Uf(?_ 8C>0q THE WORLD BANK DEVELOPMENT ECONOMICS DEPARTMENT URBAN AND REGIONAL ECONOMICS DIVISION URBAN AND REGIONAL REPORT No. 80-4 THE EFFECT OF POPULATION GROWTH, THE PATTERN OF DEMAND AND OF TECHNOLOGY ON THE PROCESS OF URBANIZATION RAKESH MOHAN March 1980 These materials are for internal use only and are circulated to stimulate discussion and critical comment. Views are those of the author and should not be interpreted as reflecting the views of the World Bank. References in publications to Reports should be cleared with the author to protect the tentative character of these papers. PREFACE This paper has resulted from work originally done for my Ph.D dissertation at Princeton Uni7ersity (Mohan, 1977). I wish to thank my advisors Edwin S. Mills and Sherman Robinson for helpful guidance, Kemal Dervis who provided useful comments. Financial support for this research was provided from a grant to the Princeton University Economics Department from the Sloan Foundation and from the Income Distribution Project of the Research Program in Development Studies at Princeton. ABSTRACT This paper uses a non-linear, three sector, two region wage and price endogenous dynamic general equilibrium model to study the effect of population growth, the pattern of demand and of technological change on urbanization in the context of a low income developing country starting at a low level of urbanization. The model represents a closed economy and is therefore more suited to a large country. It is validated on Indian data and traces its development path well from 1950 to the present. The sectors modelled are agriculture, industry and services with the latter two being located e:clusively in urban areas. The three sectors are linked with an input output matrix which subsumes transportation costs in- curred between urban and rural areas. The model is designed to investigate long term changes, e.g. over a thirty year period and factor mobility is therefore assumed to be "almost perfect." The model demonstrates that rapid agricultural productivity growth, high rates of investment and Engel demand effects combine to produce a continuing increase of.urbanization as development occurs in an economy. The rate of urbanization is not necessarily dependent on high overall population growth: indeed, under certain conditions., a lowering of overall population growth might speed up the rate of urbanization. The pattern of demand and changes in the pattern can affect the rate of urbanization significantly: in particular, Engel type demand changes serve to make the process of urbanization logistic. Technological bias effects are not very strong but effective appropriate technology policies might speed up urbanization. I. INTRODUCTION: URBANIZATION IN THE CONTEXT OF DEVELOPMENT It is now a commonplace observation that cities in poor countries have grown at unprecedentedly high rates in the past two or three decades. Some cities have grown from a population of less than a million people in 1950 to about four million now. The provision of essential services * like water, sewage, sanitation, roads and electricity for a city growing by six or seven percent a year is no mean task. It is not surprising then that many policy makers view the phenomenon of urbanization with a great deal of trepidation. Policies and measures to contain urbanization then result: as for example, the city of Jakarta was declared closed in 1970, and a system of residence permits introduced to keep people from migrating into the city. Other countries have tried less drastic measures like encouraging investment in preferred areas and restricting it in large cities. Such policies have been put into effect without a clear understanding of the process of urbanization. We still do not have a very good idea of the structural causes of urbanization: economists have yet to develop specific ideas on what makes particular economic activities characteristically urban. The phenomenon is usually seen in a short term context and only partial explanations are generally offerred. For example, rural/urban migration is explained by the existence of a rural/urban wage gap; or by "push" from the country-side related to the pattern of land holdings; or by "pull" from the cities related to employment opportunities, bright lights, amenities of living, etc. A proper.understanding of urbanization should, however be attempted in a long term context. What are the underlying structural cuases which create. -2- these wage differentials? Why are fewer people required in farm employment as development occurs through time? What happens to the structure of demand which shifts the composition of goods.produced to induce more urban type activities? Before proceeding further, a distinction must be drawn between the growth of large cities and that of urbanization as a whole. Much of the present concern is focused on the problems arising from the rapid growth of large cities. This study, however, is not concerned with these problems and views urbanization merely as the shift of people from rural to urban areas in general. The level of urbanization is then the proportion of urban population in total po?ulation. Its rate of growth is the growth of this proportion. The growth rate of urban population then indicates the growth of urbanization only when it is greater than overall population growth. What is sought to be studied here therefore is the long-term process in which there is a shift of people from rural habitation to urban habitation and the structural causes thereof. An adequate study of urbanization needs to look at the structure of production, the patterns of demand for different commodities in urban and rural areas and how these interact inthe context of changing incomes and technology. I attempt to do this by developing a dynamic general equilibrium model for a large, poor developing country which is calibrated on the post independence Indian experience. It is only an "attempt" since the model is imperfect in that it places all industrial and service activities in urban areas and only agriculture-related activities in rural. areas. This is obviously not strictly true but it does capture the essence of urban and rural activities. -3- Urbanization has long been associated with industrialization: indeed they have been considered synonymous. However, cities have existed for a long time while industry has not. Many cities evolved originally as market or trading centers which was necessary for product markets to expand and consequently for economic growth. Thus cities have traditionally been more known for their "service" sector activities than for industry. Manufacturing activities in cities are of a relatively recent.vintage but these have been more associated with urbanization in the last two centuries because of the prominence of the industrial revolution and all its visible fruits. Indeed, in the development of Western countries, rapid urbanization coincided with rapid industrialization while in the early periods the proportion of employment in the urban service sector usually declined. The situation is now turning full circle: services now employ a larger proportion of people than industry in the richest countries and this proportion is still tending to increase. In less developed countries, services have tended to expand as fast as industry so that the process of urbanization is .a movement of people to both industry and seivices from agricultural activities. The essential ingredient for this to be possible--both in the early stages of Western urbanization and current LDC urbanization--is a consistent increase in agricultural productivity. What is somewhat different for developing countries now is that as latecomers to the development process the labour productivity in industry is also very high. It is only the service sector that lags in productivity changes and therefore employs -4- much of the.incremental urban labour. It is essential, therefore, that models of development and urbanization explicitly take account of the service sector: a sector neglected in most of the dual economy development models. It is this neglect of the service sector and the association of urbanization with industrialization (percent of labor force in industry or share of industrial product) that set off the debate started by Hoselitz (1957). He asserted that many LDCs are currently "over-urbanized" since they have smaller proportions of labor force in industry than was the case in European countries in the last century when they.were at similar levels of urbanization. In so doing, Hoselitz implicitly asserted a linear relationship between the levels of industrialization and urbanization. The other consequence of his assertion was that current urbanization is being caused more by rural push rather than urban pull. Sovani (1962) and Kamerschen (1969) have both questioned this implication and have found little correlation between levels of urbanization and indices of rural push. In refuting his over-urbanization thesis, they separately find that the levels of urbanization and industrialization ae more closely correlated in LDCs