World Bank Reprint Series: Number 305 William F. Steel and Yasuoki Takagi Small Enterprise Development and the Employmnent-Output Trade-Off Reprinted with permission from Oxford Economic Papers, vol. 35, no. 3 (November 1983), pp. 423-46. Public Disclosure Authorized Public Disclosure Authorized Public Disclosure Authorized Public Disclosure Authorized Public Disclosure Authorized Public Disclosure Authorized Public Disclosure Authorized Public Disclosure Authorized
Transcript
World Bank Reprint Series: Number 305
William F. Steel and Yasuoki Takagi
Small Enterprise Developmentand the Employmnent-OutputTrade-Off
Reprinted with permission from Oxford Economic Papers, vol. 35, no. 3 (November 1983),
pp. 423-46.
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World Bank Reprints
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No. 281. Bela Balassa, "Trade Policy in Mexico," W orld DevelopmL';itNo. 281a. Bela Balassa, "La politica de comercio exterior de Mi6xico." Comercio ExteriorNo..,. 282. Clive Bell and Shantayanan Devarajan, "Shadow Prices for Project Evaluation under
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Oxford Economic Papers 35 (1983), 423-446
SMALL ENTERPRISE DEVELOPMENT AND
THE EMPLOYMENT-OUTPUT TRADE-OFF
By WILLIAM F. STEEL and YASUOKI TAKAGI*
THIS paper analyzes the potential of small-scale enterprise development forabsorbing labor while maintaining outpuit growth in developing countries.Addition of a small-scale, intermediate sector to the modern-informalframework of a Harris-Todaro type model demonstrates that negativemigration and unemployment responses to urban job creation can beavoided. The multi-sector model shows that observed characteristics of largeand small firms are explainable by capital market segmentation, and themodel is used to analyze the effects of changes in policy variables. Expan-sion of demand for small-scale products is a particularly promising ap-proach. Conditions for an employment-output trade-off to arise areanalyzed to show the need for balance between small and large scale sectorexpansion.
Introduction
Research on. small-scale enterprises (SSEs) in less developed countries(LDCs) has flourished during the 1970s with the popularizing of the conceptof the "informal sector" (Hart, 1973; ILO, 1972). The term focusedattention on activities outside the modern, organized sector that enable largenumbers of urban workers to earn income. These activities were omittedfrom dualistic Lewis-type models of economic development and migration,which treated work outside the modern sector as a form of temporaryunemployment while awaiting an opportunity in the modern sector (Harrisand Todaro, 1970; Todaro, 1969). Such models were nevertheless useful inexplaining the continuing expansion of excess urban labor supply in spite ofthe inability of the modern sector to absorb it. Investigations of informalactivities indicate that they are permanent features in the urban developingworld and that they do not necessarily represent a form of disguisedunemployment.
The dualistic approach presents a policy dilemma in the form of atrade-off between output growth and employment. Modern productionmethods embodying technical efficiency, economies of scale, and corporate
*The authors are members of the African Development Bank and Doshisha University,respectively. Some of the research leading to this paper was assisted by grants from theVanderbilt University Research Council and the Joint Committee on African Studies of theSocial Science Research Council and the American Council of Learned Societies. We aregrateful for comments from Frank Child, David Dunlop, Michael Farbman, Simon Fass, DonKeesing, John Knight, Jed Shilling, and a referee of this journal, as well as seminar participantsand other colleagues at Vanderbilt University, Kyoto University, and the World Bank. Wealone are responsible for any remaining errors.
424 SMALL ENTERPRISE DEVELOPMENT
organization appear to provide the most effective use of capital to generateoutput growth. The observed inability of large-scale, modern firms to absorbthe expanding urban labor supply in LDCs, however, conflicts with the goalof full employment. Absorption of this labor into the informal sector to raiseemployment is seen as inconsistent with maximum output growth becauseaverage productivity is lowered.
Recent evidence on the economic characteristics of SSEs is not consistentwith the preceding notions about the modern and informal sectors. Many ofthe SSEs implicitly included in the so-called informal sector appear to usecapital at least as productively as modern sector firms, and to employ laborproductively. The evidence suggests that the employment-output trade-offcan be resolved by channeling resources into small-scale rather than large-scale establishments. Some countries have attempted to pursue this prospectthrough assistance to SSEs. Policies based solely on observed relationshipsare risky, however, unless the reason for the observed relationships and theconditiogis under which they hold are known. One purpose of this paper is toinvestigate conceptually the conditions under which important economicpolicy consequences follow from sectoral differences.
The first problem is how to incorporate the observed characteristics ofinformal activities into a model that explains their existence in equilibrium.The views of empirical researchers range from characterizing a portion ofinformal activities as the "modern informal sector" (Nihan, et al., 1979) toconsidering as invalid any arbitrary differentiation of different parts of thecontinum of employment activities (Breman, 1976). This paper opts forincorporating SSEs as a third, or intermediate sector between modern andinformal-type activities, to analyze the consequences of replacing thedichotomized model by a closer approximation of the continuum.
In order to justify the assumptions through which this small-scale (inter-mediate) sector is introduced, the paper first seeks to clarify intersectoralrelationships observed between it and both the large-scale (modern) sectorand the residual portion of the informal sector. In particular, the evidenceon capital and labor market segmentation is reviewed. The object is todevelop a simple multi-sectoral model in terms functionally related toeconomic conditions and policies found in LDCs, so as to analyze theimplications of policies to promote SSEs. Although the model is a variant ofthe Harris-Todaro model, introduction of an intermediate sector generatesquite different policy conclusions. The analysis shows that segmented capitalmarkets and capital-based incentives to the modern sector provide a reason-able explanation for the observed characteristics of small versus large firms.Stimulating demand for SSE output offers an especially promising approachfor generating self-sustained employment and output growth. Extending theavailability of official (low-cost) capital is likely to have perverse employ-ment effects, and may not increase output as much as does demand stimWua-tion.
