World Development, Vol. 19, No. 8, pp. 1075-1093, 1991. 0305-750X/91 $3.00 + 0.00 Printed in Great Britain. © 1991 Pergamon Press plc

Poverty and the Forward-Falling Labor Supply Function: A Microeconomic Analysis

M O H A M M E D SHARIF* University of Rhode Island, Kingston

Summary. - - Existing subsistence, efficiency, target income and limited aspiration theories impose a backward-bending labor supply behavior on poor workers in less developed countrics. Recent empirical studies of worker behavior in the unorganizcd sectors of LDCs contradict this view and report evidence of both a forward-falling and an upward-rising labor supply. This study formulates an increasing elasticity of substitution utility function model to analyze the observed behaviors. The function displays both nonhomotheticity and variable elasticity properties, and is capable of generating labor supply curvcs with forward-falling and upward-rising segments. While thc upward-rising supply is considered to be usual worker behavior, the forward-falling segment represents a below-subsistence distress sale phenomenon, and the subsistence income of the worker is implied to occur at the turning point joining the two scgments of the supply curve. Econometric estimates of the utility and the labor supply functions provide support to the theoretical results,

l. I N T R O D U C T I O N

Poor workers I in the unorganized sectors of less developed countries (LDCs) have been observed to increase the quantity of labor they

z supply as wage rates drop. Traditionally this behavior is treated in the literature as a pheno- menon of backward-bending supply. Conse- quently analyses based on the assumptions of "target income" (Berg, 1961), "'limited aspira- t ion" (Mellor, 1963), and "subsistence mental i ty" (Lewis, 1954) are put forward to explain it. Myint (1971) points out that "'forward falling in the downward direction" labor supply at low wages is not the same as "backward sloping in the upward direct ion" supply at high wages. Recent studies of the "working poor" employment prob- lem show that these workers "'involuntarily" engage in low paying but physically exhausting work for lack of better paying employment opportunit ies (Thorbecke, 1973). They have also been observed to work an average of 10-11 hours a day seven days a week (Farouk, 1980).3 In spite of these long work hours, they are found to earn incomes inadequate to satisfy their basic needs of subsistence (Thorbecke, 1973; Dandekar and Rath, 1970). Moreover , the large quantity of labor supplied becomes even larger as the wage rate declines. But the income earned by greater labor inputs at lower wages is reduced, showing a situation of "economic distress. "'4

This paper analyzes the observed forward- falling labor supply behavior characterized by economic distress. I develop a general theory of labor supply by specifying a nonhomothet ic utility function with a special structure. The fundamental characteristics of this utility func- tion are as follows: at survival levels, food and physical rest are consumed almost in a fixed proportion. As the level of survival improves to subsistence and beyond, food and rest become bet ter substitutes. People with high standards of living have the ability to substitute between food (and other goods) and rest (and other forms of leisure) without impairing their health or that of their families. Because elasticity of substitution increases monotonically along any ray from the origin, I call this function an "increasing elasticity of substitution" (IES) utility function. This IES function is flexible: by adjusting its parameters , it can be used to generate a wide variety of different shapes for the labor supply function. I

*An earlier version of this paper was presented at the 1987 Winter Meetings of the Econometric Society, December 28-30, in Chicago, I am grateful to Michael Manove, David Wheeler, Peter Doeringer, Paul Streeten, Pranab Bardhan, Amartya Sen, John Burkett, Gilbert Suzawa, Harold Barnett, and two anonymous referees for their valuable comments. I would like to thank Marjorie Blanch for suggesting improvements.

1075

1076 WORLD DEVELOPMENT

have used numerical methods of utility maximi- zation to derive the demand function for physical rest (and hence the supply function for labor) from the IES utility function.

The IES utility function is of interest because it can generate the specific labor supply function suggested in this study (see curve MNS in Figure 1 and its derivation in Figure 2). This labor supply function has a forward-falling section at low wage rates and an upward-sloping section at high wage rates. The subsistence-wage turning point provides the link between them. 5 While a reduction in wages on the upward-sloping section of this supply function indicates a reduction in the standard of living, a wage reduction on the forward-falling segment depicts physical im- poverishment for the workers and their family members. Thus the forward-falling supply im- plies that poor workers survive at different levels of physical impoverishment. Because the tradi- tional sector in LDCs is characterized by the absence of trade unions, 6 minimum wage legisla- tion and unemployment and other welfare benefits, the expansion of labor by the poor when their wages fall shows their attempt to maintain their minimum survival consumption of food. Attempts to maintain food consumption, how- ever, encroach upon the consumption of physical rest. Thus, a decline in the wage rate forces poor laborers to combine food and physical rest at a lower level of consumption. This means physical impoverishment in two ways: expansion of labor (hence a fall in the amount of rest) and a reduction in the consumption of food. The behavior of poor laborers under these circum- stances can be termed the distress sale of labor which is associated with the involuntary 7 sacrifice of physical rest.

I define the subsistence income of an indi- vidual as the minimum level of income that does not involve the distress sale of labor. Since the forward-falling segment of the labor supply curve involves economic distress and such distress disappears on the upward-sloping section, the turning point of the curve provides an estimate of subsistence - - the lowest income free of distress. This definition of subsistence is consistent with the common nontechnical usage of the word which implies a minimum standard of decent living in the society. The subsistence income of an individual defined in this way is a function of the individual's needs and preferences for food and rest. I believe that this view of subsistence is more useful than conventional definitions which are exogenous, determined either as scientific norms of nutritional needs, or as standards of social prescriptions (see Sharif, 1986). This endo- genization of subsistence implies that the method

can not only lead to an empirical determination of subsistence for individuals, but also it can reveal individual differences in their subsistence needs. Thus, identification of such incomes for different groups of people through an empirical estimation can provide very important guidelines for policies such as food subsidies, income maintenance, negative income taxation.

In Section 2, the relevant literature is reviewed and a case presented for the postulated labor supply function. The structure of the IES utility function is developed in Section 3. I have found a novel way of combining numerical utility- maximization techniques with a nonlinear esti- mation method in order to estimate empirically the labor supply function for poor workers. Results of these estimations are presented in Section 4. The Indian National Sample Survey (NSS) data on the time disposition and wage rates for landless and near-landless laborers have been used for this estimation. Estimates for all 12 sets of data for different sex, age and household groups provide strong support and the hypothe- sized labor supply function. The estimated labor supply curves for four of the 12 data sets are presented in Figure 3 for illustration. Implica- tions of the estimates for distress sale of labor and determination of subsistence are then dis- cussed; and the study is concluded in Section 5 with a summary of the main findings.