now and in rich countries in the last century, than in rich countries now. These studies have been valuable in providing some insights into the ielated phenomena of economic development, industrialization and urbanization but the basic assumptions of their methodology need to be questioned. Urbanization is essentially a dynamic phenomenon. This, if there is a connection between industrialization, development and urbanization, it should ideally be studied in a dynamic framework within the context of -5- one system.. Doing a cross-country analysis -- as was done by Hoselitz (1957) and Davis and Golden (1954) -- involves the assumption that the current cross-section of different levels of development replicates the historical process of the system under investigation. An associated problem with such cross-section analysis is that political entities, i.e. nation-states are usually taken as the appropriate data points. Thus a country as large as India is one data point as is a country as small as Kuwait. The implicit assumption is then that nation states form self- contained economic geographical systems. This may not be.the case at all except in large systems such as Brazil, the United States, Russia, China and India. Such analysis would be improved if attempts were made to group together certain sets of geographically contiguous countries which can then more reasonably be regarded as self-contained systems. A third problem with cross-section analysis is that linear relations of some kind are usually posited -- particularly if linear regression analysis is used. If, however, (a) the relationship between industrialization and urbanization is non-linear,and (b) the trend of urbanization in a system is non-linear, e.g. logistic, linear analysis clearly gives misleading results. Since there is a logical limit (100 percent) to the level of urbanization, its trend of growth is likely to be asymptotic and probably logistic like many other growth series (Price, 1975). If this is the case, it is not surprising that Kamerschen finds that the level of correlation between industrialization and urbanization is low for rich countries now. The fourth problem is a consequence of the assumption that the historical process can be captured by observing co-existing different levels now. This implies that the process undergone in the last century was similar -6- to that now.. That this may be erroneous and that the current LDC experience is quite different, needs some elaboration. A primary factor is that the overall population growth rate is much higher than ever before. The growth rate of cities is high without migration. Technical change in agriculture which raises farm productivity has to provide for the growing rural population in addition to the burgeoning urban population. In times when overall population growth rates were less than 0.5 percent, a 3 percent growth in agricultural productivity was tremendous. The second major difference from the European experience is the coexistence of high and low technology in LDC cities. High population growth and technological growth makes it possible to have cities with a multimillion population at low levels of income. This was just not possible in the last century. The sewage disposal, water supply and transport problems of a city of 8 million are qualitatively different from those of a city of half a million, which was the size of major Westera cities at similar income levels. The third major difference may be the decline in relative prices of transportation and communication. There are, therefore, reasonable a priori expectations that the current urbanization experience of LDCs may well be different from the historical European experience. Th,. foregoing is , an attempt to show that cross-section cross- country analyses of urbanization though valuable in themselves are not likely to yield the causes of urbanization. The contention of this study is that explanations of long-term trends of urbanization and of its relationship with economic development and industrialization will more likely be found if the performance of a system is studied over time. The ideal way of doing this would be: -7- i) to catalogue the different sets of activities which take place in urban and rural areas; ii) to investigate if there are underlying differences in the conduct of these activities. One example of "underlying differences" is the existence of different production functions in urban and rural areas; iii) to indentify the above differences and model the production structure of each area; iv) to model the demand side of the economy and devise methods for-achieving a static equilibrium (or rules for existence of disequilibrium); v) to model the growth of the economy, i.e. find rules for invest- ment, population growth, etc.; vi) simulate the system thus created and investigate the effects of different assumptions on urbanization. The implications of such a scheme need to be spelled out: 1/ (a) Urbanization is being regarded as primarily an economic process; (b) -it is being seen as an integral part of the development process. Thus the process of urbanization is seen as a result of the interaction of a set of complex forces in a general equilibrium (or general disequilibrium) framework. The causes of urbanization being sought are therefore not regarded as being simple. The answer is expected tobe of the type:,A, B, C, D, E, etc. interact together in certain constellations to produce an X level of urbanization; rather than A produces X (e.g., rural pressures produces urbanization). (c) While the schema may be general enough to be applied to different systems, it is not expected that.specific levels of appropriate urbanization can be prescribed for each level of industrialization or development. There can, however, be notions of appropriate levels within the context of specific systems. 1/ See B. J. L. Berry (1973) for non-economic reasons for existence of cities in pre-industrial times. -8- In the schema given above, (i) and (ii) are the most difficult since'they involve the interaction of spatial and production theory. In this study, it is assumed that industrial and service activities are exclusively based in urban areas and agricultural activities in rural areas. Each activity has a different production function in accordance with (iii) above, so a sharp distinction is made between the patterns of urban and rural production activities. The result of such an exercise can be summarized as follows: An increase in agricultural productivity contributes to increases in per capita income. In general, income elasticities of demand are different for different goods, being low for agricultural goods and high for industrial and service goods, i.e., high for urban type goods. Surprisingly, in periods of rapid urbanization, the rate df technical change of productivity change in agficulture is usually found to be higher than in industry and services; that for services usually being the lowest. Thus the process of urbanization is one that results from a number of factors that operate simultaneously. As an economy grows from low incomes, the proportion of income necessary to buy food declined and thus demand is created for non-food goods. Technical change in agriculture permits labor to be released to work in urban pursuits. The lack of technical change or productivity growth in agriculture would slow down the rate of urbanization. It is a moot question to say which comes first: income growth, technical change or urbanization. What is important to understand is that they happen simultaneously, one reinforcing the other. Rapid population growth is not -9- necessary for rapid urbanization. It is a popular misconception that high population growth rates induce urbanization, though high urban population growth rates are obviously affected by high population growth. Indeed, the rate of growth of urbanization can increase with zero population growth if there is accompanying technical change in agriculture and incomes are rising. Moreover, the provision of some urban services which may be perceived as required for urban living may themselves induce a higher rate of urbanization and a higher rate of income growth. It is a characteristic of recent development experience that urban capital-labor ratios are considerably higher than those in rural areas; thus high rates of investment are necessary for 'rapid urbanization. The increase in urban labor demand at later stages, as stated earlier, is more because of service demand than industrial demand as the rate of productivity growth is characteristically low in the service sector. The difference in capital labor ratios between the urban and rural sectors is much larger now, that is for "development latecomers", than it was for the currently rich countries in their early stages of development. Thus the labor-using technology in agriculture and capital-using technology in urban areas has had the effect of slowing down.urbanization in LGDCs. If technology policy in these countries succeeds in introducing the adoption of "appropriate" technology, the rate of urbanization may well increase. Furthermore, if such policies attract more labor into the industrial sector, there would be a concomitant increase in demand for labor from the service sector. However, the importance of these technological bias effects is usually exaggerated and their impact on the rate of urbanization is at best secondary. - 10 - II. A SUMMARY DESCRIPTION OF THE MODEL The model used in this paper was designed to study the long term process of development and structural change which can occur in a large relatively closed economy starting from very low levels of income using India,as the model economy. A study of urbanization is therefore a by- product of this model. This section gives a brief description of the model (hereafter called DYNURB) and its validation of Indian data.