From domestic manufacture to Industrial Revolution: long-run growth and agricultural development

Transcription

1 # Oxford University Press 2006 Oxford Economic Papers 58 (2006), All rights reserved doi: /oep/gpl001 From domestic manufacture to Industrial Revolution: long-run growth and agricultural development By Jacob L. Weisdorf Department of Economics, University of Copenhagen, 6 Studiestraede, DK-1455 Copenhagen, Denmark; jacob.weisdorf@econ.ku.dk The classical story of industrialization always begins with agriculture: the modernization of rural institutions, involving both the enclosure of open fields and a shift from peasant farming to larger scale capitalist farming, generates a rise in agricultural productivity, which in turn fuels industrial development. An emerging view, however, turns the old story on its head, arguing that agricultural improvement is a response to urban development. This paper follows the line of this emerging view, demonstrating that productivity growth in commercial manufacture is crucial to the performance of farmers and thus to the transfer of labour from agriculture to industry. JEL classification: O14, J21, J22 1. Introduction One of the most important factors in the historical process of industrialization was the release of labour from food-generating activities. In 1500, the share of the English labour force engaged in agriculture was 74% (Allen, 2000). By 1800, that share was only 35% (Allen, 2000). Even adjusting for food imports, which by the beginning of the nineteenth century represented about one fifth of all English food consumption (Crafts, 1985a), this change in the occupational structure reflects an astonishing performance of English agriculture during that period. Not surprisingly, the standard, and indeed intuitive, story of industrialization, therefore, always begins with agriculture: the modernization of rural institutions, involving both the enclosure of open fields and a shift from peasant farming to larger scale capitalist farming, generates a rise in agricultural productivity, which in turn fuels industrial development. An emerging view, however, turns the traditional story on its head, arguing that agricultural improvement occurs in response to urban development (e.g. Hoffman, 1991; Campbell, 2000; Allen, 2003). This paper follows the line of this new view,

2 j. l. weisdorf 265 exploring a mechanism by which industry affects agriculture, and furthers industrialization. The current work is inspired by the two salient observations about the pre-industrial economy made by Boserup (1965) and others, namely that surplus labour existed in agriculture and could be allocated in a variety of ways, and that output per farmer was not limited by the state of knowledge of how to increase output, but by the fact that a higher output demanded more hours devoted to agriculture at a cost to other activities. In the current paper, the allocation of labour between food activities and non-food activities and the pattern of consumption of non-commercial manufacture versus commercial manufacture are determined endogenously, depending on agricultural terms of trade. It is demonstrated that development in commercial manufacture is crucial to the performance of farmers and thus to the transfer of labour from agriculture to industry, which prompts the process of industrialization. More specifically, the current paper shows that productivity growth in commercial manufacture improves agricultural terms of trade, i.e. increases the price that a farmer receives for a unit of food. This motivates farmers to allocate more hours to agrarian activities, a change that occurs with a cost to time spent producing domestic (i.e. non-commercial) manufacture. However, the lower consumption of domestic manufacture is compensated for by a larger consumption of commercial manufacture, which is obtained by selling the additional food produce in the market. Given an inelastic demand for food, growth in food output per farmer releases labour from agriculture, thus increasing the share of workers available for commercial manufacture. Altogether, this explains why technological breakthroughs in commercial manufacture, such as the mechanization of the English textile industry, would lead to a transfer of labour out of agriculture, with no new agricultural knowledge or technology required. In effect, the process of industrialization outlined in this paper is essentially demand-driven. It has been argued that population size, over the very long-run, constitutes a scale-effect on economic development through its influence on the emergence of new technology and knowledge (e.g. Kuznets, 1960; Boserup, 1965). In accordance with this view, a construction is proposed by which an economy s overall level of technology grows with the size of its population. Thus, if commercial manufacturers use the overall technology more efficiently than do domestic (i.e. non-commercial) manufacturers, more densely populated regions will become more industrialized than will sparsely populated regions, even though all regions will be using the same agricultural technology. This occurs because farmers in densely populated regions will spend more hours of work in their fields at a cost to time allocated to domestic manufacture. The current paper is organized as follows. After discussing the related literature in Section 1, historical evidence upon which a model is built is presented in Section 2. Section 3 presents the model, Section 4 includes an analysis, and Section 5 provides conclusions.