W. F. STEEL AND Y. TAKAGI 425
Review of studies on small-scalellarge-scale differences
Studies comparing small-scale and large-scale production in LDCs consis-tently find small size to be associated with less capital per worker, lowerlabor productivity, and more output or value added per unit of capital.' Mostof these studies also indicate that a range of activities (especially those inmanufacturing) included in the broadly-defined informal sector are poten-tially competitive with modern sector production rather than cormplemen-tary, as is often presumed for informal activity.2 An. interesting policyimplication is that small-scale establishments using intermediate technologymay generate more output as well as more employment for a given invest-ment than does the modern sector.3 Even if their products are not perfectsubstitutes for those of the modern sector in terms of quality, they substitutein the sense of satisfying the demand for simple manufactures that resultsfrom rising income per capita. These findings, together with disappointingperformance of large-scale import substitution industries, are leading anincreasing number of LDCs and international organizations to adopt policiesassisting SSEs.
The source of observed differences between small and large firms must beknown in order to direct policies at the appropriate economic variables.Several possible explanations for the association between size andcapital/labor ratios arise out of the literature. The evidence on and policyimplications of these explanations are reviewed briefly as a basis for theasumptions of the model that follows.
1. Capital-based economies of scale
Certain production processes may be characterized by economics of scalethat can be captured only through capital-intensive methods (White, 1978).Aggregate figures that include such industries would therefore show a biastoward capital intensity among larger firms. Within a single industry, however,
'Berry, 1972; Byerlee et al., 1979; Child, 1977; Joshi, Lubell, and Mouly, 1976; Liedholm,1973; Morawetz, 1974; Nihan, Demol, and Jondoh, 1979; Shetty, 1963; Steel, 1977; Todd,1971. Dhar and Lydall (1961), however find lower output/capital ratios in smaller firms incertain industries.
2Studies that describe the informal sector as complementary to and dependent on themodern sector include Bose, 1974; Mazumdar, 1975; Moser, 1978; and Tokman, 1978. Thedegree of competitiveness between intermediate and modern sector products depends on how,strictly quality differences are considered. In practice, small-scale firms may produce a lower-quality product that fulfils the same function for lower-income consumers as does the higher-quality product of a modern factory for upper-income consumers (e.g., furniture, clothing,beverages). Even if the products of the two sectors are not presently identical, they may beconsidered substitutes in terms of satisfying the needs of the population or in terms of theirpotential (Nihan et al., 1979). To the extent that different sectors satisfy needs of differentincome groups, sectoral bias of policies has important income distribution implications.
3 Byerlee et al., 1979; Child, 1977; Liedholm and Chuta, 1976; Mazumdar 1976; Morawetz,1974; Steel, 1977; Steele, 1975.
426 SM.ALL ENTERPRISE DEVELOPMENT
this explanation would apply only if small-scale labor-intensive techni-ques have recently been rendered obsolete by capital-intensive methods thatcapture economies of scale. The traditional method could compete for sometime with new investment because its capital costs are sunk rather thanvariable. The limited direct evidence available on this hypothesis suggeststhat increasing returns to scale are insufficient to explain large-scale/small-scale differences, and that firms of different sizes and capital intensitiesco-exist because of different relative factor prices (Byerlee, et al., 1979; Ho,1980). In any case, the existence of economies,of scale would not warrantpolicies that discriminate against (or favor) SSEs. Small-scale production thatis inefficient at all factor prices would soon be driven out, and should not besubsidized.
2. Segmented capital markets
Capital markets are commonly segmented in LDCs both in terms ofaccess to credit and its cost.4 Credit from "modern" financial institutions isgenerally available only to large investors with established credit experience.Small-scale investors must rely on "traditional" sources, especially personaland family savings, and to a lesser extent cooperative credit/savings schemesand money lenders. The limited availability of such savings and credit forcesthem to economize on capital. Others (especially farmers) who are unable togenerate personal savings and who are not known to moneylenders assuitable risks have no source of capital other than credit from suppliers ofgoods.
The official cost of institutional capital is usually held low as a stimulus toinvestment, thus favoring intensive use of capital relative to other factors byborrowers from financial institutions. The high opportunity cost of personalsavings (as well as high interest on loans from moneylenders) relative toregulated interest rates, on the other hand, further encourages conservationof capital in small firms. Interest rates generally range from under 10 percent per annum for official institutional loans, to an average for the unor-ganized money market around 25-35 per cent, to 100 per cent or more forshort-term moneylending. 5 Segmentation persists in spite of these differen-tials because the unorganised money markets are highly localized and thereis little penetration of financial intermediaries that could mobilise availablesavings for use by organised investors, so that there is no link between loanrates and deposit rates.6
Policies that create or reinforce segmented capital markets tend to biasthe investment decisions of large firms toward capital-intensive products and
technology ly lowering their cost of capital relative to its opportunity costand relative to labor. A policy of raising the official interest rate is oftenrecommended to induce more efficient use of resources and shift demandtoward labor. The success of this approach may, however, be inhibited bystructural segmentation and by other price distortions (Abdi, 1978; Berry,1978). Another approach is to stimulate SSEs, which are observed to berelatively labor-intensive. The labor intensity of SSEs, however, is itselfachieved within the context of the original segmentation and interest ratedifferentials. Hence, whether policies to expand SSEs represent appropriatecorrective measures depends on what instruments are used. Analysis of theimplications of such policies for capital and labor flows and productivitymust incorporate the capital market segmentation observed to characterizeLDCs.