-/ DYNURB is a non-linear, three-sector, two-region, wage and price endogenous dynamic general equilibrium model. The three sectors are agriculture, industry and services, with agriculture being exclusively based in rural areas and the other two exclusively in urban areas. Consumption of all three goods takes place in both regions and capital and labour are'mobile between sectors and regions. Transportation is an intermediate good which is used whenever goods are transferred across regions. The special features of the model include the specification of transportation and that of a service sector. Particular attention is paid to the specification of technical change which is seen as primarily capital and labour augmenting. The model also allows for completely exogenous (or "manna-.from heaven" type) technical change. The model neglects international trade and can therefore be seen to depict a large economy in which trade is unimportant. The model in its present form is designed to reflect the Indian economy*in particular over a 30-year period starting in 1951, i.e., the 1/ Fora detailed description of the development, solution and validation of the model see Mohan (1977). - 11 - period after Indian independence. It is therefore seen as a long term model. The model solves recursively over time -- it finds an equilibrium for a period, then grows, and then again for the next period. Such a process may be characterized as "lurching equilibrum" as aptly expressed (though in a slightly different sense) by Adelman-Robinson (1978). It is recognized-that this does not reflect reality where the adjustment process takes time and capital and labor are not perfectly mobile. The justification for ignoring this is that in a long-term context, factors may be regarded as more mobile. Thus the model is wrdng in that it finds an equilibrium for every period but is probably not too misleading in showing trends over an extended period of time. DYNURB bears the most resemblance to the work of Kelley, Williamson and Cheethfam (1972), Keliey and Williamson (1974) and is also related to Yamaguchi (1973), on the one hand and in its computation and modelling philosophy to Johansen (1974), Adelman and Robinson (1978), Dervis (1973) and Fakhruddin Ahmed (1974). Table 1 gives the mathematical specification of DYNURB. The key features to note are: Production: All three sectors--agriculture, industry, services--- have constant elasticity of substitution production functions. The agriculture production function has four factors: land, livestock, capital and labour. Capital and labour "combine in a C.E.S.. technology" to generate and index which is then combined with land and livestock in a Cobb-Douglas technology. Thus a C.E.S. function is nested in a Cobb-Douglas production function for agriculture. The value added production structure has an underlying inter-industry input-output structure for intermediate goods. 1/ Sector 1, the agriculture sector, includes agriculture, forestry and logging, fishing. Sector 2, the industry sector, includes mining manufacturing, construction, utilities, transport and communication. Sector 3, the service sector, includes wholesale and retail trade, hotels and restaurants, banking and insurance, real estate, public administration and defense. Table 1: SPECIFICATION OF DYNURB 4. Interregional Wage and Rental Structure A. The Static Model (time subscripts oitted) 2,3 1. Sectoral Production Functione (CES) Agriculture LMALPH LVSTKGAM BET R +R1 (4 equations) Industry Q2 2 T25. Savings YLABi yiWili i 1,2,3 Services Q3 QT3 YCAP X1R1 + RENT * LAND + RLVSTK * LVSTK ai-1 i1 at Q Y -B -1,2.31 QTi B xi X a + (1- iLil YaAPa iRK i 2,3 (income from labor and capital) (n equations) YSAVE - SLABi YABi + SCAP *YCAP i - 1,2,3 2. Net Price Equations (income savedY (3n equations) 6. Demand System it 11 j ji i1,2,3 YCONSi . (1-SLAB). YLABi + (1-SCAPi) * YCAPi i - 1,2;3 (n equation) 3. Factor Demand (Return - Marginal Product) (disposable income) aq. POP i1 1,2,3 i Wages: Wi i i1 1,2.3 i WPRi D YCONS - I kj kMI k * POP Capital Rentals Ri P ii BK 1 . (demand for good i in sector j) i - 1,2,31; j 1.2,3 Q Price Equation,s Land: RENT P P LAND P12 pi3 i = 1,2,3 LVSTK: RLVSTK P11 LVSTK (2n + 2 equations) P12 P 11 (1 + a1) ; P (1 + a ) i - 2,3 1/ These equations are actually somewhat different in the model because a (n + n2 equations) transport input-output coefficient, , has also been included, B. Dynamic Equations 7. Investment Demand 1. Technical Change 3 DINV - YSAVEL (1 equation) 22 i-1 yi,t+1 it(1 +a); Xi,t+1 'it( + 2) i 1,2,3 (factor augmentation) 8. Factor Employment 3 3 Bi,t+1 Bit(1 + GB1) i - 1,2,3 KTOT = K ; LTOT L L (Exogenous neutral technical change) (3n equations) URBPOP - POP2 + POP3 ; RURPOP m POP1 2. Growth of Labour URBL 1JURBL (1 + GURBt URBL *q + L ; RURL* L (6 equations) t+1 T ) (regional population and labor) RURLt1 RURL (1 + GRUR) ""t+l t~ 9. Material Balances H LTOTt+ - UIMLt+1 + RURLt+1 Q1- D1 + La1Q Q+ + + Q i(3 equations) 3. Growth of Capital, Land, Livestock Q2 - ID2j + as2j + DINV +DTRAN KTOT - KTOT + DINV - 6KTOTt q3 D 3j+ aN J . INDt+1 - LANDt (1 + GLANDt) t+1 t DTRAN Demand for transport as an intermediate product. LVSTK LVSTK (1 + GLVSTK) (3 equations) (n+l equations) 4. Savings 10. Price Normalization SLAB i,t+1 SLABit(1 + GSLABi) Si 1.0; S1 . i 1,2,3 (in the first period) S CAP1 ,t+ - SCAPit(1 + GSCAPi) (n+1 equations) FMINt,t+1 FMINit(1 + GFMIN ) (3n equations) (The Static Model has 13 n + n2 + 15 equations. With n -3, this is 63 equations. With Walras' Law Operating, there is one redundant equation. Thus the static model has 62 independent equations.) List of Exogenous Variables and Parameters List of Endogenous Variables KTOT1, LTOT1 2 Initial total capital stock, labor force, Qi,Ki,Li 3n Sectoral gross outputs, capital stocks, labor force. LANDI. LVSTKJ 2 Land endowment and livestock 2 P na Price of commodity i in sector j. yil I 2n Initial sectoral labor, capital quality n P Net prices Bil n Production function scaling parameter Wis A 2n Sectoral Wages, Capital Rentals litoi 2n Sectoral capital intensity parameter and elasticity of substitution RENT, RLVSTK 2 Land rent, return to livestock ALPU, GAM, BET 3 Share of land, livestock, and (capital + labor) YCAPip YLAD 2n Sectoral property, labor income in agriculture I aij aT +1 input output, transport coefficients YSAVE, YCONS 2n Sectoral savings, disposable income 01.41 2n wage and rental differentials POP I Sectoral population SLABil, SCAP i 2n Initial savings rate from sectoral labor and D 2 n Demand for commodity i in sector j H capital income i capitalincomeDINV 1 Investment demand-D GSLABI, GSCAP 2n Growth rates in sectoral labor and capital income savings rates S n Price weights L'PR n Sectoral (regional) worker participation ratio URBPOP, RURPOP 2 Urban and Rural population 2 n Marginal budget share of commodity i in sector j URB, RRL2 Urban and Rural labor FMIN Y Minimum subsistence levels DTRAN 1 Transport demand I11 12 "2n Labor and capital augmenting rates These are 12n and 2n + 8 62 endogenous variables which equal the number GB1 n Neutral technical change rates of independent equations in the static model.. GURB, GRUR 2 Natural growth rates of urban and rural labor & 1 Rate of capital depreciation CLAND, GLVSTK, 2 Rate of land, LVSTK increase GFMINI n Rate of Increase in FRIN, Thus there are 17n + 2n2 + 13 - 82 numbers required tc run a simulation of DYNURB: a relatively small data set. - 15 - Technical change: The C.E.S. structure allows for the most flexible framework for modeling technical change. Factor augmenting technical change is allowed at different rates in different sectors (i.e. each of Aij can be different) along with differing rates of exogenous neutral technical change (of the "manna from heaven" type). Thus what are really freely mobile and homogenous between sectors are efficiency units of factors. The implication is that when a person moves from a rural to urban area he acquires all the characteristics of the urban area, i.e. more efficiency units. The same holds true for capital. Transport: An input-output coefficient, aT, is added to the normal input-output structure to regard transport as an intermediate output. Thus whenever a commodity is transferred from one region to another, it is deemed to incur intermediate transport costs. Thus, when the