3 266 agricultural development 1.1 Related literature The work presented in the current paper is inspired by the historical developments in the Western world, particularly in England. This is the case as well for an extensive series of theoretical studies that also examine the long transition from economic stagnation to sustained growth associated with the Industrial Revolution, including work by Goodfriend and McDermott (1995), Galor and Weil (2000), Jones (2001), Galor and Moav (2002), Galor et al. (2002), Hansen and Prescott (2002), Lucas (2002), Tamura (2002), Lagerlöf (2003), and Weisdorf (2004). Common to most of these papers is a Malthusian building block, according to which a fixed amount of land generates decreasing returns to labour when technology is held constant. Economic growth thus reflects the interaction between new technology, demographic growth, and diminishing returns to labour. However, whereas the Malthusian model implies that productive opportunities in agriculture are fully exploited, the model in this paper, inspired by Boserup s theory about agricultural development, suggests that farmers in fact are able to expand their food production by shifting labour-resources from other activities, such as domestic manufacture or leisure time. The inclusion of Boserup s theory in long-run growth models is not entirely new. For example, Lee (1988) proposes a Boserupian construction by which greater population density encourages technical progress; Strulik (1997) employs a learning-by-doing mechanism that acts as a positive externality that, in a Boserupian manner, increases with the size of the population and helps it to overcome diminishing returns to labour; Klausen and Nestmann (2000) use Boserup s demand-driven technological change in an extension of the growth model presented in Kremer (1993); and Lagerlöf (2005) includes a Boserupian feature in which agricultural productivity progresses as a result of population pressure. All of these contributions, however, lack an important aspect of Boserup s theory concerning the labour costs associated with expanding agricultural output. One issue that is closely related to the work of Boserup concerns the role of the agricultural sector in the process of development. Whereas the new growth theory often neglects the importance of food production, development economists have long stressed that, due to an income-inelastic demand for agricultural products, improvements in agricultural productivity are a significant source of economic growth since they enable a transfer of labour from food activities into non-food activities. This issue is addressed in a body of work, mainly following in the footsteps of Jorgenson (1961, 1967), that examines the structural transformation of a dual economy (e.g. Matsuyama, 1992; Echevarria, 1997; Duranton, 1998; Laitner, 2000; Kögel and Prskawetz, 2001; Kongasmut et al., 2001; Gollin et al., 2002; Chanda and Dalgaard, 2003; Galor and Mountford, 2003). The main insight gained from these papers, most of which address the cause of the disparity in income per capita in contemporary countries, is that non-homotetic preferences,

4 j. l. weisdorf 267 with an income-elasticity of demand for agricultural goods below unity, create a positive link between improvements in agricultural productivity and economic growth. The work presented in the current paper is most closely related to the studies by Duranton (1998), Kögel and Prskawetz (2001), and Galor and Mountford (2003). Kögel and Prskawetz, who allow for increasing returns to labour in manufacturing and hold constant the share of workers employed in agriculture, demonstrate that a balanced growth path exists, upon which growth in the agricultural sector s total factor productivity will lead to economic as well as demographic growth. However, their model does not explain the declining share of workers employed in agriculture, which plays an important role in the process of industrialization. Moreover, changes in commercial manufacture do not influence farmers behaviour, as is the case in the current model. Duranton s (1998) and Galor and Mountford s (2003) studies consider the role of international trade in the process of development. Duranton addresses the puzzling question of why some countries, often those that are newly industrialized, are able to combine a low total factor productivity in agriculture with a high degree of industrialization, a condition that Duranton shows to be attributed to the mere circumstance that countries are open to trade. The current paper is capable of replicating Duranton s result, even though it considers a closed economy, because a high degree of industrialization, within our framework, is possible using a relatively inferior agricultural technology when farmers invest a relatively large amount of time in their fields. Galor and Mountford s paper illustrates how the current distribution of world population can be classified according to the different roles that international trade played in the timing of the demographic transition in agricultural as well as industrialized countries. An important feature of their work, which is comparable to the current work, is that the level of agricultural productivity is determined endogenously. In their model, the agricultural sector s total factor productivity increases with the economy s overall level of technology, which in turn is positively correlated with the population s level of human capital. Unlike the present model, however, the food output per farmer is not the result of farmers optimization behaviour. Nor is economic development achievable, within their framework, without improvements in the agricultural sector s total factor productivity, which is the case in the current model. In general, the current paper combines three important elements from the existing literature. First, the current work questions the idea that pre-industrial farmers fully utilized their productive potential in agriculture. Inspired by the thinking of Boserup (1965) and others, it is shown that when more food units per farmer come at a cost to labour, and when utility is derived from non-agrarian activities, such as domestic manufacture, a farmer may decide not to produce the highest level of food output possible, which is why productive opportunities in agriculture need not be fully exploited. Such an anti-malthusian approach is also voiced by economic historians such as Persson (1988), who argues that