3. Labor market segmentation
The existence of a wage gap between the modern sector and the informalsector is well documented in the literature on labor markets in LDCs.7 Therange of wages outside the modern sector is wide (Sabot, 1977), but theevidence suggests that the average wage for unskilled workers in small-scalefirms is on the order of half that in large firms.8 The fact that the modernsector wage is consistently above the minimum wage while small-scale wagesare frequently below it indicates that this gap is at least partly attributable toinstitutional factors.9 The visibility of large firms makes them subject tominimum wage requirements, union demands, pressure to appear progres-sive, and other institutional determinants of wage structure. Smaller firmscan more readily escape regulation, and their wages are more likely torespond to excess labor supply by falling. The evidence is increasingly clearthat workers find permanent employment in the latter firms, rather thanregarding them as a temporary transition to modern sector employment.10
Segmentation can persist because large firms are reluctant to risk payingillegally low wages, and because the wide range of opportunities in self-employment enables some people to earn more than they would in the
I See for.examply Berry, 1978; Berry and Sabot, 1978; Breman, 1976; Knight and Sabot,1980; Mazumdar, 1976; Morawetz, 1974; Page, 1979; Tidrick, 1975; White, 1978.
8 A wage for unskilled workers in the small-scale sector of about 50 per cent of that in thelarge-scale sector is reported by Byerlee, et al. (1979), Mazumdar (1979), and Page 1979. Steel(1977) finds that workers in small manufacturing enterprises without full-time non-family wageworkers earn about 54 per cent of the median wage in large-scale firms with 10 or more employeesin Ghana, while the median wage in small-scale firms with 1-9 employees is 86 per cent of thatin large firms. Child (1977) similarly finds a wage gap between the intermediate and modernsectors in Kenya, with approximately two-thirds of the Kenyans employed in the modern sectorearning more than the median wage of semi-skilled intermediate sector workers.
9 Other explanations (besides the argument that labour is heterogenous) that have someempirical support are returns to education and experience (Mazumdar, 1978) and the lowersupply price of migrant workers found disproportionately in small firms (Mazumdar, 1979).
10 Breman, 1976; J. Harriss, 1980; Knight and Sabot, 1980; Mazumdar, 1979; Nihan, et al.,1979; Sabot, 1977.
428 SMALL ENTERPRISE DEVELOPMENT
modern sector. In addition, a portion of non-modern employment is pro-tected by barriers to entry, and workers obtain some degree of job securitythrough dependency relationships (apprenticeship being the most commonexample).
Labor market segmentation pala.lels capital market segmerntation andreinforces the factor price differentials that tend to make capital/labor ratiosrise with firm size. The model that follows incorporates both types ofsegmentation, but focuses on capital market segmentation, which is gener-ally seen as the more significant and interesting policy variable. There islittle evidence that elimination of minimum wages would greatly affect wagegaps or technology choice. Nevertheless, it must be remembered thatremoval of distortions in both factor markets is necessary to achieve unam-bigously desireable results (Berry, 1978).
Urban sectors: modem, intermediate, residual
In order to analyze the implications of capital market segmentation and ofpolicies to offset it, two divisions of productive activities are necessary. First,those activities that require fixed capital investment must be distinguishedfrom those with negligible capital requirements. Second, capital-using in-vestments must be divided into those that do and do not have access tolow-interest official capital.'" Recent studies of urban labor markets haveemphasized the superiority of this three-sector approach over the dualisticmodel."2 The "modern-informal" dichotomy does not adequately representsmall firms that are on more labor-intensive portions of the same productionfunction as large firms. "Informal" is associated primarily with easy-entryactivities in which surplus urban labor can gain an income without substan-tial capital or skill requirements, and which therefore tend to be over-crowded and unproductive.' 3 In our model, capital is a barrier to entry thatseparates these activities from those that combine labor more productivelywith capital-the exact relationship depending on policies affecting supply ofcapital and demand for output.
"1 This borderline between the large-scale and small-scale sectors in the model thereforedepends on policy as well as on the nature of firms. A number of countries (e.g., India,Cameroon, Morocco) have introduced new institutions or regulations to channel capital to smallenterprises that previously lacked access to official capital. Although these policies sometimesinvolve introduction of new capital into the economy (notably from the World Bank), they donot resolve the large difference in cost of capital to borrowers from official and non-officialsources and they cannot meet the needs of all small-scale entrepreneurs desiring to undertakefixed investment. Hence, the analysis of the model still applies, even if the composition of thesectors changes.
" The ILO (1972) report that helped popularize the term "informal" used it partly toemphasize the potential productivity of certain activities outside the modern sector, and mostusers recognize the diversity of activities included. In a dichotomized model, however, thecharacteristics of the opposite extremes are inevitably attributed to the two categories.
W. F. STEEL AND Y. TAKAGI 429
Although these distinctions apply within both urban and rural sectors, ourmodel focuses on urban production and employment. It is consistent withmodels of the Harris-Todaro type, enabling us to show that their policyconclusions are significantly altered by the introduction of SSEs. The large-scale sector (LSS) has access to official institutional capital and pays aninstitutionally-determined wage (wn).`4 The residual sector represents theinformnal sector defined strictly to have no fixed capital requirements (orother significant barriers to entry) and a wage determined by the averageproduct (so that marginal product can fall to zero).' 5 The small-scale(intermediate) sector falls between these two, with capital requirements(fixed assets or investment in human capital) but no access to low-interestinstitutional credit and with a market-determined wage based on the margi-nal product of labor. Although conceptually clear, these borderlines markpoints on a continuum, and operational definitions for empirical work mustdepend on observable differences and local policies regarding capital re-quirements and accessibility. The labor market assumptions also represent asimplification; in reality, the most appropriate operational divisions bylabour market criteria may not correspond to those for the capital market.
where the sectors are 1 = large-scale, 2 = small-scale, 3 = residual, 4 =unemployment, and U= urban; X= production, N= employment, K =
capital (fixed assets), T = technology (given), w = wage rate, and P = price ofoutput.