2. EXISTING LITERATURE AND FORWARD-FALLING LABOR SUPPLY

FUNCTION

Studies analyzing the labor supply behavior of assetless poor workers in LDCs assume a given subsistence (Lewis, 1954; Ranis and Fei, 1961), efficiency (Bliss and Stern, 1978; Mirrlees, 1975; Rodgers, 1975; Stiglitz, 1976), or target (Berg, 1961) income. This invariant income is the result of social provision, employer optimization or worker preference; however, all the theories imply a very high consumption of leisure by these workers. This high consumption of leisure is assumed to be the direct result of work-sharing in labor-surplus situations; hence the implication for a hyperbolic labor supply function given by K N R in Figure 1.

Serious shortages of labor at the peak of the agricultural season (Byerlee and Eicher, 1972; Lal, 1976), together with a very low unemploy- ment rate for rural labor households (Hart, 1980, 1986; Habibullah, 1962; Ahmed, 1981; Krishna, 1973; Cain and Mozumder, 1981), contradict the hypothesis of surplus labor. Furthermore, these poor workers have been found to have very little

FORWARD-FALLING LABOR SUPPLY 1077

S

iiiiiiiiiiiiiiiiiiiiiiiii! ii i i iiiiii i i iiiiiiiiiiii!iiiiiiiiiiiiiiiiiiiiiiii

w q - M

~iiiii~iiiiiiiiiiiiiiii~iiiiiiiiiiiiii~iii~i~i~iiiiiiiiiiiiiii~i~Miiiiii!~!~i~] Ls Lm

Labor supply

Figure 1. The forward-falling labor supply function and the subsistence theory of labor supply.

physical rest. In addition to the works cited in Section 1, other studies report very long hours of hard work by these workers (Habibullah, 1962; Hart, 1980, 1986; Cain, 1977; Cain and Mozum- der, 1981). The NSS data used in this study also show an average of 70 hours of work per week by adult males in both landless and near-landless households. The marked seasonal variation of the wage rate (Bardhan, 1979b; India, 1976a) and serious fluctuations in the indices of wages for agricultural laborers over time (Khan, 1977; Lal, 1976; FAO, 1974) fail to support the notion of an institutional wage rate required to offer workers a given subsistence income (Ahmed, 1981; Cain and Mozumder, 1981).

The strong evidence against this subsistence theory is, moreover, supported by the basic needs analyses that estimate the nutritional deficiencies of different categories of people in LDCs. About 48% of the total population in Bangladesh, India and Pakistan is in absolute poverty (Ahluwalia, 1979; World Bank, 1975; Khan, 1977; Naseem, 1977). 8 These people spend 90% of their total income on food and food preparation. Their attainment of calorie inake only, leaving aside the question of other nutritional and nonfood needs, however, ranges from 50%-95% of the official prescription of 2,248 kcal per capita per day (Dandekar and Rath, 1970; Khan, 1977 and Naseem, 1977). Both the serious deficiency in food intake and the wide variation in this deficiency for different households speak of something other than a given subsistence income.

Drawing on such empirical evidence, this study

contends that the forward-falling supply function lies somewhere in the shaded area below the curve KNR in Figure 1. Thus both rest and food are sacrificed at very low wages. One such curve is given by NM. 9 Including the above-subsistence segment of it, the complete labor supply function is given by MNS.

None of the existing theories of the negatively sloping supply function attempts to identify the lower and the upper limits of this function. Given the flexibility in the wage rate, none of the existing studies considers how far its downward movement will bring forth expansion in labor supply nor how far the opposite wage trend will continue to reduce it. In fact, the assumption that the wage rate is an institutional datum eliminates these questions altogether.

This study argues that the lower bound will be provided by the physical tolerance limit given by the point at which the wage rate is just sufficient to replace the additional expenditure of energy in work. The upper bound is set by the disappear- ance of the distress sale effect, and the earning of the subsistence income given by the area of the rectangle OW~NL~ in Figure 1.

Although there is no theoretical analysis in the existing literature to account for distress sales of labor, there is empirical evidence showing both negatively sloping and positively sloping supply functions (see note 2). Determinants of whether these functions are negative or positive are found to be the economic condition of the workers and the nature of the markets in which the workers participate. Within the traditional sector supply functions for poor workers have been found to be negatively sloping, while for relatively well-to-do workers they are positively sloping (Huang, 1976; Sharif, 1991). The supply function from the traditional to the modern sector, however, has been found to be positively sloping irrespective of the economic condition of the workers. The subsistence income point fit into this existing evidence establishes the missing link between them.

The only theory which recognizes the mini- mum survival requirement of income and physi- cal rest is that of Barzel and McDonald (1973). Incorporating asset income, they specify a utility function to generate different shapes for the labor supply function. Yet their formulation can generate the kind of labor supply function relevant for this study only when the elasticity of substitution between income and rest is greater than one and asset income is less than survival income. Moreover, Barzel and McDonald 's im- position of a larger than one elasticity of substitu- tion at and near the survival consumption is not a realistic assumption; nor do they explain why the

1078 W O R L D D E V E L O P M E N T

supply curve should turn its slope from negative to positive at a certain wage rate,

3. A N IES U T I L I T Y F U N C T I O N A N D A G E N E R A L T H E O R Y O F L A B O R S U P P L Y

As has been noted in Section 1, the consump- tion bundle of poor workers can be assumed to consist of only two commodit ies - - food F and physical rest R. Thus the utility function U I~ can be written,

u = U(F, R) (~)

Since the use of labor L is the only source of income F, the income constraint can be written as

F = W L (2)

where W is the wage rate in terms of food. The time constraint is given by

R = T - L (3)

where T denotes total t ime available for rest and work. Given the constraints, utility is maximized at

U ' ( R ) / U ' ( F ) = W (4)

It is hypothesized that at very low levels of consumption, there is little substitutability be- tween F and R. As a worker 's consumption level increases, however , the substitutability increases. At the limit, as the consumption level approaches zero, the elasticity of substitution between F and R approaches zero; the elasticity goes on increas- ing as F a n d R increase; and at the limit, elasticity approaches infinity as F and R become very large.

To design a utility function with these prop- erties, one can begin with an indifference map that approximates all the possible CES indif- ference curves, starting with Leont ief at the bot- tom, passing through Cobb-Douglas in the middle and approaching the linear function at the top. If one moves along a ray through the origin, a higher indifference curve shows a higher elasticity of substitution. In o ther words, given the propor t ion of the two commodit ies , a higher level of consumption will provide higher substi- tutability be tween them. This, in fact, explains the non-homothet ic i ty of the required utility function.