5 268 agricultural development pre-industrial growth is not constrained by endowments or resources, and that economic development is achievable through specialization and division of labour. Second, the present paper endogenizes agricultural output, an approach that is in accordance with economic historians such as Hoffman (1991), Campbell (2000), and Allen (2003). Allen (2003) argues that the demand for labour in cities pushed up wages, which farmers responded to by turning to more productive technologies. Hoffman (1991) speculates that French agricultural development resulted from improvements, for example, in capital-market access, made possible by urban development. Similarly, Campbell s (2000) explanation for the low productivity of medieval English agriculture is the small size of the urban sector at that time. Third, the current work includes domestic (i.e. non-commercial) activities. Models that deal with long-run growth from a historical perspective tend to neglect the fact that in societies with an occupational structure dominated by agriculture, a significant share of the manufactured goods that are consumed by farmers are produced by the farmers themselves. This subject is examined in a number of papers, most of which are rooted in Becker s (1965) theory of time-allocation, that explore the distribution of labour in a farm household (e.g. Hymer and Resnick, 1969; Gronau, 1977; Locay, 1990; Devereux and Locay, 1992). The current paper builds upon work by Hymer and Resnick (1969), who, in a partial equilibrium analysis, investigate the role of non-agrarian activities in an agrarian economy. Comparable to their study, the analysis is extended here by incorporating the agricultural sector s activities in a general equilibrium framework. The framework is then used to show that the shift in consumption of manufactured goods, from goods produced domestically to goods produced by a commercial sector, was an important element in the historical process of industrialization. 2. The evidence Contrary to common belief, the process of industrialization was not confined to the past two centuries. In the words of Hicks (1969, p.141), [t]he Industrial Revolution is the rise of modern industry, not the rise of industry as such. In today s terms, Hicks is referring to the concept of proto-industrialisation. Mendels (1972), the author of the modern version of this concept, writes that [w]ell before the beginning of machine industry, many regions of Europe became increasingly industrialized in the sense that a growing proportion of their labor potential was allocated to industry (Mendels, 1972, p.241). Mendels statement encapsulates well the way in which this paper attempts to define an economy s degree of industrialization, namely, as its share of workers devoted to commercial manufacture. According to Engel s law, which proposes that demand for food is incomeinelastic (e.g. Crafts, 1985b), the transfer of labour out of agriculture is inseparably linked to improvements in the agricultural sector s performance. Intuitively, one would expect therefore that the historical movement of workers into commercial

6 j. l. weisdorf 269 manufacture awaited advances in the knowledge of how to increase output per farmer. One of the most striking aspects of Boserup s (1965) theory about agricultural development, however, is that agricultural productivity in the pre-industrial era was not limited by the state of knowledge of how to increase output. She convincingly argues that pre-industrial farmers were virtually always capable of increasing output by increasing the number of hours that they spent in their fields. More contemporary studies support Boserup s theory. Grantham (1999, p.212), for example, asserts that intensive cultivation during the Middle Ages demanded more labour and capital per acre of land than traditional farming, and therefore cost more per hectare, but they did not require advances in knowledge. 1 In order to increase output per acre of land, Grantham argues that fields were seeded more thickly and that farmers weeded, ploughed, harrowed, and hoed their fields more frequently and more intensively (Grantham, 1999). Clark (1987), providing evidence that output per farm worker in the northern United States and in Britain in the early nineteenth century was many times greater than it was in Eastern Europe, claims that [t]echnical progress explains little of the high American and British productivity..., nor, in the American case, does abundant land per worker. Instead, most of the differences derived from more intense labor (Clark, 1987, p.419). But did surplus labour really exist among pre-industrial farmers, and if so, what made farmers agree to the inherent decrease in other activities that would accompany a higher food output? It has been argued that systems of land use and cultivation can be understood only if considered as a part of the pattern of social organization as a whole. The pre-industrial economy is commonly thought of as being dominated by agriculture, when in fact, as pointed out by, e.g. Reynolds (2000), it is actually dominated by domestic production. Reynolds estimates that up until 1700, 80 90% of the European population lived in rural areas, on isolated farms or in small villages close to the farmland. In these rural households, Reynolds notes (2000, p.80), [e]ach family produces not only most of its own food, but most of its housing and clothing, plus a wide range of services. Commercial manufacture gains a foothold to the extent that farmers decide to expand their production of marketable foods. But from where do farmers get the labour needed to improve their agricultural performance? Based mostly on studies of developing countries, Boserup (1981) concludes that before the Industrial Revolution, agriculture was, in part because of its seasonal character, a part-time occupation. 2 She claims (Boserup, 1981, p.120) that farmers used their sparetime to produce domestic (i.e. non-commercial) manufacture for own-use consumption or, as also proposed by de Vries (1972), in leisurely activities. 1 In fact, Grantham claims that the techniques that were used to increase output per acre of land during the Middle Ages had been around since the Iron Age. 2 She notes, however, that seasonality can be overcome by shifting to other types of agrarian activities, for instance, to fodder production, and hand-feeding of animals (Boserup, 1965).