Profit-maximizing behavior is assumed for both the large and small scale,sectors, so that equilibrium ratios of factor marginal productivitic-s (MPK=
14 R. A. Berry's (1978) model using these assumptions shows that low-cost capital availabilityto a limited group of firms diminishes output and demand for labor through excessive expansionof these firms into the decreasing cost range.
15 This sector corresponds to the traditional sector (agriculture) in a Lewis-type model. Harrisand Todaro (1970) treat all non-modern activities with unemployment.
430 SMALL ENTERPRISE DEVELOPMENT
fK, gK; MPL=fN, gN) equal the ratios of capital costs (k) to wages:
Profit maximization
Large-scale f-- -l (9)fN WI
Small-scale gK 2 (10)gN W2
Segmented capital markets are represented by assuming a given officialinterest rate to the large-scale sector such that k, < k2.'6 The resultingdifference in relative factor prices gives a lower equilibrium MPL and higherMPK in the small than the large scale sector, consistent with the observedrelationship.
We focus on the employment decision of labor (assumed homogeneousand unskilled), first among urban sectors and then including the rural/urban(migration) choice. In equilibrium, the expected value of income E(Y) mustbe equalized between unemployment and the small-scale and residualsectors: 17
E(Y 2 )= E(Y 3 ) = E(Y4) (11, 12)
Open unemployment exists in equilibrium if workers have a higherexpectation of obtaining LSS employment if they remain unemployed than ifthey are working."5 Taking into account the probability pl,j that a worker insector i will get a modern sector job, the present discounted value (at rate r)of expected income may be represented generally as:
Realilstically, the probability of employment in a large-scale firm is afunction of the size of the LSS and the number of available workers:
16 An equivalent approach would be to fix the amount of capital allocated to the large-scalesector (KJ)'7 Labor is completely free to enter the residual sector, by definition. Factor substitutability isassumed in the small-scale sector, so that unskilled workers can find employment there (at adiminishing wage), even though the capital investment barrier may prevent them from enteringas entrepreneurs.1' A positive relationship between probability of employment and time spent in job searchgives this result (see Feldstein, 1973, and Eaton and Neher, 1975). Educated labor forceentrants may also refuse employment that is below their expectations (which may later berevised). Furthermore, unemployment is rational even if job search does not raise probability ofemployment as long as enough support is available (from relatives, friends, or unemployment
benefits) and the leisure time provides more utility than does working.
W. F. STEEL AND Y. TAKAGI 431
P1,4 = p(nl), where n1 = N/INu."9 For simplicity, the probability of enteringthe LSS through the small-scale and residual sectors can then be representedas a proportion (a) of the probability for the unemployed:20 P1,2 = P1,3=
ap1 ,4. Using a two-period model for convenience, we have:
E(Y) = + -W! + apw w i=2 3 4 (13' 14' 15')
p= p(nl) (16)
Substituting equations (13'), (14'), and (15') in (11) and (12) and assumingthe unemployment wage W4 = 0:
(+1 + r) 2 + 1+r Wm = 1± Wm (11')
( 1± + r)W 3+ Wm= PWm (12')
l9 The total supply of workers seeking urban modern sector employment is presumed to beN2 + N3 + N4. The rates at which new modern sector jobs open up each period is defined as thenet of turnover (through firing, retirement, and death) plus output growth minus productivitygrowth. The probability of an unemployed worker obtaining such a job is a function of the ratioof these variables:
PI,4 = (N+ N3 + N4)
Substituting from equation (4) and dividing through by N,:
+(sn,
or if s is assumed to be constant:
P, 4 = p(n,), p' >.
This latter formulation is used for simplicity, although the impact of policies that affect s couldalso be investigated. For detailed discussion of different models and formulations of thisprobability, see Collier, 1975; Harris and Sabot, 1978; Harris and Todaro, 1970; and Stiglitz,1974.
20The probabilities could be differentiated between the small-scale and residual sectors.Small-scale employment is sometimes viewed as a conduit to the LSS by providigg experienceand training that make workers more valuable to modern sector employers than unemployedvworkers. SSEs may also include former LSS workers who have gone into business forthemselves, but who would have a relatively high probability of re-entering the modern sector,in view of their experience. The expectation that SSE training enhances future job prospectsexplains why many people are willing to become apprentices for very low renumeration (oreven for a net payment to the master). In order to abstract from training and skill effects,however, we are here assuming homogeneous labor and equal probabilities of LSS employ-ment. The implication of equations (11') and (12') then is that w2 = w3.
The training effect of SSE employment could also be introduced to give its workers a higherprobability of large-scale employment than the unemployed (a = 1). On the other hand, whereemployment exchanges do not work efficiently, inemployed workers have the advantage ofbeing able to devote more time to job search. Again abstracting from skill differentials, weassume that the latter effect dominates, so that a < 1, Note that this is a necessary condition foropen unemployment to exist in equilibrium.