agriculture sector uses 1 unit of good 2 (industrial good) as an intermediate good, it also used aT units of transport. Since, in DYNURB, transport is always produced by the industry sector, this additional demand is always produced in sector 2. The net price equations then become non-linear-in aij and aT and are highly "irregular" in structure. Factor Demand and Inter-Region Wage Structure: The returns to factors are equal to their marginal value products. Thus factors are demanded until their marginal products equal their wages or rentals. An inter-region-wage structure is maintained: urban wages are higher than rural wages but efficiency units are still regarded as homogeneous. Thus a person earns more in an urban area than in a rural area (a) because efficiency units earn more and (b) because he "eabodies" more efficiency units in the urban area. The justification for this inconsistency is as follows: In such an aggregated model what we call "labour" is really an index of labour inputs of different levels of skills and education levels. We can supposs that, in general, only higher quality members of the labour force move to the urban area. These members possess higher than average efficiency units in the agriculture sector. Thus it can be consistently maintained that efficiency units of a.factor are homogenous as well as perfectly mobile and are augmented at different rates in different sectors. The appropriate equalizing (within the given wage structure outlined next) is then for the returns to the efficiency units of the factors. Thus, if it is sought to equalize wages across all sectors what is equalized is the wage per efficiency unit. The wage per person, or augmented unit, may well be different. This interpretation therefore conveniently maintains factor homogeneity and mobility along with different rates of technical change.in factor quality. However, even this difference does not account for the total urban/rural wage differences observed. There is ample evidence that urban and rural earnings differ for the - 16 - same skill and that there is no -tendency for this gap to be closed. Reasons for this are not entirely clear but among them are the different costs of living, under- utilization of skills in rural areas due to deficiency demands and differences in skill and education mix within the same professional or'craft category. Whatever the reasonq are, an inter-region.-wage structure is imposed to approximate reality. Savings: DYNURB allows for different savings rates out of labour and capital income as well as different rates in each sector. Houthakker (1965) and Bhalla (1978) provide evidence for different savings rates from different sources of income and Panikar (1970) and NCAER (1965) for different sectoral savings rates. Thus the savings function is only partially Kaldorian in that everyone saves but at different rates. Savings rates grow with time as in a developing economy. Demand System: The Stone Linear Expenditure System.is used but savings are deemed to occur first, then committed expenditures are made (for subsistence requirements) and then discretionary expenditures. Ideally, committed expenditures should be made before savings but this form has been used here for practical computational convenience. In using this function, distinction is made between the labour force and population not usually 'made in such models: only people active in the labour force work but the whole population consumes. One property of the Stone system is that individual demand functions aggregate perfectly if all individuals have the same utility function. In DYNURB consumers in each of the 2 regions, urban and rural, are identical so aggregation can be done within regions but not across regions. The Stone system is particularly appropriate for modelling low income economies since we can interpret the committed expenditures (FMINi) as subsistence requirements. It can be shown 1/ that if only food is a subsistence requirement (i.e. FMIN1 > 0, FMIN2 = FMIN3 = 0) then the income elasticity of demand for food is less than unity and that for other goods is greater than unity. Thus the Stone system captures Engel demand effects well and is particularly suited for modelling a low income developing economy. Furthermore, the system is price responsive, the own price elasticity being -1 if the good is not a subsistence good and smaller in magnitude (appropriately) if it is a subsistence good. Population Growth: DYNURB has exogenously different natural rates of population growth in urban and rural areas. Thus, because of migration, total population growth is partially exogenous. 1/ See Mohan (1977), pp. 83-85 for the derivation. - 17 - Model Solution DYNURB is therefore, though a relatively small model, quite complex and has a high degree of closure. Because of this, DYNURB faces one solution problem not faced by other models in the same genre. Both wages and capital rentals being endogenous, both capital and labour allocations have to be determined simultaneously. Other models usually fix either wages exogenously or capital allocations. Here,with constant returns to scale production functions the long run supply curve is flat. Thus, if one sector is more profitable at one level of production, it is so at all levels. If one attempts to find equilibrium wages and rental simultaneously, there is a tendency for all resources to shift to the most profitable sector. One resource therefore has to be made "less mobile" -- in this case capital -- to be able .to find the solution. Figure 1 illustrates the solution process. A set of initial prices are assumed along with a set of labour and capital allocations by sector. Total labour and capital stocks are fixed for the period. The labour market is then solved for market clearing wages as if capital allocations were fixed. Given resulting factor incomes, product demands are calculated along with intermediate demands and investment. Excess demand equations are formed, and prices changed in response. The labour market is then solved again followed by the product market until a set of market clearing wages and product prices are found -- all the while acting as if capital allocations were fixed. It is only then that an excess demand capital equation is formed and capital rentals changed accordingly resulting in a revised allocation of capital. This allocation - 18 - -Figure 1: The Solution of DYNURB Ki,Lr ,P Net Prices . Outputs C Wages (1) L demands 2(4) Labour Market K Rentals (3) / Demand System Product Market Prces Solution :To Next Period K Rentals I (3)1 K Demand K Market KO Suply - 19 - is then treated as fixed and the whole process repeated until a final solution is reached in all markets: the labour market, the goods markets and the capital market are all in equilibrium and give a set of solution wages, rentals and prices. Associated with these are sectoral capital and labour allocations and outputs. Thus the model essentially solves 5 markets: the markets for labour and capital and the markets for the 3 goods. The dfficiency labour and capital are homogeneous and have a given intersectoral wage structure. Each is therefore regarded as an economy-wide market. The solutidn technique can be regarded as simulating a market economy: capital is "less mobile" than labour and prices adjust in response to excess demands. As mentioned earlier, if labour and capital are made equally mobile, i.e., solved simultaneously, the constant returns to scale nature of the production function shifts all production to one sector. Capital is therefore "artificially" fixed for the solution of the labour and goods markets. As shown in Table 1, the number of equations in DYNURB is equal to the number of endogenous variables in the static model. This provides assurance that a solution is feasible. With neoclassical production functions and the demand system used, it is reasonable to expect that a unique solution exists for the model. This study does not investigate the existence properties of the model, nor its stability properties any further. However, given that there is more than one consumer, the theoretical probability of non-uniqueness exists. Practically, it is likely that the solution.is, indeed, unique since various initial conditions were found to lead to the same solution. - 20 - III. APPLICATION TO INDIA DYNURB was tuned to approximate the Indian economy in 1950. Parameter values were selected, as far as possible, from existing studies 6n India so that they were close approximations to actual estimates. Some (e.g. the elasticity of substitution in agriculture) were mere guesses if no estimates existed. In addition intial values had to be chosen for variables such as total factor stocks to start off the simulation. This section presents selected results from the base simulation (hereafter called the BASRUN) which is regarded as tracking the Indian economy quite well. Table 2 shows the re6ult of the BASRUN along with actual values for India for the growth in total output. The two sets of series are in remarkably close agreement considering the many unrealistic assumptions incorporated in