7 270 agricultural development Reynolds (2000, p.80) asserts that out of the time available to the pre-industrial rural household agricultural activities take perhaps 50 to 60% of the total, the remainder going to industrial and service activities (Reynolds quotation marks). Due to a lack of data, only a few studies have examined in depth the existence of surplus labour in pre-industrial agriculture (see, e.g. Allen, 1988; Campbell and Overton, 1991; Clark, 1991). Recently, however, a study by Karakacili (2004) provides overwhelming evidence that surplus labour was indeed present during the Middle Ages, even at a time thought to have had the lowest agrarian labour productivity rates in the pre-industrial era, namely, in the period shortly prior to the Black Death. Presuming that surplus labour did exist in pre-industrial agriculture, to what extent did farmers allocate this labour to the production of marketed goods? According to de Vries (1994), the Industrial Revolution was preceded by an industrious revolution during which a broad range of households made decisions that increased both the supply of marketed commodities and labour and the demand for goods offered in the marketplace (de Vries, 1994, p.255). If pre-industrial farmers in fact did increase the volume of marketed foodstuffs, then this should be mirrored in the share of workers employed in agriculture. Allen (2000), reporting such data for pre-industrial Europe, estimates that the proportion of England s labour force engaged in agriculture declined from 74% in 1500 to 45% in 1750 (see Table 1). This seems to indicate that, in the English case, a significant increase in output per farmer occurred in the centuries leading up to the time of the Industrial Revolution. What was it that inspired farmers to increase their food production? During the early modern era there appears to have been an overall upward movement in agricultural terms of trade, i.e. in the amount of commercial manufacture that a farmer received for a unit of food. This improvement in agricultural terms of trade may have encouraged farmers to expand their agrarian activities with the aim of increasing the amount of foodstuffs that could then be traded in exchange for commercial manufacture. Figure 1 illustrates agricultural terms of trade between 1500 and 1749, calculated using data from Agrarian History of England and Wales (Thirsk, 1985). The data reveal that in c. 1750, 210 industrial units were needed to buy the same volume Table 1 Estimated English population distribution Year Total (mio.) Agri. (mio.) Agri. (pct.) Source: Allen (2000).

8 j. l. weisdorf 271 Fig. 1. Agricultural terms of trade for England and Wales, of agricultural goods that 190 industrial units would have bought in c. 1700, 181 units would have bought in c. 1600, and 108 industrial units would have bought in c If improvements in agricultural terms of trade encouraged farmers to increase their output, then one should expect to find an inverse relationship between agricultural terms of trade and the share of workers in agriculture. Allen (2000) reports that the proportion of England s population employed in agriculture (see Table 1) declined over the years from 74% in 1500, to 69% in 1600, 55% in 1700, finally dropping to 45% by As suggested, agricultural terms of trade and the share of labour in agriculture moved in opposite directions. 4 3 The years for which Allen s (2000) data correspond with data from Agrarian History of England and Wales are indicated in Fig Note, however, that the relationship between agricultural terms of trade and the proportion of labour in agriculture is affected by changes in population level. All other things being equal, a population increase, due to diminishing returns to labour in agriculture, will dilute the effect of higher output per farmer on the shift of labour out of agriculture. According to Allen (2000), the English population increased by 76% between 1500 and 1600, but only increased by 18% between 1600 and Improvements in agricultural terms of trade, therefore, ceteris paribus, should have had a stronger impact on the transfer of labour out of agriculture in the seventeenth century than it did in the sixteenth century. This appears to have been the case: despite a relatively large increase in agricultural terms of trade between 1500 and 1600 (from 108 to 181 industrial units), only a five percentage points decline in the share of agricultural labour (from 74% to 69%) is observed. Between 1600 and 1700 agricultural terms of trade improved only slightly (from 181 to 190 industrial units). Yet, over the same period, the proportion of labour in agriculture declined by 14 percentage points (from 69% to 55%).

9 272 agricultural development Fig. 2. Agricultural terms of trade for England, A similar tendency applies to England between 1750 and Figure 2, which is based on data reported by O Brien (1985), illustrates that agricultural terms of trade more than doubled during the second half of the eighteenth century. Within the same time-frame, the proportion of England s population employed in agriculture dropped from 45 to 35% (see Table 1). 5 Overall, improvements in agricultural terms of trade seemed to go hand-in-hand with a shift of labour out of agriculture, suggesting that higher relative food prices could have encouraged farmers to increase their food output. In support of this view, Reynolds (2000, p.89) mentions that [a]s agricultural production becomes more labour-absorbing and more profitable, and as manufacturers can be purchased from outside on more favorable terms, the rural family sheds some of its goods-producing functions and passes them over to the specialized producers. Along similar lines, Boserup (1990, p.35) notes that around the time of the Industrial Revolution [s]ome family members had produced textiles and other non-agrarian products for home consumption, but when prices of such products declined steeply, home production was replaced by the purchase of industrial products. Home workers either gave more help in agriculture, or they began to work in or for the new factories. There is very little information about the allocation of farmers labour between agrarian and non-agrarian activities in the early modern era. 5 As in Fig. 1, the years for which Allen s (2000) data correspond with data from O Brien (1985) are noted in Fig. 2.