432 SMALL ENTERPRISE DEVELOPMENT
At this point, we have a closed urban model for a given Nu." Morerealistically, the urban labor supply Nu is a variable, with migration occurringwhenever the expected value of rural income E(YR) plus migration costs Cis below the expected value of income in any of the urban sectors:22
E(Y2 ) = E(Y3) = E(Y 4 ) s E(YR) + C (11, 12,17)
Nu+NR=N (18)
where VR = rural labor and N= total labor (given). For simplicity, weassume a given rural wage WR and a perfectly elastic supply of labor at thatwage,23 or in a two-period equilibrium:
2+r p2+r WR+C = 1 Wm (17')1+r 1 +r
We now have an open urban employment model of the Harris-Todarotype, with small-scale and residual employment represented explicitly.24 Theequilibrium configuration is shown in Fig. 1. The shaded areas representtotal production in each sector; urban surplus labor is assumed sufficientlylarge to have MPL3 to zero.
Effects of policies to promote sectoral expansion
The model permits analysis of the implications of various policychanges:2 5 in demand (e.g., due to income redistribution; represented in the
22 The model has a recursive structure: equations (1). (6) and (9) determine N1, K1 , and X1;these determine K2 and p through equations (5) and (16); these in turn determine w2 and W3through equations (1 1') and (12') and then N2 and N3 through e,'iations (7) and (8); theremaining variables, X2, X3, N4, and k2 are determined by equations (2), (3), (4) and (10). P3is set = 1, and everything else is given. Equations (13')-(15') have been dropped by substitutioninto (1 1)-(12). If wvR, C, Wm and r in equation (17') are unchanged then p is determined and n1in equation (16) does not change. Since n1 = N1/N,, then Nu must increase (through rural-urban migration) whenever N1 does, to maintain this ratio.
22 Potential migrants are implicitly assumed to have accurate information on urban jobprospects, and to expect to be unemployed or engaged in the small-scale or residual sectorbefore entering the modem sector. If potential migrants base their expectations principally onthe modern sector wage and overestimate the probability of obtaining it, then the migration-stimulating effects of LSS expansion are increased, while SSE expansion is even less likely tohave an effect. Equation (17) may involve an inequality in equilibrium because return migrationdoes not occur unless E(Y4) + C> E(Y 4).
23 Rural labor is treated as earning WR with certainty and as having access to modern sectoremployment only by moving to the city. Under the assumptions used here, probability is afunction of the size of the modern sector (equation (16)). A rise in expectations or inaccurateinformation flows could have the same effect.
The rural sector could be articulated through equations corresponding to (1-3) and (6-8),representing modem plantation agriculture; market-oriented farming (or nonfarm intermediateproduction, i.e., Hymer and Resnick's [1969] z-goods) with positive marginal product; andsubsistence-type farming with income-sharing arrangements and negligible marginal product oflabor. Migration would then raise rural wages and result in output losses that would offset gainsfrom urban expansion. in the analysis, however, agriculture is treated as if it were entirelysubsistence with surplus labor.
24 The structure is as described in footnote 21, except that p is now determined by equation(17'), Nu by equation (16), and NR by equation (18).
2 5 See Appendix with mathematical presentation of the comparative statics.
W. F. STEEL AND Y. TAKAGI 433
Outputvalue
P Awlin
W2 w3 Cc{ E(Y4=)-E(Y 3 )>E(Y,)
E(Y,R)
___ ___ ___ ___ ___ ___ L abor
( T S F R O
Large Small Residual Unem- Ruralscale scale (N3) ployed (NR)(N,) (N2 ) (N4)
FIG. 1. Static equilibrium of urban three-sector model
model by relative price changes); in the interest rate; in capital allocation(e.g., social overhead capital); and in technology or management (rep-resented by T).
An increase in demand for LSS products translates into increased demandfor labor and capital through the initial rise in the values of their marginalproducts that results from a higher product price, given a fixed minimumwage and interest rate. An increase in large-scale employment raises theprobabil -y of modern sector employment and therefore generates expe tedincome differentials both within the urban sector [E(Y4) rises more thanE(Y2) or E(Y3)] and between urban and rural areas. Rural-urban migrationoccurs until the probability of modern sector employment returns to itsformer level.26 Residual sector employment also returns to its original level,as a result of this migration, after an initial outflow to the large scale sectorand/or unemployment. The LSS's increased demand for capital, however,reduces capital available to the small-scale sector and leads to a contractionin its employment and output.27 A net decline in marginal product of bothcapital and labor results.
The initial job-creation from expansion of the LSS is more than offset byrural-urban migration and contracted SSE employment, so that unemploy-ment actually increases, In a dualistic model, this "Todaro paradox" can beresolved only by lowering the minimum wage or by direct restrictions, bothgenerally unacceptable to J;DC politicians. A demand shift toward the
2 6 This result follows from the assumption of perfectly elastic supply of rural labor; otherwise,the new equilibrium could be reached at a higher p.
27 This contraction is even greater if the large-scale demand increase comes at the expense ofsmall-scale demand (i.e., P2 falls). The likelihood that unemployment will increase is alsoenhanced.
434 SMALL ENTERPRISF. DEVFLOPMENT
residual sector (represented by a decrease in both P1 and P2) offers littlepromise: its increased employment comes at the expense of some LSSemployment and possibly even some SSE employment (unless capital re-leased from the LSS more than offsets the fall in VMPL2 associated with adecreased P2), while LSS (and possibly SSE) production falls with nooffsetting increase in residual sector output.
An increase in demand for (price of) small-scale sector products, however,raises its marginal product of labor and creates an expected income differen-tial between it and both residual employment and unemployment, withoutaffecting the rural-urban differential.28 Workers therefore shift into SSEsfrom residual employment (causing a temporary rise in that sector's wage)and from unemployment. Unemployed also move into residual employmentuntil its wage returns to its former level. MPK2 and k2 rise in the small-scalesector while MPL2 falls, heightening incentives to conserve capital by usinglabor-intensive methods. Small-scale output increases without any offsettingreduction, and unemployment decreases.29
The effects of different policy variable changes on output and employmentare shown in Table 1. The impact of improvements in technology ormanagement (T) in each sector on output and employment correspond tothose of increases in demand, as does reduction of the interest rate facingthe LSS (or an increase in capital allocated to it). Reducing the interest rate(or raising capital allocation) to SSEs is not a direct policy option in theoriginal model, but can be accomplished indirectly by raising the interestrate or reducing the capital allocation to the LSS (col. 2).