DYNURB. The income lags somewhat towards the end of the period. This is probably because i) population growth tends to slow down in DYNURB with increasing urbanization; ii) the last year for which data is shown, 1974-75, was the third of a succession of bad years in India. Table 3 shows the BASRUN growth rates of gross national product along with those for per capita national product. The feature tonote is the acceleration of growth rates. The DYNURB economy grows faster and faster with the passage of time. Estimates for growth in GNP in different period for India are given. below: 1949 to 1955 2.92% 1954 to 1961 3.63% 1961 to 1967 3.61% 1949 to 1969 3.41% 1954 to 1969 3.62% (Dholakia, p. 20) Table 2: NATIONAL PRODUCT IN CONSTANT PRICES (Index, 1951 = 100) BASRUN ACTUAL Year GNP Per Capita GNP Per Capita 1 2 3 4 1951' 100 100 100 100 1954 110.7 104.5 114 107 1957 122.7 109.4 124 110 1960 136.4 114,8 134 112 1963 151.7 120.7 151 118 1966 169.1 127.1 166 121 1969 188.5 133.9 184 129 1972 210.5 141.2 210 137 1975 235.5 149.2 217 136 1978 263.5 157.6 1981 295.0 166.7 1984 330.5 176.5 SOURCES: Cols. (1), (2) BASRUN Simulation. Cols. (3), (4) Dholakia (1974), Government-of India (1976), M. Mukherjee (1969). NOTES: (1) The simulation results are in constant 1951 prices. (2) The "Actual" data are in 1948-49 prices for the years 1991 to 1966, while later years are in 1961 prices. Table 3: GROWTH RATES OF NATIONAL PRODUCT (percent per year) Year Growth Rates From 1951 to: GNP Per Capita 1954 3.45 1.49 1957 3.48 1.52 1960 3.51 1.55 1963 3.54 1.58 1966 3.56 1.61 1969 3,59 1.63 1972 3.61 1.66 1975 3.63 1.68 1978 3.65 1.70 1981 3.67 1.72 1984 3.69 1.74 SOURCE: BASRUN Simulations. DYNURB's success in tracking the Indian development record over 25 years gives reason to believe that the structure of the model is plausible and that the parameters used are well founded even though they were not systematically estimated. - 23 - Correspondence between these estimates and the BASRUN is good. The average for the later:years, 1969-75, however, is not as high as suggested by DYNURB. This is partly because of unusually adverse weather conditions during 1972 to 1975. Table 4 shows the population of India as estimated in DYNURB as compared with the actual data. Table 4: POPULATION OF INDIA (in millions) Year BASRUN Actual 1 2 1951 362 361 1961 430 439 1966 482 485 1971 540 548 - 1974 571 577 1981 640 695 1984 678 Source: (1) BASRUN, Table A.8 (2) a/ Up to 1974, Government of India (1979), p. 2 (taken from the Indian Census). b/ 1981, Bose (1973), p. 423, estimate. That population is estimated well by DYNURB is not very surprising because the urban and rural natural population growth rates are exogenously specified. The only endogeneity is caused by rural/urban movement and therefore the model is also tracking that movement well. The definition of urbanization places all labour that works in industry and services in the urban region even if some of the activities -24 - are actually located in the rural region. Thus, while the actual level of urbanization in India was 17.3 percent in 1951, and 19.9 percent in 1971, in the BASRUN the levels were 26.7 percent and about 32 percent for the two years respectively. The levels were are not comparable but the trends are: Growth Rate of Urban Population BASRUN Actual 1951-61 2.96 2.64 1951-71 2.84 2.96 It is clear therefore that DYNURB models the trend of urbanization well. A model such as this can then give a.benchmark against which we can measure the rate of a country's urbanization. If the structure of such a model is regarded as sound then the rate of urbanization given by simulation can be regarded as the trend that "ought" to exist in the modelled economy. If the rate of urbanization is faster in the actual economy it is then, perhaps, justified in calling it over-urbanized. Recall, however, that DYNURB assumes full employment: thus a higher rate of urbanization in the actual economy accompanied by rising urban unemployment would be a good index of over-urbanization This is, in principle, better than an internationally derived norm from cross sector data. An improvement of DYNURB which could allocate some industry and service employment to rural areas would give better answers to the appropriate level of urbanization as a country develops over time. The model was further validated by examining the sectoral distribution of output and factor stocks as they changed over time in the 30 year simulation of DYNURB. These distributions compared well with actual data giving further confidence in the structure of DYNURB. - 25 - In summary, therefore, the simulation shows that the transfer of labour from rural to urban areas is as much to service sector occupations as to industrial occupations. Thus it is essential to study structural change in at least a 3-sector context as distinguished from the usual 2-sectors. As evidenced from the demand coefficients used in the simulation, the demand for services is particularly significant in urban areas and its neglect, therefore, would miss one of the most important components of structural change in a growing economy. Other key results from the simulation include confidence in the modelling of technical change. Its essential ingredients are: (i) A labour-saving bias in urban areas along with aeapital saving one in rural areas. (ii) A higher rate of technical change in agriculture compared . with the other two sectors. This is essential to provide enough food for the increasing population and for the increasing urban, i.e., non-rural based demand. (iii) Capital and labour augmentation account completely for technical change in the urban based sectors but "unexplained" change is necessary in the agricultural sector. The BASRUN also shows that even with a "respectable" savings and investment rate a very low income economy like the one simulated has difficulty achieving very high rates of growth: particularly per capita growth when population growth rates are high. This is partly caused by the large proportion of consumption expenditures being required for food subsistence purposes. Thus, as population grows, much of the investment has to be directed towards agriculture to keep food production in line with population growth. Correspondingly, the pace of structural change, i.e. urbanization and industrialization is slow, - 26 - Cause and effect are characteristically difficult to separate in a general equilibrium model. The next section provides a better idea of some of the underlying causes of structural change through the use of sensitivity tests of the model, now that its plausibility has been demonstrated. - 27 - IV. SENSITIVITY TESTS Cause and effect are characteristically difficult to disentangle in a general equilibrium model -- even when it is a relatively small one such as DYNURB. Moreover, as has been pointed out, though small in size, DYNURB has a high degree of closure and hence the relationships among its parts are complex. Analytical results are virtually impossible. So sensitivity tests have to be used to obtain a better understanding of the workings of the model and, by inference, of the economy it represents. Drawing strong conclusions from the results of sensitivity tests on a simulation model is, however, hazardous. It is not easy to distinguish results caused by technical quirks in a model from those that are consequences of the structire of the economy. A large number of tests were conducted, each of which involved a change in one of the parameters. In this paper I investigate the effects of different rates of population growth, of changes in the pattern of demand and of the role of different kinds of technology on the process of urbanization. In so doing one also obtains a number of insights into the development process, but I concentrate on urbanization here. One general result worth reporting is that the dynamic general equilibrium system incorporated in DYNURB behaves much like a buffalo -- as does the Indian economy' Exogenous shocks, i.e. changes in parameter values, do not make radical differences in the growth path of the economy -- even when these changes are of a substantial magnitude. A shock in one component produces - 28 - ripples across the economy and equilibrating forces are set in motion dampening the long run impact. This is what should be expected from a general equilibrium system with an unchanging structure. Population Growth The experience of extremely high rates of urbanization in LDCs in recent decades has partly been attributed to high population growth rates. Thus, tests are conducted here to judge the quantitative effects of different rates of population growth. A range of tests was performed with small changes in the growth rates (GURB and GRUR) and with large changes. Tables 5 and 6 report the extreme results: those with zero population growth and with a growth rate of 2.5 percent per year. The .latter is high by Indian standards though Latin American population growth rates are characteristically in the region of 3 percent. The most interesting result is that with zero population growth, (ZPG), urbanization proceeds at a more rapid rate as shown in Table 5. In 33 years, the level of urbanization is about 42 percent as opposed to 35 percent in the BASRUN. The reasons are not difficult to find. With ZPG, the growth of per capita income is greater and with the income elasticity of demand for food being less than unity, the shift in consumption patterns toward urban goods-is correspondingly faster. This shift would be even more significant if another demand system was used in which all income elasticities did not approach unity in the long run.