10 j. l. weisdorf 273 However, Voth (2000), who investigates the working hours in England during the Industrial Revolution, estimates that a 19% decline in the total number of workers in agriculture between 1760 and 1800 was accompanied by a 45% increase in the annual number of hours spent per person in agriculture (Voth, 2000, Table 3.34). Note that this significant increase in hours devoted to agrarian work coincides with a strong improvement in agricultural terms of trade (see Fig. 2). Since the shift of workers out of agriculture is reflected in the occupational structure, and since commercial activities are more readily detected and measured than are those performed by the household, 6 one would expect to see a negative relationship between the proportion of workers engaged in agriculture and the economy s output per capita. Figure 3, which plots the share of workers in agriculture against the (log) GNP per capita in 134 contemporary countries, 7 clearly indicates that countries that employ a relatively small proportion of workers in agriculture also enjoy a relatively high standard of living, consistent with the idea that economic growth is strongly linked to the shift of workers out of agriculture. The evidence presented in this section suggests that a shift in the farm household s consumption of manufactured goods, from goods produced domestically (i.e. non-commercial goods) to similar goods produced by the commercial sector, represents an important component in the historical process of industrialization. Moreover, it appears that the shift in the demand for manufactured goods was accompanied by an increase in output per farmer, which could have resulted from an increase in the number of hours that farmers spent in their fields, without new agricultural knowledge or technology required. In the following, a simple model that supports this evidence is presented. The model is then used to clarify the underlying factors that could have prompted the process of industrialization. 3. The model Consider a three-sector, one-period, non-overlapping generations model that includes the production and consumption of food as well as manufactured goods. Food is produced by an agricultural sector. Manufactured goods are produced by a domestic (i.e. non-commercial) sector (for self-supply only) as well as by a commercial sector (including the putting-out system associated with proto-industrialization as well as factories). The economy consists of N identical individuals, out of which the share s 2 (0, 1] is engaged in agriculture. Residually, the share 1 s is engaged in commercial manufacture. The size of s is determined endogenously below. 6 See Devereux and Locay (1992) for a discussion. 7 The data are derived from World Bank (1999, Tables 1.1 and 1.15). There were 148 countries in the data set, but 14 of these are not presented here due to missing observations.

11 274 agricultural development Fig. 3. GNP per capita versus the share of workers in agriculture, 1997 Each individual is endowed with l units of time. As apparent below, this timeendowment is divided between domestic manufacture, on the one hand, and food production or commercial manufacture, depending on the individual s occupation, on the other. 3.1 Food production It is assumed that food production has constant returns to land and labour. Throughout the paper, we suppress the use of capital; this is not an uncommon simplification in growth models that investigate pre-industrial development (see, e.g. Kögel and Prskawetz, 2001). 8 8 The inclusion of capital goods will hardly affect the qualitative results of the model.

12 j. l. weisdorf 275 There is a fixed total amount of farmland of X units. For convenience, we assume there are no property rights over the land, and that land is divided equally among farmers. 9 With N the size of the total labour force and s the share hereof engaged in agriculture, each farmer, when X is normalized to 1, thus receives x ¼ 1/sN units of farmland. With constant returns to land and labour, the output per farmer (superscript A for agrarian goods) is y A ¼ A l x 1 ; 2 ð0; 1Þ; ð1þ where l is the number of hours that a farmer spends producing food, x measures the units of farmland disposable to the farmer, and A is the total factor productivity in agriculture. It follows that y A is a measure of a farmer s income, expressed in terms of food. Note that, through variations in agrarian work hours l, a farmer, at least to a certain extent, is capable of controlling the food output. It follows from equation (1) that the economy s total food output can be written as Y A ¼ y A sn ¼ A ðlsnþ X 1 A ðlsnþ ; X 1: ð2þ Both the share of workers that are employed in agriculture, s, and the number of hours that a farmer spends producing food, l, are determined below. 3.2 Preferences In accordance with Crafts (1985b), we assume that the demand for food, unlike other goods we consider, is income-inelastic. More specifically, we assume that a units of foodstuffs are required per individual in order to ensure the individual s survival. 10 Suppose that having consumed the a units of food that are required for survival, the individual then derives utility from the consumption of 9 Introducing a class of land-owners who rent land to peasants or hire them to cultivate the land is unlikely to affect the qualitative results of the model; however, such a construction severely complicates matters. 10 Note that assuming a negative price elasticity strengthens the quantitative results of the model: if individual food demand goes down when food prices go up, then the higher the price of food is, all other things being equal, the more people a farmer is capable of supporting. A positive income elasticity, however, works in the opposite direction: if individual food demand increases with income, then the higher the income level is, ceteris paribus, the fewer people a farmer is capable of supporting. Whether a positive income elasticity will affect the quantitative nature of the model s results thus depends on the size of the income elasticity: the smaller the income elasticity, the more likely it is that the model s results hold true.

13 276 agricultural development manufactured goods. 11 There are two types of manufactured goods: a commercial type (denoted c) and a home-made or domestic type (denoted d). Domestic manufacture is produced by the individual in his or her spare-time for selfsupply only. Commercial manufacture is produced by the share of the labour force, 1 s, that is employed in commercial manufacture, henceforth denoted as, manufacturers. Domestic and commercial goods are considered to be perfect substitutes. The representative utility function can thus be written as uc; ð dþ ¼ c þ d c þ d; 1; ð3þ with being the subjective value of domestic relative to commercial manufacture. The parameter is assumed to be the same for all individuals. For convenience, is set to one. Note that the consumption of the a units of food that an individual needs in order to subsist does not provide any utility but is necessary for survival Food market clearing With N individuals who each demand a units of food, the food market equilibrium condition implies that total demand, an, equals total supply, Y A, described in eq. (2). From the food market equilibrium condition it follows that the share of workers required in agriculture to satisfy the economy s total food needs is s ¼ 1= an1 1 A l : According to eq. (4), the proportion of agricultural workers, s, increases with the size (or, since land is fixed, the density) of the economy s population, N, and decreases with the level of the total factor productivity in agriculture, A. For the story that we are going to tell here, however, the most important observation is that the proportion of workers engaged in agriculture, s, decreases with the time that a farmer decides to allocate to agrarian activities, measured by the variable l. 3.3 Manufacturing There are two types of technologies available for producing manufactured goods: domestic technology (denoted D) and commercial technology (denoted C). Both are assumed to exhibit constant returns to labour, which implicitly means that land ð4þ 11 A similar construction is found in Kögel and Prskawetz (2001). It is possible, but severely complicates matters, to have food consumption entering the utility function such that, once a given amount of food has been consumed, individuals care about food as well as manufactured goods.