A direct policy of low interest or increased capital to SSEs can beintroduced by increasing the total supply of capital-e.g., from an interna-tional loan for re-lending to SSEs. Although qualitatively similar to in-creased demand in its output and employment effects, this approach haslimitations because the lower cost of capital reduces SSEs' incentive tosubstitute labor for capital and because it does not provide increaseddemand to absorb the additional supply.30
Analysis of the trade-off
The effects of policies to promote the LSS and SSEs can be compared toanalyze the conditions under which an employment-output trade-off occurs.Policies may be defined as comparable or equivalent when they result in thesame additional capital invested in a sector. Under the assumptions of the
28 This is based on the assumption that potential rural migrants respond to the probability ofmodern sector employment only. If they instead react to average urban income, small-scalesector expansion would have some effect on migration, albeit much less than a comparablelarge-scale sector expansion.
2 9 These effects are enhanced if the increase in SSE demand comes at the expense of demandfor LSS products, although there is some offsetting contraction in LSS output and employment.
30 I.e., if demand is not perfectly elastic at P2, then P2 must fall, which reduces the totalimpact on SSE expansion and employment.
W. F. STEEL AND Y. TAKAGI 435
TABLE 1
Effects of policy changes on output and utemployment
Sector directly affected by the policy measure:Large-scale sector Small-scale Residual
Outputc dX1 > O, dX2 < od dX1 <O, dX 2>0 dX 1 =O, dX2 >0 dX,<O,dX2 ;-0OUnemployment dN4 >O dN 4 §O dN 4 < O dN4 Z O
a An improvement in technology or management in the residual sector raises X3 (in existingproduction, even though marginal product of labor is nil), increases N3 , and reduces N,; othervariables are unaffected.
b Not a policy variable in the original model, but may be introduced by increasing totalcapital without making it available to the LSS.
I Residual sector output does not change. Agricultural output is also assumed to beunchanging.
d if total capital is increased by the same amount as the increase in K1, then dX2 = 0.
model, LSS expansion increases unemployment as well as output. Introduc-tion of a small-scale sector in the model potentially resolves this conflict.That is, under certain conditions a policy favoring expansion of SSEsgenerates more output than a comparable policy favoring expansion of theLSS (quadrant a in Table 2 and Fig. 2a), as well as reducing rather thanincreasing unemployment. Net output from a given increase in investmentcan be higher for SSE than LSS expansion because of the offsettingreduction in SSE output under LSS expansion and because of changes inlabor productivity with increased employment. In general, this result is morelikely: the closer is SSE marginal product of labor and capital to that in theLSS; the slower MPL in the LSS rises with increased capital; the moreresponsive is the expected probability of modern sector employment (andhence migration) to LSS expansion; and the slower MIL in SSEs falls withincreased employment or decreased capital. Considerably less likely is theprospect of LSS dominance (quadrant d), which requires unresponsivemigration, weak labor absorption in SSEs, and high labor absorption in LSSfirms-inconsistent with policies biased toward capital-intensive LSS invest-ment. The likelihood that comparable policies would generate greaterunemployment absorption in the LSS than in SSEs may be similarly dis-counted (quadrant c). Both c and d are inconsistent with the assumptions ofthe model.
436 SMALL ENTERPRISE DEVELOPMENT
TABLE 2Comparison of policies to expand large and small scale sectors
Net impact of policies on unemployment (dN4)
LS Difference LS DifferenceNet policy impact on outcomea (LS_SS)b outcomea (LS SS)boutput value
(P1 dX, + P2 dX,): - -+ +difference (LS-SS)b
+ (d) LS policy superior (b) Trade-off:in both output and LS policy maximizesemployment effects output
SS policy minimizesunemployment
- (c) Trade-off: (a) SS policy superiorSS policy maximizes in both output and
output employment effectsLS policy minimizes
unemployment
a LS outcome=result of policy promoting the large-scale sector. Under the strictassumptions of the model, net output and unemployment both increase (quadrants aand b). The unlikely possibility of large-scale expansion reducing unemployment is alsoincluded to allow for different assumptions and for completeness (represented by curveE0 m' in Fig. 2).
b LS-SS = effect of policy promoting the large-scale sector minus effect of equivalentpolicy promoting the small-scale sector. These policies may be any of those listed inTable 1; they are considered equivalent when they result in the same additionalinvestment in a sector. The net output increase from a policy favoring the LSS may beless than that from an equivalent SS policy because of indirect effects on other sectors.The relationship between equivalent LS and SS policies may change as the scale ofimplied investment increases because of differential rates of change in capital and laborproductivity.
The presumed trade-off between maximizing output through LSS promo-tion and absorbing labor through SSE expansion is represented by quadrantb (Table 2 and Fig. 2). This situation occurs when the net output increasefrom expanding the LSS exceeds that from an equivalent policy favoringSSEs, while the LSS policy worsens unemployment (mb in Fig. 2a) orabsorbs less than does the SSE approach (mb). This outcome requires asubstantial differential of factor productivity in the LSS over the SSE sector.