-/ The absence of the additional demand for food from increased population and a faster shift to urban goods produces an increased demand for urban labour 1/ This distortion is not critical at low levels of income where subsistence requirements are still substantial. Table 5: EXPERIMENT No. 1 Zero Population Growth GURB = GRUR = 0.0 (NEWRN) (See Notes Below) GURB = 0.017, GRUR = 0.020 (BASRUN) 1951 1963 1972 1984 1. GNP Per Capita Growth BASRUN - 1.58 1.66 1.74 Rate (% -per year) NEWRN - 2.39 2.40 2.41 2. Level (% Urban) BASRUN 26,73 30.04 32.25 35.01 NEWRN 26.73 33.01 37.01 41.74 (% Difference) 9.87 14.74 19.23 3. Growth Rate of BASRUN 0.98 0.90 0.82 Urbanization NEWRN 1.77 1.56 1.36 (% Difference) 81.25 73.73 65.61 4. Growth Rate of BASRU1N 2.92 2.84 2.76 Urban Population 9EWRN 1.80 1.59 1.39 Notes on Tables on Sensitivity Tests Results of experiments are reported in the same format for each case. 1. BASRUN - The value of the variable in the BASRUN which tracked Indian economy well. 2. NEWRN - The results of simulation with the change in parameter as noted above the table. 3. Percentage Difference - Percentage change in variable at time t as compared with value in the BASRUN. 4. Growth Rate of Urbanization: This is the growth rate of the urbanization level, i.e., the growth rate of the share or urbanization. 5. Growth Rate of Urban Population: This is the.growth rate of total population in urban areas. - 30 - and consequently increasingly higher levels of urbanization. This result depends on the assumed rates of technical change which permit labour to be released from agricultural production. To the extent that agricultural terms of trade tend to deteriorate, it would be reasonable to expect an induced effect on the rate of innovation in agriculture. Indeed, the rate of technical change could slow down, thus requiring more labour in agriculture and consequently resulting in a slower urbanization rate. To predict such changes, a more sophisticated theory of technical change is required which, alas, DYNURB does not incorporate. Heie only different possibilities can be investigated. Although the rate of tirbanization is increased significantly the rate of growth of urban population obviously declines. The important point, however, is that these growth rates are significant (line 4, Table 5), even with the extreme assumption of ZPG. With more reasonable assumptions, i.e., natural population growth rates of between 1 to 2 percent per year, the rate of growth of urban population is in the range of 2.0 to 2.5 percent per year as compared with about 2.8 percent in the BASRUN. The lesson then is that a decrease in the natural growth of population will not remove urbanization problems in LDCs. The six to seven percent urban population growth rates characteristic of some Latin American countries would only decline to 4 to 5 percent if the natural population growth decreased to about 1.5 percent from the current 3.0 percentvayear. These results are very important because they demonstrate that the decline in bitth rates (or population growth) is not going to solve the urbanization problem and that we can expect cities to grow along with the development process. This is already being observed in Latin America where population growth rates have declined drastically in recent years - 31 - from about 3.0 percent to about 1.5 to 2.0 percent a year. Cities are indeed contihuing to grow at rates of 4 to 5 percent per year instead of the earlier 6 'to 7 percent., The early Japanese development experience in the Meiji era was somewhat similar to this characterization. Agricultural productivity had increased but the growth rate of population was low. Consequently, a relatively small increase in agricultural productivity did result in significant income changes and high rates of urbanization. It is worth delving further into the simulation-results to understand the mechaaism of DYNURB which produces these results. The most dramatic result in the ZPG simulation is the reversal in the terms of trade making urban goods more expensive. This has a dampening effect on the demand for urban goods including capital go.ods. The proportion of net investment to GNP declines: the economy indogenously adjusts for a slower populatin growth rate. The converse happens with an increase in populationagrowth: the proportion of investment increases, thereby mitigating somewhat the negative effect on per capita incomes. Note, however, that the change in investment decreases in later years and would probably equal the BASRUN in a long enough simulation in both cases. The economy therefore has built in stabilizing influences over the long run which can only be captured by a general equilibrium model. To the extent that these influences tend toward a dynamic equilibrium, the implication is that policy choices may not make a substantial difference over a long period, but do over a period like 5-15 years. Put another way, policy choices can determine the path taken by an economy to reach an bbjective but perhaps not the objective itself. - 32 - Table 6: EXPERIMENT No. 2 High Population Growth: GURB = GRUR = 0.025 (NEWRN) (BASRUN GURB = 0.017 GRUR = 0.020) 1951 1963 1972 1984 1. GNP Per Capita Growth BASRUN 1.58 1.66 1.74 Rate.(% per Year) NEWRN 1.34 1.43 1.52 2. Level (% Urban) BASRUN 26.73 30.04 32.25 35.01 NEWRN 26.73 29.14 30.88 32.74 (% Difference) - -3.00 -4.25 -6.50 3.. Growth Rate of BASRUN - 0.98 0.90 0.82 Urbanization NEWRN - 0.72 0.69 0.62 (% Difference) -26.18 -23.20 -24.98 4. Growth Rate of Urban BASRUN - 2.92 2.84 2.76 Population NEWRN - 3.23 320 3.12 As should be expected with ZPG, wages increase substantially, K rentals decline and therefore the wage rental ratio increases with a corresponding increase in the overall capital labour ratio. Since the elasticity of substitution between capital and labour is 1.2 in agriculture, capital is substituted for labour to a larger extent in that sector and the labour share consequently declines despite a substantial rise in wages.. The implication is that if the elasticity of substitution in the two urban sectors was higher than the assumed 0.6 and 0.8, more capital would be employed, demand for labour would decline and wages would tend to decrease. (Some of these effects are investigated later in experiments with the elasticities of substitution). When population growth rates are low, low elasticities of substitution are better for labour! - 33 - The opposite result holds for high population growth. Higher elasticities of substitution in the urban sectors would increase the demand for labour, cause higher wages and a higher urbanization rate. Those who call for "appropriate technologies" and a better allocation of factors in the interest of employment generation in the context of high populationgrowth, should be aware that higher urbanization rates will be one of the results of such policies. This result is not dependent on the assumption of full employment. It would be the same even if unemployment is allowed and migration behaviour conforms with the Harris-Todaro (1970) hypothesis or one of its variants. The share of the service sector in total output increases more than that of industry. Thus labour absorption in urban areas is more due to service sector expansion. A model not including the service sector would not have this detail and would therefore show a slower rate of labour absorption. It is the neglect of the service sector or its perception as a sponge that lead to fears of widespread urban unemployment along with high urbanization growth rates. The explicit inclusion of the service sector in DYNURB is therefore once again shown to be illuminating a crucial aspect of development and urbanization. Recall the the relatively faster growth in the demand for service goods is determined in DYNURB by specification of the demand parameters. The conclusions drawn above therefore depend on the validity of the numerical magnitudes used. These have alzeady been justified, hence these conclusions must be deemend to be valid. - 34 - The last result of ZPG worth noting is that the increase in the growth of per capita income is not striking and that the difference relative to the BASRUN declines over time. The implication is that, ceteris paribus, over a long enough period, a high population growth rate does not necessarily mean a smaller growth in per capita income. This is partly because endogenous adjustments induce a higher investment rate. What is true, though, is that per capita income is increased with lower population growth in the short run and it is likely that such