to recover the ground lost as numbers increase. (See p.181 of Boserup. These themes are also the focus of her book
The Conditions of Agricultural Growth and Change.)
Whether it is more correct to refer to the changes brought about by the pressure created by increased density as induced changes in technique rather than induced technological change per se, the Malthusian model of population encourages us to gloss over all that preindustrial societies were able to accomplish in the face of the pressure population growth and increased density created. Despite diminishing marginal returns to labor, the Malthusian demon of diminishing marginal returns to land, rising rents, and the positive checks a population of famine and starvation are held at bay. The preceding, of course, describes not the benefits that flow from increased density but rather points to what must be done if higher levels of population density are to be sustainable. What possible benefits could large numbers of people crowded into a given area provide?
The benefits of higher density: infrastructural investment, division of labor and urbanization.
In an era of high rates of population growth in already densely settled areas (most notably India and China) and urban overcrowding throughout the developing world one tends to think of population density only in terms of costs. It is a challenge to think in terms of benefits. This is why it is important to make a clear distinction between the rate of approach to a certain population size (the rate of population growth) and population density itself. The more densely settled an area already is, the more fragile its environment, and less likely it is that the benefits of increased population and therefore increased density will be felt.
Before the twentieth century we see a positive correlation between economic power and population. Although by modern standards, real per capita income was quite low throughout the world, what set what can be thought of as economically more powerful areas were (1) a much sharper division of labor than found elsewhere, (2) a better developed infrastructure and (3) a higher degree of urbanization. Following Boserup I will argue that these hallmarks of economic “power” are more the consequences than the causes of increased density.
Social overhead capital: infrastructural investment
The importance of infrastructural investment, especially transportation facilities, is emphasized by all economic historians but it is often overlooked that such facilities require a certain density of population. (Boserup, 1981, p.68) Assume that there are a series of projects that could be carried out to significantly increase an economy’s stock of social overhead capital, its infrastructure. Further assume that through the sort of induced technological changes already discussed that real per capita income is constant and that as density and aggregate output grow the costs of completing these projects, both in terms of resources required and in monetary costs are constant as well. In short, assume an economy with a series of infrastructural projects that will cost less and less in
per capita terms. As the per person costs go down, the likelihood of individual benefits exceeding costs one is being asked to bear rises. Even if the benefits to the average person are quite small, the more widely construction and maintenance costs are shared the less likely any one individual or group of individuals might be to oppose these projects. This does not mean that there will not be resistance to infrastructural investment. However, the way will be far easier the larger the numbers are because the burden per person becomes lighter as numbers grow.
The Division of Labor
Smith emphasized the role an economy’s geography plays in determining the extent of the market and therefore the scope for specialization, i.e. a greater division of labor. However, the rise in numbers and aggregate output in a given area that
can follow higher population density (assuming that real per capita income does not fall) make further specialization or division of labor possible. In part, this is due to the build-up of infrastructure I have just discussed. As roads and canals are built, harbors made deeper, docks and public squares finished the costs of transport and exchange will be lowered. Assuming that food supply systems have successfully adjusted to increased density, the first force leading to an increased division of labor will be played out on the stage set via increased infrastructural investment. Although aided immensely by the build-up of infrastructure, increased density increases the likelihood of someone being able to find full-time employment if they are to specialize.
In his book the Great Divergence Ken Pomeranz notes “…one cannot generally support oneself doing certain tasks that each person needs done only occasionally unless there are many people in one’s market area”. (Pomeranz, p. 27) In other words, it is only as numbers grow that the general homebuilder is able to shift from being a part-time carpenter, mason, painter, plumber, and electrician – jack of all trades, master of none – to being able to focus her talents on one of these areas or focus on coordinating and supervising these activities. Boserup points out that “…the areas in Europe which first developed manufacturing were the ones with the highest population density”. (Boserup, 1981, p. 102) Echoing this, E. A. Wrigley emphasizes that premodern growth was “specialization growth” and that this was – to a point - intimately connected to population density. (see his
Continuity, Chance, and Change)
Urbanization
The third and final benefit of increased density Boserup highlights is increased urbanization. Her point is that in pre-industrial societies, agricultural households are at best capable of giving up only a small fraction of their output to feed, clothe, and shelter an urban population. As a result, all else being equal, growing numbers in the surrounding countryside, higher rural densities, make large urban centers possible. Lack of coastline, an unreliable and a relatively poor system of navigable rivers or a mountainous terrain all raise the costs of transporting goods to market. In such a situation, to support a city of a given size, agricultural density must be even higher in the area immediately outside it. If the surrounding countryside is successful in supporting an urban area long enough, economies of agglomeration for both physical and human capital are at the very least possible.