When an indifference map is constructed using unmodif ied CES indifference curves of increas- ing elasticity of substitution, the outer curves intersect the inner ones. To prevent this from happening, it is necessary to vary the elasticity of substitution along each curve. Thus, for a given

level of utility, a combinat ion of F and R is assumed to exist that shows the highest elasticity of substitution. As this combinat ion is changed in ei ther direction, substitutability decreases and, at the limit, approaches zero, implying that as one approaches the axes all indifference curves (in- cluding the linear ones) develop curvature and become asymptotic to the axes.

An appropriate mathematical form for the utility function (1) having these propert ies is developed in the following way. Beginning with a simple utility function,

U : ( F - ' + R - ~ ' ) tl/ ' t (5)

and

1

~ - 1 (~) O

where U is the utility, F food, R physical rest and ¢~ is the exogenous elasticity of substitution parameter , the IES function may be created by endogenizing o as the following function of F and R:

F R o - ( 7 )

F + R

Note that equation (7) is linearly homogeneous so that o increases linearly from zero to infinity along any ray from the origin. 1~

Having specified the general structure of the utility function, its proper parameterizat ion is now required. Since the units of measurement for F and R are different, appropriate normalization of F and R for this difference is necessary. Parameters c~ for F and [] for R can serve as the scaling factors, The most important function of these parameters is to determine how fast the elasticity of substitution changes in wlrious direc- tions. It is clear from equat ion (9) below that the larger the values for ~ and [3, the bigger is ~, and therefore , the smaller is ~. Thus, relatively large values for c~ and [:; imply that elasticity of substitution changes slowly, and subsistence is earned at a higher level of F and R than if they are smaller. Given the standard units of measure- ment of F and R, if c~ is relatively larger than [~, the function implies a higher consumption of food than of rest, and vice versa.~2 In addition, inclusion of the usual CES distribution parameter 6 for F and ( 1 - 6 ) for R will show the relative shares of F and R in the potential expenditure of the individual. Thus, our completely para- meter ized utility function is given by

U = [6(F/cz) ~ + ( 1 - 6 ) ( R / f ~ ) - " ] Iv-r') (8)

where

FORWARD-FALLING LABOR SUPPLY 1079

[3 F + ctR g - 1 (9)

FR

This IES function subsumes all the possible CES functions and displays both variable elasti- city of substitution and nonhomotheticity proper- ties. It shows that elasticity of substitution changes continuously from one consumption bundle to another throughout the relevant con- sumption set represented by the indifference surface. Here o is a function of both the level and the ratio in which F and R are consumed. Thus the IES function is a complete generaliza- tion of the CES functions with the Leontief function at the lower and the linear function at the upper limits. ~3

Because of the nature of the IES utility function, identification of its comparative static properties, as well as its associated demand functions for R and F in analytical forms, is not mathematically tractable.

It is quite possible, however, to identify these functions through a numerical procedure using Taylor series approximations to the first order conditions. Thus I derive an R demand function using an iterative numerical procedure to approximate the utility maximizing value of R, given the parameters of the utility function and the wage rate (see Sharif, 1989). For a given set of parameter values, determining the relevant utility maximizing values of R for different wage rates leads to a numerical specification of the demand function for R.

'°- i i / / \ \ \ s

', \ \

0 ~ L 0 0'.4 018 1'.2 1.6 2.0

Physical rest

Figure 2. Indifference map of the 1ES utility function and the derivation of the wage-consumption curve showing the relative strength of the negative substitution and the positive income effect of wage changes on the

demand for rest.

The indifference map of the IES utility func- tion (8) for parameter values of c~=l, [3=.2 and 6=.5 is drawn in Figure 2. The curve M N S traced through the points of equilibrium is the R demand function. I call it a "wage-consumption curve" as it shows the levels of consumption at different wage rates.

This wage-consumption curve M N S illustrates the relative roles of positive income effects and negative substitution effects. At point N where the worker is just making his or her subsistence of F and R and where the elasticity of substitution between F and R assumes the value of one, the two effects cancel each other. Below N on the M N segment of the curve where substitution elasticity falls below one, income effect domin- ates the substitution effect; consumption of both F and R declines with increased labor implying distress sales of labor; and the farther the worker is below N, the greater is the distress sale. Above N on the NS segment (with substitution elasticity greater than one) the substitution effect domin- ates the income effect, indicating higher stan- dards of living for the worker at higher wage rates. The function thus implies that while operating on the forward-falling segment, the workers' prospect of a better living is limited to reducing the extent of distress sale and earning their subsistence; however, on the upward- sloping segment this prospect is determined by the workers' awareness of a higher standard of living.

The requirement of physical rest is a function of food along with other variables - - a lower intake of food and hence a lower nutrition level increases the need for physical rest on the forward-falling segment of the supply curve. (As the need for food and rest increases and their affordability falls, the substitutability between them declines.) On the upward-sloping section of the supply curve, when nutritional needs are properly satisfied, the requirement for physical rest declines. Moreover, what the worker gives up on the upward-sloping segment is a voluntary transformation of leisure into income compared to what he or she sacrifices of physical rest involuntarily below subsistence. This view is supported by the fact that the elasticity of substitution between food and physical rest is smaller than, equal to and greater than one on the supply curve below, at and above the subsistence point, respectively.

The IES utility function (8) is sufficiently general so that it can generate labor supply functions with a wide variety of shapes. To show this, I have derived different wage-consumption curves by changing parameter values of the utility function (the only function that could not be

1080 WORLD DEVELOPMENT

generated was horizontal). A set of these curves is graphed in Appendix B. The forward-falling supply function is only one of these shapes; hence a general theory of labor supply is a better name for this analysis. H

4. ESTIMATION OF THE IES UTILITY FUNCTION

Given the impossibility of an analytical deriva- tion of a labor supply function from the IES utility function, I estimate the parameters of the utility function directly by using a numerical method and then construct the supply function from those estimates (see Sharif, 1989). The Indian National Sample Survey (NSS) data (India, 1976a) regarding the time disposition and wage rates of the poorest groups of the rural labor households are used for estimation. The survey provides information about two classes of households: landless labor households whose only source of income is the sale of labor, and the small farmer households comprising the poorest 10% of the rural households with cultivated lands. The main part of the income of these small farmer households, however, comes from their wages; therefore, a better name for them is near- landless labor households.