Conceptually. the choice between two mutually exclusive policies involv-ing a trade-off can be made on the basis of a social welfare function. In Fig.2, the LSS policy represented by ml is above the indifference curve (UI)through the equivalent SSE policy equilibrium (s,) and is therefore superior,whereas mb is inferior. More interesting and realistic is the choice of anappropriate combination of policies when simultaneous expansion of bothsectors is possible: e.g., if additional capital is to be made available, or if
EO= initial equilibrium.s= new equilibrium from a given policy to expand the SSE sector.ma., m, mb = alternative new equilibria from an equivalent policy of LSS expan-
sion, representing SSE dominance (quadrant a), no trade-off, and employment-output trade-off (quadrant b), respectively. Prime indicates a new equilibriumfrom LSS expansion with the same output increase but with decreased instead ofincreased unemployment; the expansion path E,m' requires flexibility in WR (orW-).
demand for both sectors can be stimulated to different degrees. A trade-offfrom capital expansion is especially likely if MPK in the SSE sector fallsrelatively rapidly as larger amounts of capital are added, so that the slope ofthe SSE expansion curve E,s falls faster than does the LSS curve Eom orEom'. The range of choice is then represented by the curve slmb in Fig. 2b.A higher level of social welfare (U1n) can be attained by the combination ofsectoral expansion represented by the tangency point E* than by a policyaimed at one sector alone.
Policy conclusions
A model with an intermediate, small-scale sector explicitly rejects thedualistic model common in the literature on modern and informal sectors.Capital market segmentation can be introduced by assuming that SSEs lackthe modern, large-scale sector's access to low-cost institutional capital butrequire a minimal capital investment. The barrier to entry represented bythis fixed capital requirement distinguishes SSEs from easy-entry informalactivities that provide income to the residual labor force. Differential accessto capital is shown to be sufficient to explain observed associations betweensize and capital intensity or productivity.
Harris-Todaro type models imply that modern sector wage reduction isnecessary to avoid the paradox that urban job creation only stimulates more
438 SMALL ENTERPRISE DEVELOPMENT
unemployment through migration. Analysis of our model, however, showsthis conclusion to be dependent on dualistic assumptions. Policies to expandthe SSE sector can generate more output as well as more employment thancomparable policies promoting the LSS, provided that marginal product oflabor is reasonably high in SSEs and that migration is relatively unrespon-sive to SSE growth.
Improvement of demand conditions for products of SSEs provides aparticularly promising means of absorbing labor productively while maintain-ing output growth. Demand-oriented policies generate upward pressure onthe value of labor's marginal product in SSEs while maintaining theirincentive to use capital efficiently. Income redistribution in favor of lower-income groups that have a high propensity to consume SSE products is themost general demand-oriented policy. Elimination of taxes, duties, and feespaid by SSEs can improve their ability to compete with larger ones (whichfrequently are granted exemptions). In practice, however, such measures arelikely to benefit less productive residual activities as well as SSEs, therebyreducing the net output gain for a given employment absorption. Demandcan be targeted more specifically at SSEs by restricting the expansion of (oravciding subsidies to) large-scale producers of goods that compete directlywith small-scale production.
The appropriate policies with regard to capital are to facilitate linkagesbetween organised and unorganised money markets and to raise its cost tothe LSS, thereby encouraging more efficient use of capital while improvingthe ability of SSEs to compete. Subsidization or direct allocation of capital toSSEs has several important drawbacks. First, a limited capacity of thesmall-scale sector to absorb official capital means that actual output genlera-tion may be less than expected on the basis of average capital/output ratios.In particular, providing industrial estates or other infrastructure for SSEsimmediately raises their overall capital/output ratio, offsetting their advan-tage in conserving capital. Second, supply-side assistance does not ensure amarket for increased intermediate sector output; demand is not likely to beperfectly elastic, as implicitly assumed in the model. Finally, capital assis-tance for investment (as distinct from working capital) risks replacing thepersonal savings predominantly used to finance small investments. Inter-mediate technology development, management assistance, and accessibilityof raw materials are supply-side policies that should be explored as alterna-tives (or complements) to capital assistance.
In evaluating the ability of SSE promotion to resolve the employment-output conflict involved in LSS expansion, research should focus on thie twosectors' relative labor productivities and importance to potential migrants.Further research is also needed on the small-scale sector's ability to absorbadditional resources, its degree of substitutability for other sectors' products,its input-output interrelationships with other sectors, its reinvestment ofprofits, and other dynamic considerations. The model presented in thispaper shows the importance of introducing an intermediate small-scalesector into the modern-informal framework for policy analysis and for
W. F. STEEL AND Y. TAKAGI 439
understanding the appropriate long-run balance between large-scale, small-scale, and residual sources of employment.