Costs of higher density
The costs of higher density – as suggested earlier – are far easier to enumerate than its benefits. Stress on natural resources, congestion and pollution are all easily understood costs of crowding more and more people into a given area. With these costs in mind, the process of premodern economic growth – here defined as growth in aggregate output and population but without significant growth in real per capita income – can be viewed as a rough balance being struck between the costs and benefits of increased density. Despite stagnant and relatively low levels of real per capita income, in the premodern world what were considered prosperous economies (what I earlier referred to as economic powers) all exhibited extensive division of labor, well-developed infrastructure, and relatively high rates of urbanization. More sparsely settled areas are the ones that failed to achieve high level of urbanization, division of labor, and infrastructural development. And in turn, sparse settlement was largely a function of geography, geography having stacked the deck against these areas. Their climate and terrain simply could not produce the food, fiber, fodder, fuel, and building materials needed to sustain larger numbers.
What emerges from Boserup is then a much richer explanation of the steady state than that found in Solow. Before the advent of the modern era, numbers and aggregate output grew with painfully little advance in the standard of living. This was because it was difficult in the extreme to do much more than offset the costs of increased density with specialization, infrastructure, and urbanization.
In areas where a population’s ‘back was to the wall’, where new lands were not open, where mountains, deserts, oceans and other boundaries stood in the way of movement more and more people had to be supported in a given area and the sort of development we have described here, based on what Arnold Pacey has referred to as survival technology, came into play if possible. Only where the development of such technologies was not possible and population was hemmed in was the Matthusian model relevant.
Much of Sub-Saharan Africa stands as an example of this case. “This region had a small and scattered population whose main centers were cut off from one another by vast areas of desert and impenetrable forest, so the diffusion of technology was so slim…the density areas near the West African coast were sparsely inhabited and there were few crops which could be grown in the very humid climate until bananas and Asian yams were introduced after A.D. 500. (Pacey, p. 38))
Europe was far from hemmed in until relatively recently. As Boserup described Europe’s geography: “The European continent is a large open area with good conditions for agriculture nearly everywhere. The temperate, humid climate permits the growth of one crop per year without irrigation; most of the territory consists of large plains or gently sloping hillsides; and surface water for drinking and other purposes is available nearly everywhere. So when population increased, it was easy for the population to disperse without any need to adopt other types of food or change the way of life. (Boserup, 1981, p. 57) Looked at in this way, Europe’s dark ages may at least in part be due to its ability to avoid the sting of higher numbers by replicating itself in new areas rather than taking the higher cost route of adaptation and change.
In contrast to Europe, Asia – particularly China but India, Japan, and parts of western and southeastern Asia as well - bumped up against progressively more and more constraints that it could, with added effort, overcome. Areas such as southern China, Japan, and the eastern region of India had relatively high density thanks to wet sub-tropical and tropical climates that permitted the harvesting of rice and cotton for calories and cloth and fish for protein. Squeezing more from the land and water by more labor-intensive techniques was far easier than in the wool-wheat-dairy-linen and leather economies of the west.
Although cotton is quite hard on the soil, drains the water table, and requires much moisture when planting and growing but a hot dry climate when maturing, rice can be sown more than once a year, does not deplete the soil, and requires about a third of the land that wheat does to support someone on a 2400 calorie diet. Up to a point at least, the superior capacity of rice and cotton economies to support a dense population meant that more of the benefits outlined above could be enjoyed. The dominant position of Asia historicall was due to its ability to more readily absorb ever increasing numbers. Highly urbanized and technologically-developed economies rich in infrastructure, with a considerable division of labor were the consequence not the cause of higher density. As important as all of this is historically and although it is compatible with Solow it is completely neglected in standard textbook treatments of Solow. In addition to this it diverts attention from the fundamental forces driving modern economic growth and the industrial revolution where, as I argue elsewhere, for the first time the benefits of increased density were more than able to offset the costs of increased density thanks to coal.