The survey was a two-stage stratified random sample - - the first stage being the villages and the second the households - - for both the strata. A total of 16,800 sample households for each stratum in 8,400 villages throughout India with a minimum of 720 households for each state ~5 were investigated. The sample households were, however, divided into four subrounds, each consisting of a minimum of 180 households for each state. The subrounds were four quarters of the year 1970-71 beginning July 1970.

Information was collected and published sepa- rately for individual members of the household in different sex-age groups. This study uses 12 sets of data relating to three age 1~' and two sex groups in both the household groups. Since the data are published in the form of state averages of the observations for the four subrounds, there are around 70 observations for each of 12 sex, age and household groups. 17

While the data used in this study are state averages, they are averages of individual obser- vations not those of the household. This is consistent with my analysis of the individual

18 labor supply function. Heterogeneity of house- hold labor is the reason for preferring the individual to the household as the unit of analysis. The different sex-age group workers are

hired for different specific types of activities and are paid distinctly different wage rates (Dasgupta, 1977; Connell and Lipton, 1977: Cain, 1977; Cain and Mozumder, 1981: and Hart, 1980, 1986). This evidence suggests that the labor supply functions of different working groups are different economic relations.

The estimation of equation (8) requires two variables - - real wage rate (RW) and labor supply (LS). NSS reports the daily nominal wages received by the workers, v~ These nominal wage figures are deflated by a food grain price index to derive a measure of RW. Since the cost of living indices for agricultural laborers reported by different states are not comparable across states, I have constructed the food grain price index comparable over time and across states by using the wholesale prices of two major food grains, rice and wheat. 2°

The investigation recorded the disposition in percentages of total time by workers during the reference week. The total labor supply variable LS is constructed using the workers' desired work-time given by their wage employment, self- employment and (involuntary) unemployment, e~ I have also constructed a market supply variable LSo by eliminating self-employment from LS. Plots of LS and RW show a distinctly common pattern for all 12 sets of data, but those for LS,, and RW show mixed and indistinct results. Because self-employment also generates income, the total supply of labor LS is expected to provide better results and is therefore used for estimation.

Using the observations on LS and RW 22 in a numerical procedure (see Sharif, 1989), esti- mates for equation (8) are derived for all 12 sets of data. The estimates are the final convergent values derived through iterations with different starting values for the parameters. Results are presented in Appendix A, Table A1. Almost all estimates are significant at the 5% level or above. Although only one explanatory variable (RW) is used, 23 the model explains over 84°/,, of the variation in labor supply for virtually all 12 sets of regressions. 24 Using these estimates, labor sup- ply functions are constructed. Six of the functions have both the forward-falling and upward-rising segments, while those remaining display the forward-falling section only. Functions for the four adult male groups, graphed in Figure 3 for illustration, show both forward-falling and upward-rising segments. The other two similar functions are those of the landless male children and the near-landless adult females of ages 45-59 years. Functions for the female children, the near-landless male children, the landless adult females of ages 45-59 years and all adult females

FORWARD-FALLING LABOR SUPPLY 1081

Equation (2) landless male adult

8- Ages 15-44 years

7-

°- / 5-

4. ( 3-

1 ~ o.75 o.~ o.~5 o.9o o.~5 l.bo

Labor supply

-d

Equation (3) landless male adult

8- Ages 45-59 years

6-

5-

4-

3-

1 0.75 0.~0 0.~5 0.b0 0.~5 160

Labor supply

g-

7-

6-

5-

4-

3-

2-

Equation (8) near-landless male adult

Ages 15-44 years

| i I

0.75 o.~ 0.15 0.9o 0.95 1.~ Labor ~pply

Figure 3. Estimated labor

Equation (9) near-landless male adult

8- Ages 45-59-years

6-

5-

4-

' - (.. 2-

1 0.75 o.~ o.15 o.~ o.;5 l .~

Labor supply

supply functions.

of ages 15-44 years have only forward-falling portions.

Workers who display both the segments of the supply curve are regular participants in the labor market, while those with the forward-falling functions only enter the labor market at relative- ly low wage conditions and exit from it as the household's economic condition improves with higher wages. This view is supported by the average labor supply figures listed in Table A2 in Appendix A. Adult male workers are found to supply an average of 70 hours a week, a5 compris- ing 84% of their total available time (considered to be 12 hours per day). The adult females' average supply is estimated at 40%, which is 34 hours a week. While the male children supply an average of 28% (24 hours a week), their female counterparts supply only 19% (16 hours a week).

The estimates of labor supply elasticity (e) presented in Table A3 show very low figures (< 1 in absolute sizes) consistently for all workers.

These low estimates on the forward-falling seg- ment of the curve imply that with reductions in the wage rate, while labor supply expands, total income is reduced, thus lending support to the hypothesis of economic distress. These low numbers also suggest that the workers are operating at the proximity of their physical maximum (84 hours per week) with little poten- tial for adjustment. Despite a poor ability to make adjustments, however, workers hav.ing both the segments of the function, except for the nearqandless adult females, display a larger wage response on the forward-falling than on the upward-rising segments - - clearly a manifesta- tion of distress sale effects. The very low esti- mates of elasticity of substitution between food and physical rest (o) listed in Table A2 provide additional support to this view.

Estimates of o for children are generally lower than those for adults, as are those of females compared to those of their male counter-

1082 WORLD DEVELOPMENT

parts. This finding supports our previous indica- tions that females and children enter the market only under pressure of economic distress while adult males work full time or overtime in all situations. This view is strengthened by estimates of labor supply elasticity (~). The estimates of

for children are higher than those for adults and the estimates for females are higher than those for the males. Since children and females supply less labor than their adult and male counterparts, it is clear that they make the largest response to wage changes under economic distress.e"

The subsistence income of the worker is determined by the turning point of the supply curve. Three of the six estimated functions having this turning point relate to hmdless workers and are used for this purpose. :7 Subsis- tence is determined at daily wage rates of Rs2.40, Rs4.41 and Rs4.14 for children, and for adult males of ages 15-44 years and 45-59 years, respectively. These wage figures converted into food grains become 2.26 kg, 4.16 kg and 3.91 kg per dav. The corresponding labor supply figures are .25 (two hours a day), .85 (6.8 hours a day) and .75 (six hours a day), respectively for the three groups. Thus, 0.56 kg, 3.53 kg and 2.93 kg are the predicted grain incomes to be earned at subsistence by a male child, an adult male worker of 15-44 years and an adult male worker of 45 59 years, respectively. To determine the daily sub- sistence income for an average hmdless house- hold, these grain incomc figures are multiplied by the actual number of earning menlbers in their respective age groups, added together, converted into grain calorie equivalents (using averagc calorie contents of rice, flour and pulses per kg), and adjusted for the household size. The result shows an estimate of 2,822 kcal per capita per day for an average landless household. This estimate of subsistence, derived from the income earning behavior of the landless workers, is 26% higher than the nutritionists' norm of 2,248 kcal (Dandekar and Rath, 1970). It is not surprising that a subsistence income has a purchasing power exceeding the nutritionists" norm for calorie consumption; after all, the income must cover not only calories, but also clothing, shelter and other needs.