African Development Bank, Ivory CoastDoshisha University, Japan
APPENDIX. COMPARATIVE STATICS
The equations of the model may be grouped as follows:Grouip A determines N1, K1, X1, and p,
XI = f(N1, Kl, T1) (1)
PfN = wm (assuming w, - w,,,) (6)
k, = PlfK (substituting (6) in (9)) (9')
PWm 2 + r +C (17')1+r 1+rW+
Group B and the above deter-mine K2, w2, W3, and Nu:
K2 =K-K1 (5)
W1+1 mp p( a)m (11')
+r) W3 = m (12')
-P(!=PNIlNU) (16)
Group C and the above deterrrine N2 and N3:
W2 = P2gq(N2 , K2, T2) (7)
W3= h(N3, T3)/N3 (8)
Group D and the above determine X2, X 3, N4, k2, and NR
X2 = g(N2, K2, CT2 ) (2)
X3 = h(N3, T3) (3)
N4 = Nu-N-N 2 -N 3 (4)
k2=P 2gK (substituting (7) in (10)) (10')
NR=N-Nu (18)
1. Increase in P1 (the relative price of X1 in terms of X 3)
From Group A, given no change in the given k, and wi;:
0 = dP,fN + P,fNN dN, + PlNK dK,
0 = dP,fK + P1fK, dN, + PjfK dK,which gives:
dNl 1 (NfKK- fKfNK) p > O
-IHI ++ p P
-1 )dP1 >d = (fKNN1-fNfKcN)
IHI +P 1
440 SMALL ENTERPRISE DEVELOPMENT
where
IHI = fN fNiK >0 from the sufficient condition for the existence of maximum profit.IfKN &Ks
Further:
dXl=fN dNI+fK dK 1 >O
dp = 0 (given no change in w,,, or wR)
From Group B:
dK 2 = -dK1 < 0
dw2=dw3 =0 (given no change in wm or p)
dNu =-pN, dNl/pNU > 0+ + -
From Group C (given no change in w2 and W3):
dN2 =-gNK dK2 /gw<O+ --
dN3 = N3 dw3/(hN-w 3) = 0From Group D:
dX2 = gN dN2+gK dK2 <0+ - + -
dX3 =hN=dN3 0
dN4=dN, -dN -dN 2 -dN 3>0
+ - 0 [Note: dNu-dN 1 = (1-n) dNu > 0
dk 2 = P2gKN dN 2 + P 2ggK dK 2, -0 °+ - - - where n, < 1 and constant for
dNR -dNu<0 given w,, CWm, r
2. Increase in P2 (the relative price of X2 in terms of X 3 )
Groups A and B are unaffected by a change in P2, so there is no change in N1, K1, X1, p, K2,W2, W3, anld Nu. From G-roup C:
dN 2 =-gN dP 2 /P 2 gNN> 0
+ + -
dN 3 =0 (given no change in w3)
From Group D:
dX2 = g, dN2+gK dK2 >0+ + + 0
dX 3 = 0
dN4 = dNu - dN1 -dN 2 -dN 3 <00 0 ±, 0
dk 2 =P2 gKN dN 2 +gK dP 2 >0
+ + + +
dNR 0°
W. F. STEEL AND Y. TAKAGI 441
3. Decrease in P1 and P2 (increase in relative price of X3)Changes are the reverse of the preceding two cases. From Group A:
dN 1<O
dK1 <O
dX 1<O
dp =O
From Group B:
dK 2>0
dw 2=O
dw 3 =0
dNu<0 (may be =0 if there are return migration costs and the decreasein urban expected income is small)
4. Improved T1 (technology or management in production of X1)
Assume Hicksian neutral technological progress so that:
X1 = Tlf(N, K1)
Wm r1 I luN
k= P1 TlfKFrom Group A:
0 = PIfN dT1 + P1 TJNN dN1 + P, TJfN dK1
= P1K dT1 + P1 TfKN dN + P TJKK dK1
which gives:
d N, = fH NKc-f-fKfNJ T>°+ - + +
dK 1 (fKfNN o fNfKN) dTi > fIHI 1,
The effects on the other variables are the same in sign as for an increase in P,.
442 SMALL ENTERPRISE DEVELOPMENT
5. Improved T2
Assume Hicksian neutral technological progress, so that:
X2 = T2g(N2, K2)
W2 = P2 T2 g
k2 = P2T2gK
Variables in Groups A and B and equations (3), (8) and (18) remain unchanged.From Group C:
dN2 =-gN dT 2/gwT 2 >0+ + -
From Group D:
dX 2>0
dN 4 = -dN2 < 0
dk2 = P2gK dT 2+P2T2 gKN dN2 > 0+ + + +.
6. Improved T3
Assume Hicksian neutral technological progress, so that:
X3 = T3h(N3)
W3= T3 h(N3)IN 3
Variables in Groups A and B and equations (2), (7), (10) and (18) remain unchanged.From Grouip C.
dN3 = h(N3) dT3/(VW3- T3hN) > O0 +
dN 4 = -dN3 < 0
7. Decrease in k,
From Group A:
0 = P1fNN dN, + P,fNK dK,
dk1 = P1JK, dNI + P1JKK dKI
which gives:
dN, = 1/ 11 (-dkItfiK) > O
dK, = 1HI1 (fN dk,) > 0
The effects on the other variables have the same sign as for an increase P1.
8. Increase in k,All signs are the opposite of case #7.
W. F. STEEL AND Y. TAKAGI 443
9. Increase in capital (K) allocated to the large-scale sector (K1)
From Group A:
dN1 =-fNK dKlIfNN > 0+ + -
dX, = fN dN, +fK dK1 > 0
dkl = PlfKN dN, + P1f&K dK, ; 0+ + -+
dp =0 (given no change in wm or wR)
From Group B:
dK2 = dK-dK1 = 0 (given that dK = dK1 )
dw2 = dw 3 = 0 (given no change in wm or p)
dN, = -PN dN,/pNU > 0,+ + -
From Group C (given no change in w2 ard W3):
dN 2 =-gNK dK 2 /gNN 0
0
dN 3 = 0
From Group D:
dX2 =dX3 =0
dN4 =dN,-dN1 20 (see case #1, Group D)
+dk2 =0
dNR =-dNJ <0
10. Increase in capital (K) with no change in sector 1 parameters:
Variables in Groups A and B remain unchanged, except equation (5):
dK4=dK>0
From Group C:
dN 2 =-gN4K dK 2/gNN>O+ + -
dN 3 = 0
From Group D:
dX 2 = gN dN 2 +-FgK dK 2 >0
+ + + +
dX 3 = 0
dN 4=-dN2 <0
dk 2 - P2 gKK dK2 <O
dNR = 0
444 SMALL ENTERPRISE DEVELOPMENT
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No. 295. RaKeesh Mohan, "The Morphology of Urbanisation in India," Economic and PoliticalWeekly
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