14 j. l. weisdorf 277 used for the purpose of manufacturing is not constrained. The total output in sector i 2 {D, C} is thus Y i ¼ i L; ð5þ where L is labour and i is the level of productivity in sector i ¼ {D, C}. In the following, it is assumed that the relationship between the levels of productivity in the two manufacturing sectors can be written as C ¼ ð1 þ FÞ D ; F40; ð6þ where the parameter F, which we assume is greater than zero, measures the degree to which the commercial sector s productivity exceeds that of the domestic sector. 3.4 Occupation, income, and consumption Each individual chooses between becoming a farmer or a manufacturer. For convenience, we assume that once the occupational decision is made, then manufacturers do not have access to farmland and farmers do not have access to commercial manufacture technology Manufacturers income and consumption A manufacturer s income consists of the wage earned in the commercial sector, which is C times the number of hours worked. Since a manufacturer has access to commercial technology, which we have assumed is more productive than domestic technology (i.e. C 4 D ), a manufacturer will not produce any domestic manufacture at all; hence, the entire time-endowment is spent producing commercial manufacture. 13 A share of the income that a manufacturer generates at work is spent on the a units of food that are needed in order to subsist. Since utility is derived from the consumption of manufactured goods, once food needs are fulfilled, the remaining income is spent on commercial manufacture. The amount of commercial manufacture that a manufacturer consumes is thus C l pa, where p denotes the price of food in terms of commercial manufacture, i.e. agricultural 12 The reason for this could be that the production of commercial manufacture takes place in urban areas that farmers are unable to reach in their spare time. The same would be true for manufacturers, mutatis mutandis. It could also be that the use of commercial technology requires certain, nonexplicated educational skills that farmers do not have time to obtain. Or it could be that commercial technology requires the use on a daily basis, which farmers, due to their agrarian obligations, are prevented from obtaining. 13 Allowing for diminishing returns to labour in manufacturing there could be circumstances under which manufacturers would produce and consume domestic as well as commercial manufacture. Introducing such a modification, besides complicating the model, will not affect its qualitative results.

15 278 agricultural development terms of trade. Since a manufacturer does not engage in domestic manufacture, the amount of domestic manufacture consumed by a manufacturer is zero Farmers income and consumption A farmer s income consists of the value of the food surplus. The food surplus is the difference between the farmer s food output, y A, and the number of food units required for the farmer s survival, a. The price that a farmer receives, measured in terms of commercial manufacture, is p per unit of food. Given that y A 4a, a farmer consumes an amount of commercial manufacture equal to p(y A a). Since farmers do not have access to commercial technology, a farmer will spend time left-over after agrarian activities, l l, producing and consuming an amount of domestic manufacture equal to D ( l l) Labour market clearing Given free labour mobility, which we assume, indifference between becoming a farmer or a manufacturer implies that the same level of welfare is achieved, regardless of the choice of occupation. Equilibrium in the labour market thus implies that the price of food in terms of commercial manufacture, i.e. agricultural terms of trade, adjusts such that all workers receive an identical level of utility. The labour market equilibrium condition therefore implies that p ¼ D Fl þ l A l x 1 : ð7þ According to eq. (7), p increases with the degree to which the level of productivity in commercial manufacture exceeds that of domestic manufacture, measured by the variable F (see eq. (6)). On the other hand, p decreases to the extent that the agricultural sector s total factor productivity, A, increases. 3.5 Optimization In the following, a farmer s optimal allocation of labour between agrarian and non-agrarian activities is identified. A farmer chooses agrarian work hours, l, such as to maximize utility. Inserting the amount of domestic as well as commercial manufacture that a farmer consumes, together with the food production function, eq. (1), into the utility function, eq. (3), a farmer s optimization problem can be written as max l u ¼ c þ d ¼ p A l x 1 a þ D l l ; ð8þ subject to the time-budget constraint that requires that l 4 l. 14 Note that if the value of the informal economy s output, i.e. the domestic manufacture, is not taken into account, then the current paper s theory implies that the wage of a manufacturer exceeds that of a farmer. In other words, urban wages tend to be greater then rural wages.