A comparison of the subsistence wage-labor supply figures with their estimated means shows that these workers are surviving in impoverish- ment below their subsistence. The mean wage rate lies much below the subsistence wage rate, and the mean labor supply above the subsistence labor supply.

! have also derived ordinary least squares (OLS) and Tobit estimates of labor supply for the

same groups of workers using multiple regres- sors, including dummy variables for slack seasons and for advanced states: a cross-income variable to account for the interaction among household members: and a dependency variable for the male workers (results not reported here). Thc only variables significant in all equations are either, both, or one of wage rate and its quadratic term, providing evidence of a forward-falling function with or without an upward-rising seg- ment. The interaction term also derives a signifi- cant estimate in most of the equations and shows an expected negative sign. The depcndency wlriable attains a significant positive estimate for the near-hmdless workers only, indicating that dependency is a function of cconomic condition derived from assetholding. Apart from thesc variables, others - - including the seasonal and regional wtriations - - do not seem to have any statistically significant effect on these workers" supply behavior: rather they appear to cxert their influcnce on labor supply through wagc changcs. Evidence of an expansion in the quantity of labor supplied, with declining wage rates during slack seasons of agricultural activities, provides sup port to this contention. That the nature of the supply function does not change across rcgious nor over agricultural seasons is supported by insignificant esfimatcs for differences in the slope parameters of the function. The cstimate for scasonal differences in the intercept term is also insignificant in almost all the equations: how- ever, the variable for regional differences in the intercept term derives a significant positivc esti- mate in some of the equations, thus showing a larger supply of labor in the wcalthier states. (A detailed discussion of these OLS and Tobit estimates is provided in ShariL 1989). es

These ()I,S and Tobit regression results not only provide significant support to the utility function estimates, but they also suggest that the utility function estimates are not nmch biased by omitted variables. Construction of the labor supply function using the utility function esti- mates appears to be a single variable estimation. Since fl)od income and physical rest are the only arguments of the utility function and they are constructed using the quantity of labor supplied and the real (food) wage rate, real wage rate seems to be the only variable explaining labor supply. The direct estimation of the utility function with this seemingly single explanatory variable of real wage rate, however, offers the same result as do the estimations of the OLS and Tobit multiple regressions. Moreover, the utility function model has greater explanatory power than does the multiple regression model. The maximum variation in labor supply explained by

FORWARD-FALLING LABOR SUPPLY 11183

any of the multiple regression models is 54.75% (see Sharif, 1989), while the utility function estimates show that most of the models explain over 84% of the variation. Since the direct estimation of the utility function combines a method of optimizing the values of the function's arguments, it incorporates the effects of all other variables relevant to the worker's decision. Sup- porting this contention is evidence that some of the variables accounting for seasonal and re- gional variations and for differences in household sizes derive statistically significant estimates in the OLS and Tobit models, but that none of them attain significance when used in the utility function model.

5. CONCLUSIONS

A large majority of workers in labor abundant LDCs supply their labor at low wage conditions under the pressure of economic distress. Labor income is the only source of living for these poor workers: if they work shorter hours, their physi- cal health and even their survival would be jeopardized. Hence, as the wage rate declines they are compelled to work longer hours to earn their survival.

Existing subsistence and efficiency theories do not provide a convincing explanation for this behavior. I have formulated a utility function model that accommodates a forward-falling supply function and provides an explanation for distress sale behavior. An interesting additional result derived from this model is a practical definition for subsistence which is considered to correspond to the turning point of the supply c u r v e .

I have specified an IES utility function on the assumption of poor substitutability between food and physical rest at low levels of consumption and high substitutability at high levels of con- sumption. Using a numerical procedure of utility maximization with a nonlinear regression tech-

nique, I have directly estimated the parameters of the utility function to find the labor supply function. All the estimated functions strongly support my hypothesis.

Estimated mean wage rates are lower than the corresponding estimated subsistence wage rates and estimated mean labor supplied is higher than the estimated subsistence labor supplied. This supports the view that rural workers are surviving below subsistence. Very low estimates of the elasticity of substitution between food and physi- cal rest, together with low estimates of the supply elasticity of labor (< 1 on the forward-falling portion) prove their distress sale of labor in the proximity of physical maximum.

The analysis of forward-falling labor supply behavior offered in this study is consistent with the neoclassical theory of labor supply. While earlier studies viewed the supply behavior of the poor as an isolated perverse phenomenon, this study provides a generalized framework of analy- sis using the traditional method of utility maximi- zation to explain the forward-falling supply as rational economic behavior. Moreover, this analysis establishes the forward-falling supply as a part of the total labor supply function.

A proper understanding of forward-falling supply behavior, in contrast to the existing belief of a horizontal, backward-bending, or upward- sloping supply, is important for manpower plan- ning. In particular, should this individual supply behavior translate into aggregate supply, it might have a significant impact on the development performance of an economy. For instance, in labor abundant LDCs, where planners usually use positive or infinite elasticity of aggregate labor supply in projecting growth rates, the negative elasticity as implied by the forward- falling supply might work as a deterrent in the realization of target growth rates. This scenario underscores the importance of further research on forward-falling labor supply and its implica- tions for development planning and economic policies in labor abundant LDCs.

NOTES

1. These are the workers in households which fail to meet a minimum of 2,248 kcal of food consumption per capita per day (Dandekar and Rath, 1970; Khan, 1977; Naseem, 1977). This norm of poverty, converted to per capita annual income, is US$75 in 1969 US prices (World Bank, 1975) or ICP$200 in 1970 US prices (Ahluwalia et al., 1979). The ICP$ is developed by Kravis et al. (1978) under the International Comparison Project of the United Nations. ICP$ uses the relative purchasing power of a country's currency at home, instead of its foreign exchange rate, to convert the

country's poverty norm into an international standard. For details, see Ahluwalia (1979).