The difficulty of maintaining balance over time
The marginal benefits of increased density could be measured by upward shifts in the production function in y(t) (real output per hour’s worth of labor), k(t) space while marginal costs could be measured by shifts down. I draw the marginal benefits of density curve (MBD) as downward-sloping because the benefits of increased density (increased division of labor, infrastructural investment and economies of agglomeration associated with urbanization, etc.) can be expected to decline as density grows. All else equal, the costs of density will continue to rise so I have drawn the marginal cost of density curve (MCD) as upward sloping.
Growth in real per capita income will be maximized when all else equal, D is such that the marginal benefits of density equal the added or marginal costs. Of course density will approach this point and eventually reach D* the optimal level. However, given n, the rate of population growth, D will continue to grow beyond this point. Therefore the speed that density approaches D* and, having crossed it, moves on is significant. The slower the better.
The marginal benefits of density take time to emerge. Therefore the faster the approach to D* (the higher n is) the lower overall and the steeper MBD will be. On the other side of D*, once optimal D, has been passed, the likelihood of an economy being able to adapt or innovate rapidly enough falls. The situation far too easily gets out of hand and it becomes quite difficult to bring the costs of density down soon enough, to prevent the marginal costs of density from rising.
Geography helps to determine how rapidly the cost of increased density rises. Areas of poor forest reserves, areas with relatively infertile soil, areas with low water tables, and those with limited access to alternate sources of energy for heating, cooking, and for fuel will feel the pressures of higher numbers far more than economies more favorably placed. And it is not too radical a proposition that the less time a system has to adjust to an increasingly difficult situation the more painful adjustment must be. Regions with poor geographic conditions and rapid rates of population growth therefore are doubly cursed. The length of time that benefits if higher density outweighs the costs is extremely short. And the economy continues on, moving away so quickly from D*, that the odds are very small that enough innovation, invention, and adaptation takes place to do much more than gently nudge MCD to the right.
Once D* has been passed, a drop in n does no more than give the system breathing room. At least for a short while, a drop in n increases the chances that a gentle nudge to MCD will be sufficient to keep real per capita income stable or slow the rate at which it’s falling.
The plight of sub-Saharan Africa and the British industrial revolution: A connection?
For every twenty news reports that focus on corruption and other forms of bad governance in various counties in sub-Saharan Africa there may be perhaps one that mentions in passing the region’s very fragile environment: its lack of arable land, poor coastlines, lack of perennial rivers, and tremendously high rates of population growth. In terms of the model I have just presented, the plight of subSaharan Africa arguably has more to do with the impact a fragile environment has on the rate at which the costs of density increase than its does corruption. In terms of the model I have just presented, the plight of sub-Saharan Africa arguably has as much to do with the impact other environmental factors such as a lack of good coastlines, annual rain-fed rivers (dependent on low and highly variable rainfall) have on the total benefits at any level of density and the rate at which these benefits increase. In terms of the model I have just presented, the plight of sub-Saharan Africa arguably has as much to do with the high rate of population growth that push such economies away from D* and therefore push them toward the point where neither new technologies can be created fast enough nor existing areas adapted to local conditions readily enough to do much good.
Whatever the steady state level of real per capita income might be, whatever investment ratios or depreciation rates might be, powerful and more fundamental forces are holding this part of the world down. In contrast, England, the home of the industrial revolution, was environmentally in a much more favorable position with more slowly rising costs, much higher and much more gradually falling marginal benefits, and although by historical standards a phenomenal rate of population growth, a far gentler (i.e., more manageable) rate of increase in population than developing countries in the 20th century experienced.
Sometimes only implied, at other times very explicitly stated, one encounters the argument that you have to look no further than culture if you wish to understand the differences in economic fortunes both now and in the past. This view resonates well with anyone currently on the top of the economic heap. After all, what it suggests is that economic prosperity is due to a lack of freedom, a lack of respect for the law, a lack of strong work ethic or an inquisitive nature. As a result, the conclusion that the rewards of wealth and freedom are there for any society willing to change its outlook. As proof of this incredibly naive outlook you need look no further than calls for government reform and an opening of trade as an answer to sub-Saharan Africa’s very real and profound problems.