increases cause other structural changes which make the growth self sustaining. This last point is worth emphasizing in the modelling context. In any structural model like DYNURB the basic structure of the economy is assumed to be stable over the long run. In reality, a short run large increase in per capita income can cause a snowball effect which then makes growth self-sustaining. The foreign sector is not modelled at all in DYNURB. One of the usual effects of high per capita income growth for a few years is a major improvement in a country's rating in credit markets and the resulting large inflow of foreign investment and credit. Such may have been the case for Korea where large U.S. aid programs in earlier years resulted in income increases in -those years and were then followed by self sustaining accelerated growth along with a substantial flow of foreign credit. DYNURB is clearly not equipped to deal with such systemic responses to a changing situation. Nevertheless, it serves to show that the rate of population growth, while undoubtedly important, as a dampening influence in a country's growth path may not - 35 - be as important as is sometimes made out. Moreover, those iqho are concerned with the problem of rapid urbanization should realize that a slow down in population growth will not solve their problems. The experiments on population growth do not allow for differential growth rates between population and labour. The participation rate is assumed to be constant though different for urban and rural areas. A richer demographic sub-model would allow the modelling of changes in age structure over time -- in particular, the lag between population growth and labour force growth. Changes in Demand Patterns Discussions of development and urbanization are typically supply oriented. Thus, a large amount of attention is paid to the possibilities of increasing efficiency in production, to inappropriate choice of techniques, to the rate of population growth and so on. It is usually assumed that Say's Law holds in low income countries, i.e., that whatever is supplied will be consumed and that the important constraints are to do with supply. Phenomena such as the "embarrassment of riches" associated with the recent bumper harvests in India indicate that demand constraints may be as important. Thus the effects of changes in demand patterns are investigated with some care in this.study. Two sets of experiments are reported. One set reports the effects associated with changes in marginal budget shares (ij s) and the other, those associated with changes in perceptions of subsistence requirements. Recalling the derivation of the Stone demand system from its associated utility functions, it is fair to say that the set of experiments with changing marginal budget shares is really investigating the effects - 36 - of changing consumer tastes. It is somewhat surprising when viewed in this manner, that growth rates of real income can be affected by a mere change in preferences! Table 7 reports the effects of an increased preference for food in urban areas. Another experiment simulated an increased preference for urban goods in rural areas. The results of one experiment are the converse of the other. Thus, only the results of Experiment 3 are discussed. As a result of the shift in urban demand in favour of food and away from urban goods (the experiment performed makes the urban demand pattern identical to the rural pattern), the level of urbanization decreases in the initial year and continues to decrease relative to the BASRUN in later years. The growth rate of urbanization decreases as well. Thus a change in preferences produces a comparative static result which tends to persist over time. In the BASRUN simulation it was assumed, in conformance with the Indian consumption pattern, that people in rural areas tend to consume more food than service goods as compared with the people in urban areas. In this experiement therefore we are merely testing what happens if everyone had rural preferences, i.e. the rural demand pattern prevails everywhere. The shift in demand towards agriculture increases the share of agriculture in total product and resources shift to that sector accordingly. Given that agriculture is a less productive sector (in the sense that an equivalent amount of resources produce less value added> the level of GNP decreases in the initial year and continues to decrease relative to the Table 7: EXPERIMENT NO. 3 Increase iii Urban.Demand for Food 1/ 1951 1963 1972 1984 1. GNP Per Capita Growth BASRUN - 1.58 1.66 1.74 Rate (% per year) NEWRN - 1.53 1.60 1.68 2. Level (% Urban) BASRUN 26.73 30.04 32.25 35.01 (% Difference) -11.60 -12.12 -11.92 -12.30 3. Growth Rate of BASRUN - 0.98 0.90 0.82 Urbanization NEWRN - 0.93 0.88 0.80 (% Difference) -5.10 -1.68 -2.97 4. Growth Rate of BASRUN - 2.92 2.84 2.76 Urban Population NEWRN - 2.87 2.83 2.74 Note 1: Demand coefficients in'the urban sector are made equal to those in rural sector, i.e., Ag. Goods: 11 = 12 13 = 0.4 (0.25) Ind. Goods: $21 = a22 a23 = 0.25 (0.20) Serv. Goods: a31 = 32 33 = 0.35 (0.55) (Bij is the budget share of good i for a consumer in sector j) Figures in parentheses are the BASRUN Urban Sector demand coefficients. - 38 - BASRUN levels in later years. The economy wide growth rate is lower. Since urban based income decreases, and because urban savings rates are higher than rural rates, the level of total investment in the economy declines. It is found, therefore, that a shift in urban consumer tastes toward food has important effects on levels of income in the short as well as over the long run. What are the effects of the converse case: when rural preferences shift toward urban goods and larger marginal budget shares are spent on these goods. Such a change induces a faster growth rate of income and higher urbanization -levels. 29.2 percent of the population in the intial period is urbanized as compared with 26.7 percent in the BASRUN. Such a difference persists over 20 years and is therefore a non-trivial effect. The effects discussed above are to be distinguished from Engel effects which are only due to different income elasticities of demand for urban goods ( >1), and for agricultural goods ( <1). The increased prefer- ence for urban goods stimulates a further structural change which could appear with rising income causing a shift away from rural goods. A better experiment would be to make the as variable over time so that the shift away from agricultural goods takes place along with rising income. The results indicate that the effects of such a structural change would be to reinforce Engel effects and to induce a progressively higher rate of growth of income and of urbanization. - 39 - Subsistence Requirements It is assumed in the simulation of DYNURB that consumers regard only food as a subsistence good and that this is some absolute nutritional minimum which remains the same over time. The next set of experiments investigates the effects of changes in the perception of consumers as to what constitutes subsistence goods. It is sometimes argued that sub- sistence requirements rise over time along increases in income. Experi- ment 4 investigates the consequences of such a shift in requirements, so that FMIN (1), the amount of food required to subsist, increases at a rate of 1.5 percent per year. Other experiments were conducted with a once and for all increment or decrease in FMIN (1). Their results were consistent with those reported from Experiment 5. The effects on the level and rate of urbanization are dramatic. The economy begins to ruralize! In 1984 the level of urbanization de- clines to 24.2 percent of population from 26.7 percent in 1951. The BASRUN level in 1984 is 35.0 percent. The growth rate of urban popula- tion is still positive though only 1.60 percent per year. The increased demand for food tends to shift resources to the agriculture sector where there is a higher preference for food as compared with urban goods. This serves to reinforce the effect and the economy begins to ruralize. All these results should be expected but what is surprising is the magnitude of the effect. The per capita income growth rate declines from about 1.75 percent to 1.5 percent. The share of agriculture is 12.3 percent higher in 1984 than was the case in the BASRUN. The magnitude of these effects is important if this experiment is considered in the context of a nutrition or food subsidy program being designed in a . - 40 - Table 8: EXPERIMENT NO. 4 GROWTH IN SUBSISTENCE FOOD REQUIREMENTS GFMIN = 0.015 NEWRN 1 GFMIN 0.0 BASRTN 1951 1963 1972 1984 1. GNP per Capita BASRUN - 1.58 1.66 1.74 Growth Rate (% per year) NEWRN - 1.41 1.46 1.51 2. Level (% Urban) BASRUN 26.73 30.04 32.25 35.01 NEWRN 26.73 25.65 13.99 24.24 (% Difference) 0 -14.63 -22.52 -30.77 3. Growth Rate of Urbaniza- BASRUN - 0.98 0.90 0.82 tion NEWRN - -0.34 -0.32 -0.30 (% Difference) - -135 -136 -136 4. Growth Rate of Urban BASRUN - 2.92 2.84 2.76 Population NEWRN - 1.56 1.60 1.62 1/ GFMIN is the growth rate in minimum food requirement FMIN The BASRUN had assumed that subsistence requirements remain