2. See Anderson and Frantz (1984), Bardhan (1977), Bardhan (1984), Berg (1961), Huang (1976), Papola and Misra (1980), Rodgers (1975), Rosenzweig (1980; 1984), Rottenberg (1952) and Sharif (1991). Some studies also report evidence of upward-sloping supply (Bardhan, 1979a; 1984; Huang, 1976; Lal, 1976; Rosenzweig, 1980, 1984; and Sharif, 1991). This differ- ential behavior might be the result of differences in the

1084 W O R L D D E V E L O P M E N T

economic condition of workers as identified in Huang (19761 and Sharif (1991).

3. Also scc Cain (1977), Cain, Khanam and Nahar ( 19791, Cain and Mozumder ( 1981), Habibullah ( 1962 ) and Hart (1986).

4. Kalpana Bardhan (1977) uses this concept of distress sale of labor to explain a negative relation- ship between the quanti ty of labor supplied and the in- take of food by landless workers in Uttar Pradesh, India.

5. The shape of this labor supply curve can bc explained in terms of the s tandard concepts of income and substi tution effects.

6. Kcrala in India is a small exception.

7. The sacrifice is involuntary in the sense that it is necessary to minimize the loss of health. By sacrificing rest, the impoverished workers are causing harm to their health through overwork; but if they do not make this sacrifice, they are faced with a greater loss of health because of starvation; so they prefer the lesser of the evils. Their "'positive f reedom" (for an exposition of this concept see Sen, 1988) from impover ishment arising from overwork and undernour i shment , how- ever, is compromised. This curtai lment of "positive f reedom" results in a choice that can be considered invohmtary.

8. Some authors , however, argue that the propor- tion of populat ion in absolute poverty is lower (Paync and Cutler, 1984; Srinivasan, 1977; Sukhatme, 1982).

9. This postulated shape for the fi)rward-falling labor supply function implies increasing distress with decreasing wages, and conversely, declining distress with rising wages. Since these workers suffer from deficiency in food intake, rising income deriving from higher wages is expected to be allocated mostly toward reducing this deficiency, thus implying a high income elasticity of demand for food. A recent est imate of unit income elasticity of demand for food in rural South India (Behrman and Deolalikar, 1987) supports this contention. The est imates of the elasticity of demand for calories, the most important nutritional e lement of food for these workers, however, do not provide unambiguous support to this view. Sahn (1988), in his study on rural Sri Lanka, shows an est imate of unity, and Bchrman and Deolalikar (1987), in their study on rural South India, report a very low est imate of (I.2. While the implication of the forward-falling theory is for poor landless workers, both the Sahn and Bchrman- Deolalikar es t imates relate to the rural population - - landed and landless together. As Sahn and Alderman (1988) show, nonearned income (enjoyed by the landed households only) has a significant negative effect on the demand for calories. Thus , the est imation of income elasticity of demand for calories for the landless households can be expected to offer better results: however, until such results are derived, the issue remains unresolved.

111. Traditionally, a household utility function is used to analyze economic behavior of agricultural house- holds. Constra ined maximization of this function leads to the derivation of labor supply for individual mem- bers of the household, as a function of their own and cross wages and of nonearned income. These derived functions are then est imated, using observations on dependent and explanatory variables separately for each member of the household. The IES utility function specified in this study is complex and not analytically tractable: and, therefore, the correspond- ing analytical form of the well-specified labor supply function cannot be derived for econometr ic estimation. To tackle this problem, a method for approximatc utility maximization, for numerical est imation of the parameters of the utility function, and then for con- struction of the labor supply function from these es t imates is developed. The use of household utility function in this methodology, however, would require for practicality the use of aggregate household labor supply and household wage rate, and would result in the construction of household labor supply function (see Bardhan, 1979a, for an example of the est imation of household labor supply, and Singh, Squire and Strauss, 1986, for an overview of studies on agricultural household utility models using aggregate household labor supply). Thus , while labor supplied and wage rates earned by different members of the household are he terogeneous (evidence and explanation are provided in Section 4), the household utility analysis based on aggregate household labor supply and household wage rate would impose an unrealistic assumpt ion of homo- geneity on them. The use of the IES function for est imation separately for individual members of the household does not encounter this heterogeneity prob- lem, and leads to the construction of individual labor supply function. Moreover, for poor households, where all the members including the very young and the old of both the sexes (see Cain, 1977: Hart , 1980, 19861 participate in the labor force, the individual utility analysis can be expected to offer results at least as good as those of the household utility analysis. In fact, some weighted averages of the individual est imates can provide unbiased est imates for the household (see Theil, 1971). Since individuals are members of the household, their utility can bc considered to b c a function of their own consumption of rest and their own income which is consumed together in the household. Thus , while some members may earn more than their own consumpt ion, others may earn less. The est imates of subsistence reported at the end of Section 4 lend support to this view. R e s u l t s show that adult male workers earn more and women and children earn less than their own subsistence. Such evidence of intra- household transfers suggests that the est imation of the individual utility function does implicitly account for the interaction among members of the household.

11. Thankful acknowledgment to Michael Manovc who suggested this final specification.

12. To make sure that both ct and [~ (not just their ratio) mat ter , I have drawn wage-consumption curves for several scalar multiples of their values at ( 1, 1 ). The

F O R W A R D - F A L L I N G L A B O R SUPPLY 1085

results (see Appendix B figures) show that the curve changes its shape even from forward-falling to upward-sloping, with scalar multiplications of their values. I have also graphed wage-consumption curves (Appendix B figures), by changing the ratio between ct and 13, to show the effects of their relative sizes.

13. In contrast to this IES function, the CES utility functions including the nonhomothet ic ones (Sato, 1977) display constant elasticity of substitution at all levels and ratios of consumpt ion of food and physical rest. Therefore , they are not appropriate for my analysis. The variable elasticity of substitution (VES) functions, on the other hand, imply homotheticity (see Revankar , 1971). In these VES functions, elasticity of substitution is a function of the ratio, not of the level of consumption. Thus , o varies along an indifference curve as the proport ion between the two commodit ies changes, but remains constant along a ray through the origin irrespective of the level of utility. Moreover, the VES fails to include the Leontief function.

14. The flexible nature of the utility function implies that its use in est imation will not force the data to generate a specific shape for the labor supply function, and will be able to capture the pattern displayed by the data (unless the data show a horizontal supply curve which is, however, unusual for an individual worker).