16 An interior solution to the maximization problem implies that j. l. weisdorf 279 p A x 1 ¼ D : l ð9þ The left-hand side is the marginal utility that a farmer gains from devoting more hours to agrarian work. This stems from an increase in the income made from selling a larger food surplus, and thus an increase in consumption of commercial manufacture. The right-hand side is the marginal utility forgone from devoting more hours to agrarian work, which is due to a decline in consumption of domestic manufacture. Note that an increase in agricultural terms of trade, measured by p, enhances the marginal utility obtained from increasing agrarian work hours, l. 4. Analysis We now turn to the general equilibrium condition, which is used to identify the share of workers required in agriculture, denoted s. This enables us to analyse how the degree of industrialization, measured as 1 s, is affected by changes in productivity levels in the various sectors as well as by changes in demographic factors. 4.1 General equilibrium The general equilibrium condition is found by combining the food and labour market equilibrium conditions, eqs (4) and (7), with the solution to the farmer s optimization problem, eq. (9). It follows that the share of workers required in agriculture, in general equilibrium, is s ¼ 1 an 1 1= 1 A Fl : 4.2 Productivity changes In the following, we examine how changes in levels of productivity in each of the three sectors affect the process of industrialization, measured in terms of labour leaving agriculture. The following proposition summarises the results. Proposition 1 The model predicts that: (i) an increase in the agricultural sector s total factor productivity, A, reduces the share of workers needed in agriculture, s; and that (ii) an increase in productivity in commercial manufacture, C, relative to that in domestic manufacture, D that is, an increase in F reduces the share of workers needed in agriculture, s. ð10þ

17 280 agricultural development Proposition 1 follows trivially from the general equilibrium condition, eq. (10). According to the proposition, new knowledge or technology that improves the agricultural sector s total factor productivity will generate a transfer of labour from agriculture to industry. This result captures the traditional story, wellknown from the existing literature, that industrialization begins with changes in agriculture. More importantly, the model also shows that new knowledge or technology that improves productivity in commercial (relative to domestic) manufacture will generate a transfer of labour from agriculture to industry. The reason for this is that productivity growth in commercial manufacture improves agricultural terms of trade. Better terms of trade motivate farmers to allocate more hours to agrarian activities, thus expanding the size of their food surpluses and releasing labour from agriculture. Accordingly, the model shows that a transfer of labour out of agriculture can result from new technology being introduced into commercial manufacture, even in the absence of new agricultural technology. Events such as the mechanization of the English textile industry, therefore, may have prompted the process of industrialization in terms of workers leaving agriculture Demographic changes One of the most salient features of the early modern era, and one that most likely affected the process of industrialization, is the enormous increase in population. According to Allen (2000), the English population more than trebled over the three centuries from 1500 to 1800 (see Table 1). For scholars such as Boserup, a key determinant in the process of development is the pressure of an increasing population. How does population pressure affect industrialization in the current model? It follows trivially from eq. (10) that, in equilibrium, Proposition 2 An increase in the size of the population, N, increases the share of workers needed in agriculture, s. According to Proposition 2, a larger population makes it increasingly difficult (due to diminishing returns to labour in agriculture combined with constant returns to labour in manufacturing) for an economy to become industrialized. This result seems to contradict the pre-industrial evidence: despite the vast increase in population (see Table 1), the share of the English labour force devoted to agriculture steadily declined between 1500 and In fact, all factors that expand the commercial sector, such as the impact of international trade, will have a similar effect on the proportion of workers in agriculture (I thank an anonymous referee for pointing this out).

18 j. l. weisdorf Population and technology Over the years, an increasing number of studies that examine long-run growth and development have argued that diminishing returns to labour are neutralized, or even reversed, due to the fact that an increasing population positively affects the emergence of new knowledge or technology. This idea originates with scholars such as Kuznets (1960), who argues that a larger population contains more potential inventors; with Smith (1776), who attributes the adoption of more productive technologies to the impetus of increasing specialization and division of labour; and, not least, with Boserup (1965), who hypothesises that the increasingly intensive land-use that follows from the pressure of an increasing population leads to a drop in labour productivity, following which, methods that raise productivity, such as ploughing and fertilization, would be developed. A contribution by Kremer (1993) provides a number of empirical tests that support the prediction that pre-industrial societies with relatively large populations also enjoyed relatively fast technological growth. More recently, Alcalà and Ciccone (2001) report that the size of the labour force in contemporary countries positively influences labour efficiency. The current framework can easily be extended so as to capture this idea. In line with the construction in Galor and Mountford s (2003) paper discussed earlier, the current paper proposes an extension by which we allow the size of the population to positively influence not only the agricultural sector s total factor productivity, as proposed by Boserup, but the level of productivity in all of the three of sectors. It is then demonstrated that even if an increasing population has on effect agricultural productivity, the model is still able to explain the transfer of workers from agriculture to industry, due to the effect that a larger population has on productivity in manufacturing. Jones (1998), among others, argues for a model in which the growth rate and, therefore, the level of technology can be linked to the size of the population. 16 Here, a slightly modified version of Jones approach is used. It is assumed that the economy has an overall level of technology, denoted, which increases with the size of the population, N, such that ¼ N ; 2 ð0; 1Þ;4N : ð11þ Note that 2 (0, 1) implies that there are diminishing returns to labour in the creation of new technology. Note that the requirement that 4N is equivalent to the assumption F40 made on page Jones proposes a construction where the economy s stock of knowledge, measured by a variable A, grows according to the rule A t ¼ L t, where is the number of new ideas that each person, of which there are L, discovers per unit of time. This, in discrete time, means that A tþ1 ¼ L t þ A t, and is why the level of technology is positively correlated with the size of the population. 17 In Jones (1998) model, new technology occurs even in the absence of population growth. In the current model, the level of technology that is available, represented by the variable, increases only to the extent that there is an increase in the size of the population.