constan. - 41 - relatively closed economy. Where such a programme is being financed from tax revenues, it can approximately be interpreted as increasing the food subsistence requirement since taxes paid by consumers may be regarded as increased allocated price-insensitive expenditures on food. Note that the increase in food requirements is set at only 1.5 percent per year. A converse experiment was also performed (but not reported here in detail) where urban goods were also included in the subsistence bundle. It is often argued that urban dwellers have minimum needs in terms of urban infrastructure and housing such that they have a higher proportion of allocated relatively price-insensitive expenditures. The mere provision of necessary urban services such as roads, water supply, sewerage, etc. may be regarded as constituting such expenditures if they are financed through tax revenues. This is simulated in DYNURB by including both the urban goods in the subsistence bundle (i.e., FMIN2 and FMIN3 > 0). The result is inter- esting: since there is now higher "forced" consumption of urban goods, resources shift to urban areas leading to a substantial increase in the level of urbanization, GNP and per capita income in the initial period. Income continues to grow somewhat faster though the effect is alternated in the long run. The growth rate of urban population declines somewhat since it'now starts from a higher base. The conclusion is .therefore a surprising one. The provision of some minimum level of urban goods and services produces an increase in income levels as well as growth rates along with a higher level of urbanization. Such provisions should there- fore not be assumed to be a drain on the economy. Urban infrastructure investments are, apart from their other justifications, therefore "product- ive" in their own right in that they induce higher levels of incomes in the economy through their multiplier effects. - 42 - The overall conclusion from the demand experiments is that demand patterns matter and that changes which occur along with increases in income and development can have reinforcing effects that accelerate the development process. These results are consistent with the findings of Kelley, et. al. (1972). Nutrition and food subsidy programmes can have some surprisingly strong deleterious effects on growth while the provision of urban goods and services as subsistence goods may have beneficial effects. Technical Change: The Relevance of the Elasticity of Substitution and Appro- priate Technology. There is a widespread belief that the technology used in urban areas in LDCs is, in some sense, inappropriate. It is argued that the factor pro- portions used do not reflect prevailing factor prices well: in particular, industry is 'too capital intensive.' A large amount of literature is developed on the question of 'employment generation.' It is argued that the use of appropriate technology would make processes more labour intensive and therefore help in solving the problem of urban employment. The question of appropriate technology is really a debate on the existing-value of the elasticity of substitution. If the value is unity, there is then little justification in the argument that factor proportions do not respond to changes in factor prices. Thus a set of experiments was done with different elasticities of substitution. These experiments also tested the sensitivity of DYNURB to these technology parameter assumptions since, to some extent, the production function parameters were the least well informed -- especially for the service sector. - 43- Various experiments were conducted but only one is reported here where all the 'elasticities of substitution are set at unity and all the production functions become Cobb Douglas functions. (In the BASRUN the elasticity of substitution between labour and capital was set at 0.6 for industry, 0.8 for services and 1.2 for agriculture). One general result from the experiments is that the economy gains in efficiency the nearer each elasticity moves toward unity. Experiment 5 (Table 9) shows the effects of what might be char- acterized as appropriate technology. The assumption of all Cobb-Douglas production functions amounts to a technology which responds to changes in factor prices perfectly. The technology experiments show that any other elasticities induce efficiency losses. The striking result is that it is not too different from the results which had Cobb-Douglas technology in agriculture only. The main difference is that K rentals increase, which implies that capital is being used more efficiently. That labour share declines significantly in the urban sector by the end of the simulation period. This result is somewhat reminiscent of a wage equalization experi- ment where higher efficiency and income growth were accompanied by income losses to urban labour and a higher rate of urban labour absorption. The conclusions from this set of experiments are: * The choice of technique or elasticity of substitution matters. However, the effects of choices within a reasonable range do not appear to be significant enough to warrant the large amount of literature devoted to the labour absorption issue. * Efficiency losses do occur the further a:is from unity. "Smooth" production functions induce efficiency. Table 9: EXPERIMENT NO. 5 All Production Functions: Cobb-Douglas 1 a = 1.0 a = 1.0 a = 1.0 NEWRN 1 2 3 a = 1.2 a = 0.6 a = 0.8 BASRUN 1 2 3 1951 1963 1972 1984 1. GNP Per Capita Growth BASRUN - 1.58 1.66 1.74 Rate (% per year) NEWRN - 1.80 1.92 1.99 2. Level (% Urban) BASRUN 26.73 30.04 32.25 35.01 NEWRN 26.74 31.20 33.82 36.53 (% Difference) 0.04 3.85 4.87 4.35 3. Growth Rate of .BASRUN - 0.98 0.90 0.82 Urbanization NEWRN - 1.29 1.13 0.95 (% Difference) 32.24 25.22 15.69 4. Growth Rate of Urban BASRUN - 2.92 2.84 2.76 Population NEWRN - 3.25 3.07 2.89 Note 1. Bi, the production function scaling parameters are adjusted to equate g.n.p. in the initial period between BASRUN and NEWRN. - 45 - o The choice of appropriate technology is associated with significant efficiency gains but not necessarily with employment generation. Indeed,,low elasticities of substitution may be generating higher employment as well as wages. Capital owners may gain relatively more as a result of better utilization of capital! o The rate of urbanization increases with appropriate tech- nology.. This is mostly because of the labour released from the agriculture sector where that labour using sector's elasticity of substitution is reduced from 1.2 to 1.0. Factor Augmentation, Bias and Technical Change. Further sets of experiments were conducted to investigate the effects of different types of technical change in the pace.of urbanization. The quantitative results are not reported here but may be.found in Mohan (1977)1/. The BASRUN assumed a large neutral exogenous technical change in agriculture since no reasonable rates of factor augmentation produce the observed rate of total factor productivity change in agriculture. Such a neutral change is also probably appropriate for a green revolution type phenom- enon in agriculture. The key result is that a decline in this neutral technical change produces a very large decrease in the rate of urbanization. Essentially, a smaller rate of increase in income mitigates the Engel type demand effects and there is therefore a smaller demand for urban type goods and consequently for urban labour. The best prescription for containing urbanization is therefore stagnating agriculture! An improvement in rural conditions is therefore not likely to result in slower rates of urbanization as supposed by some. When the bias of technical change is reversed, that is the rate of capital augmentation is made uniformly greater than that of labour, demand for labour increases in the two urban sectors and therefore the level and rate of 1/ See pp. 261-269. - 46- urbanization-increases. Industry and services now have a labour using bias while agriculture has a capital using bias. In conclusion it is clear that the rate of urbanization does depend on the nature of technical change. Neutral technical change in agriculture produces a greater shift to urban areas than technical change which has a labour using bias. The reversal of bias in the technology, where the urban sectors become labour using, also increases the rate of urbanization as expected. The effect is small in magnitude relative to the rather significant change in the nature of technology that uses it. In general, greater effi- ciency and labour use generating technology changes induce a higher rate of urbanization. - 47 - REFERENCES Adelman, Irma and Robinson, Sherman. Income Distribution Policy in Developing Countries: A Case Study of Korea, Stanford, California, 'Stanford University Press (1978). Ahmed, Fakhruddin. Migration and Employment in a Multi-Sector Model -- An Application to Bangladesh, Princeton University, unpublished Ph.D Dissertation 1974. Berry, Brian, J.L. The Human Consequences of Urbanization. New York: St. Martin's Press (1973). Bhalla, Surjit, S. 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