15. Haryana and Punjab are the exceptions.

16. These groups are 10-14 years, 15-44 years, and 45-59 years.

17. As geographical diversities may cause important socioeconomic differences across states, the use of state level aggregate data might mean biased estimates. These socioeconomic differences, however, are not expected to cause any serious problem in est imation for the specific groups of workers who work full-time and overtime (India, 1976a; Farouk, 1980), incur about 90% of their total expenditures on food and food preparation (Dandekar and Rath , 1970), but still fall below the official line of poverty in all Indian states. The exception is Punjab where per capita income lies just at the poverty line (India, 1977). The insignificant coefficient (not reported here) of a d u m m y variable for relatively prosperous states such as Punjab and Haryana support this view.

require support from further est imation with micro- data,

19. Different modes of wage payments are prevalent in rural India. Time-cash wage rate, however, is the common mode of payment accounting for about 70- 90% of total labor transactions (Dasgupta, 1977). The investigators in this survey converted all other forms of wages into daily nominal wage rates.

20. Rice and wheat prices (India, 1972, 1976b) are used for the following reasons: It has already been ment ioned that 90% of the total household expenditure of poor workers is incurred on food. Food grains account for most of this expenditure and rice and wheat are the staple food grains generally consumed by them, al though there are pockets in some Indian states where the main staples are cereals like sorghum and millet. But price figures for the latter cereals are not available for all the states. Their prices, however, can be expected to be correlated positively with rice and wheat prices which are available for all the states. The wholesale instead of the retail prices are used because poor workers buy their grains at the farm prices which are even lower than the wholesale prices.

21. Since this variable LS is a proport ion bounded below by zero and above by one, the error term might violate normality and cause biased estimates. By using SAS's Univariate procedure I have tested for the normality of residuals for all the sets of data. The results show that the residual distribution is not significantly different from normal.

22. The use of this wage variable is justified on two grounds: first, as the daily wage rates are directly observed, not derived by dividing earnings by days worked, the variable does not suffer from measuremen t error. Second, the poor workers they relate to have little or no nonwage income and all the members of their households sell labor at low wages with virtually no influence on the market , thus implying that wage rate is exogenous for them. The effect of health and nutritional status of workers on their productivity and therefore on their wage rate (Deolalikar, 1988) also poses a problem for the use of wage rate as an exogenous variable. This endogeneity, however, is more relevant for work-efforts rather than work-time supply. Since this study is concerned with the supply of work-time by individuals with nutritional deficiencies, wage rate can still be considered exogenous.

18. A set of microlevel individual data is most appropriate for the est imation of the individual labor supply function. But state-level aggregate data set published by NSS contained the only data available to me at the time this study was undertaken. The use of aggregate data, however, can provide est imates for the individual function, which are unbiased (see Theil, 1971, p. 556). Thus , the results of est imation with this data set can reasonably be used to test the hypothesis of forward-falling labor supply, a l though the specific est imates of supply responses and those of the elasticity of substi tution should be considered tentative and

23. This single variable model is based on the assump- tion that the shift variables do not play any important role in the supply decision of very poor workers; that is, their labor supply is a stable function of wages, and any changes in. wage rate and employment are caused by the instability in demand conditions only. For evidence on the predominance of demand factors see Bardhan (1979b), Connell and Lipton (1977), Dasgupta (1977) and Habibullah (1962). The NSS data (India, 1976a) also show that at poor wage conditions, labor supply expands with relatively lower wages during slack seasons and contracts with relatively higher wages

1080 W O R L D D E V E L O P M E N T

during peak seasons of agricultural activities. 1 have tested for the role of supply shift variables by including household size and dummies tor state and seasonal variations in my estimation. The est imates for all of them have been found to be insignificant. Moreover, since the labor supply wlriablc represents workers" desired work-t ime, not actual employment , the model does not face the usual simultaneity and identification problem. The model also rules out the problem of corner solutions, as tile labor supply is the proportion o[ total time of the participating p¢)pulation.

24. The R 2 statistic reported in Table A I is defincd in the conventional manner ,

Z ( y ; - .O,)-"

i . e . . I - Z ( y ; - y ) :

Since minimization of the sum of squared residuals is achieved through rcpeated iterations, R e can be used m this traditional sense to describe the explanatory power of the model (see Pindyck and Rubinfeld, 1981, p. 265).

25. Ill a seven-day week, a person can work for a max imum of 84 hours. The unit of time for hiring labor is half a day, which is approximately four hours. In a 24-hour day, a laborer can be expected to work for at most three such units. The NSS data has an element of underest imat ion in recording work time. If workers reported four hours of work. their work is correctly recorded for half a day. If thev worked for more than four hours , however, their work is recorded as one day only, whether they worked for eight or 12 hours. This underest imat ion, however, does not seriously bias my estimates: most of the more- than-eight hour observa- lions arc expccted to cluster near the lowest observed

wage rate, with a few concentrated near the highest wage rate.

26. These findings indicate that economic distress is the result of depressed wage conditions. The expansion in labor supplied with relatively lower wages during slack scasons and its contraction with rclativcly higher wages during peak seasons of agricultural activities provide support to this contention, Since all the members of the household except thc infants and the very old (see Cain, 1977: l lart , 1980, 1986)participate in gainful (both income-earning and cxpenditurc- saving) activities, the burden of dependency is not a cause of distress sale of labor for the assctless workers. Thc insignificant est imate of a coefficient for household size (not reported hcre) in nw utility function model supports this view.

27. "lhe functions for the near-landless workers arc not suitable fl)r lhe est imation of subsistcncc, as thcsc workers derive some asset income from their land and the csl imated functions do not incorporate them, The [hrcc functions which arc used for the estimation ol subsistence arc those of tile lnalc workers m landless households. The functions for the female workers are forward-falling only, indicating that fenaale workers quit the labor market as household incomc approaches subsistence thus entrust ing thc responsibility of earning the subsistence on the male workers of tile houschokl.

28. In another study 1 have analyzed the labor suppl} behavior of workers ill different hmdholding house- holds using houschold level microdata Irom rural Bangladesh. The results show that the supply hmction lor the landless workers is Iorward-fallmg, displaying an upward-sloping segment at higher wages, but for the hmdholding workers the function is upward-sloping with a hackward-bending segment (Sharif, 1991).