19 282 agricultural development What s more, the current model, unlike that of Jones, implies that a decline in the size of the population will actually result in a reduction in the level of technology that is available to the economy. The relationship between population and technology promoted here, therefore, is somewhat similar to what Smith (1776) proposes: more people utilize more productivity technologies due to the economies of scale that arise from specialization and division of labour. Thus, the current framework, in contrast to the frameworks in the existing literature, is able to explain why major demographic catastrophes, such as the Black Death, which killed one-third of Europe s population during the fourteenth century, lead to a contraction of economic activity (see, e.g. Maddison, 2001). The idea that the level of technology in a historical perspective regresses as a result of a reduction in population density is well documented by Aiyar and Dalgaard (2002). Next, inspired by the model proposed by Galor and Mountford (2003), we assume that the overall level of technology,, affects the level of productivity in all three of the sectors. 18 However, the intensity with which each of the three sectors uses the overall level of technology is not necessarily the same. More specifically, suppose that i ¼ i ; i 2 ½0; 1Þ; i ¼ fa; D; Cg; ð12þ where i is the intensity with which the overall technology is used in sector i ¼ {A, D, C}. We then propose the following result that emerges from inserting eqs (6), (11), and (12) into (10) and then differentiating with respect to N. Proposition 3 If (i) A 4(1 )/" and C 4 D, with i being independent of N for i 2 {D, C}, or if (ii) A ¼ 0 and C 4(1 )/" þ D 5 (1 )/", then an increase in the size of the population, N, reduces the share of labour needed in agriculture, s. Proposition 3 states that if the overall technology influences total factor productivity only in the agricultural sector, and if the effect hereupon of an increase in the size of the population is sufficiently strong, then a larger population will stimulate the process of industrialization. 19 Although improvements in the agricultural sector s total factor productivity are known to have occurred throughout the pre-industrial era, this need not be the only factor that caused workers to be shifted from agriculture to industry. For reasons that were expounded above, improvements in commercial manufacture, through an increase in the number of hours that a farmer devotes to agrarian activities, might also have fuelled the process of industrialization. 18 In Galor and Mountford s (2003) model, the level of technology is positively influenced by labour s skill intensity (i.e. individual human capital) and by the level of technology in the previous period. 19 For a stylized representation that also captures this result, see Crafts (1985a, pp ). Crafts model, however, comprises a one-sector framework, which only includes agricultural production.

20 j. l. weisdorf 283 Suppose, therefore, that the overall technology has no effect on total factor productivity in agriculture (i.e. A ¼ 0), and that it only affects productivity in the manufacturing sectors. Then, provided that commercial manufacture uses the overall technology more efficiently than does domestic manufacture (i.e. C 4 D ), this means that an increase in the size of the population will stimulate the process of industrialization, despite a lack of new agricultural technology. 20 Implicitly, the second part of Proposition 3 thus indicates that variations in occupation structures across countries or regions, for example, at the time of the Industrial Revolution, could have resulted from technology differences in commercial manufacture rather than differences in agricultural technology. This would imply that the farm households in more densely populated regions would have been spending relatively more hours of work in the fields. 5. Conclusion This paper investigates the process of industrialization with specific focus on the macro impact of the farm household s decisions concerning its allocation of labour between agrarian and non-agrarian activities. The work is inspired by the two important observations about the pre-industrial economy made by Boserup (1965) and others, namely, that surplus labour existed in agriculture and could have been allocated in a variety of ways, and that agricultural output was limited, not by the state of knowledge about how to increase production, but by the fact that more output came at a cost to labour. The main conclusion of this paper is that productivity improvements in commercial manufacture, through changes in agricultural terms of trade, make a farmer increase agricultural output by mobilizing labour-resources from other activities such as domestic manufacture. The growth in the farmer s food output expands the amount of foodstuffs that is traded in the market, and thus transfers labour out of agriculture. In effect, the process of industrialization described in this paper is demanddriven. Productivity improvements in commercial manufacture make farmers substitute manufactured goods produced domestically for manufactured goods produced by a commercial sector. The model therefore explains why technological breakthroughs in commercial manufacture, such as the mechanization of the English textile industry, would have increased output per farmer and transferred workers from agriculture to industry, even in the absence of technological breakthroughs in agriculture. By assuming a positive association between the level of technology and the size of population, it is also shown that (i) more densely populated regions will be more 20 Other combinations than those proposed in Proposition 3 for example, when the overall level of technology influences the level of technology in all of the three sectors may also give rise to an increasing degree of industrialization.