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FORWARD-FALLING LABOR SUPPLY 1089

APPENDIX A

Table A1. Estimates of the [ES utility function for different working groups of poor households in rural India

Estimates Scale Parameters Distribution

Equation Number of For Food For Rest Parameter F Number Working Group Observations c~ [~ /5 R 2 Ratio

1 Landless male children 54 0.28 0.99 0,13 .86 102 (ages 10-14 years) (4.90)* (1.29) (5,87)

2 Landless male adults 70 1.63 0.70 0.43 .99 2389 (ages 15-44 years) (13.28) (4.10) (25.80)

3 Landless male adults 66 1.50 0.64 0.38 .97 670 (ages 45-59 years) (6.96) (1.90) (19.60)

4 Landless female 48 1.10 13.14 0.39 .68 25 children (ages 10-14 (4.20) (2.95) (15.22) years)

5 Landless female adults 67 0.75 1.63 0.18 .85 119 (ages 15-44 years) (84.04) (3.17) (4.10)

6 Landless female adults 61 2.48 6.08 0.24 .85 102 (ages 45-59 years) (182.47) (1.24) (0.86)

7 Near-landless male 67 0.69 1.80 0.12 .89 149 children (ages 10-14 (4.04) (3.47) (2.40) years)

8 Near-landless male 72 1.46 0.70 0.40 .99 5641 adults (ages 15-44 (24.51) (10.02) (48.13) years)

9 Near-landless male 71 0.97 0.65 0.41 .99 1831 adults (9.92) (10.02) (49.41) (ages 45-59 years)

10 Near-landless female 47 0.82 7.03 0.16 .84 74 children (ages 10-14 (19.23) (9.83) (2.26) years)

11 Near-landless female 67 1.54 3.55 0.33 .89 154 adults (ages 15-44 (18.77) (29.52) (18.93) years)

12 Near-landless female 62 0.44 0.82 0.18 .90 176 adults (ages 45-59 (5.96) (1.70) (13.19) years)

*Figures in parentheses show asymptotic t-statistics.

1090 W O R L D D E V E L O P M E N T

Table A2. Elasticity o f substitution between .food attd physical re.st at diCe,,rent points (if" the estimated ~'ttpply functions

Functions with Both l;))rward-P)zlling amt Upward-Rg'ing Segments'

Working Group* I 2 3 ,~ 9 12 Mean Observed Wage R a t e i 1.61 3.13 3.12 2.98 3.114 1.94 Mean Observed Labor Supply 0.27 0.85 0.S2 0.85 0.83 0.40

(Maximum 1)

Elasticity of substi tution at minimun3 R W (o) between food and wage LS rest at different rcal rate o wage rates (RW) and around R W est imated labor supply

mean wage LS (LS) rate o

at the R W turning LS point o

at maximum R W wagc kS rate 15

0.61 1.71 1.30 1.70 1.51 0.73 0.39 0.98 1.00 11.92 0.86 0.55 0.06 0.61) 0.56 0.63 0.76 (I.¢~1

1.64 3.21 3.12 2.95 3.(}4 13)5 t).26 0.86 0.77 I1.81 1t.82 0.37 0.82 tl.83 11.87 I).84 1.06 11.91

2.411 4.41 4.14 4.IS 2.65 2.4(I 0.25 0.85 0.75 (I.~0 0.81 O.36 I.Ilt) 1.(10 1.(10 1.()0 1.00 1.t)11

4.57 6.96 7.(~4 7.24 7.05 5.33 0.33 0.8,'-; 11.82 0.S5 0.90 11.47 1.2q 1.12 1.28 I.IS 1.34 1.41

Ftmclions with .lbrward@dling segment only

Working Group* 4 5 6 7 III 11 Mean Observed Wage R a t c t 1.29 1.94 1.84 1.75 1.35 1.92 Mean Observed Labor Supply O. 19 0.39 0.41 0.28 [I. 19 11.41

( M a x i m u m - 1)

o at different R W and LS

at minimum R W 0.62 1.19 1.01 0.73 (I.(~5 11.56 wage I.S 0.211 0.47 0.56 {).52 0.31 0.70 rate o 11.07 11.42 0.12 0.06 0.12 IL() t)

around R W 1.28 1.95 1.86 1.73 1.36 1.97 mean wage kS 0.15 0.37 0.38 11.31 1).18 0.43 rate o 0.(18 0.49 (). 14 tl.42 0.14 0.24

at maximmn RW 2.44 5.20 5.49 4.58 4.40 5.88 wage LS 0.09 t).30 [). 18 (I.21) 0.(17 (I.26 rate o 0.08 ().fit) O. 17 0.57 0.16 11.33

*See Table AI for the identification of these groups. tWage figures are in rupees deflated by the food grain price index.

FO R WA R D -FA L L IN G LABOR SUPPLY 1091

Table A3. Supply elasticity of labor at different points of the estimated functions

Functions with both forward-falling and upward-rising segments

Working Group* Mean Observed Wage Rate? Mean Observed Labor Supply

(Maximum = 1)

1 2 3 8 9 12 1.61 3.13 3.12 2.98 3.04 1.94 (/.27 0.85 11.82 0.85 11.83 0.411

Elasticity (~) of the estimated labor supply (LS) at real wage rate (RW)

near the R W bot tom of LS the curve

middle of RW the forward- LS falling part

around the R W mean wage LS rate ~:

near the R W top end of LS the curve f

Functions

11.96 1.71 1.34 1.7(1 1.52 1/.75 0.32 0.98 0.99 I).91 0.86 0.54

-1/.75 -1/.33 -0 .38 -0 .28 -0 .48 - 0 . 5 2

1.22 2.21 2.11 2.114 1.76 1.08 0.29 11.91 1/.84 11.87 0.83 0.46

-0 .37 -0 .23 -0 .22 - ( I .26 -0 .34 - ( / .44

1.65 3.22 3.14 3.06 3.04 1.93 0.26 1/.86 0.77 0.81 0.82 0.37

--(t.26 -0 .08 --0.16 --0.16 0.67 -0 .02

4.24 6.90 3.14 6.22 6.73 4.46 0.32 (/.88 0.77 0.84 0.911 0.44 0.49 0.08 0.19 0.11 0.06 0.68

with forward-falling segment only

Working Group* Mean Observed Wage Rate? Mean Observed Labor Supply

(Maximum = 1)

4 5 6 7 10 l l 1.29 1.94 1.84 1.75 1.35 1.92 0.19 0.39 11.41 11.28 (I.19 0.41

Elasticity (el of the estimated labor supply (LS) at real wage rate (RN)

near the R W 1/.69 1.21 1.14 0.8/I 11.91 1.21 bot tom of LS 0.24 1/.47 0.52 11.49 0.24 11.56 the curve ~ -1/.42 -0 .66 -0 .65 -0 .58 -1/.76 - t l .56

around the R W 1.30 1.92 1.87 1.78 1.35 1.89 mean wage LS 0.14 11.37 0.38 0.30 0.18 11.43 rate r - 0 .60 - / I .26 -0 .69 -0 .54 -11.79 (t.54

near the top R W 2.33 4.40 3.22 3.04 3.42 3.811 end of the LS (I.09 0.30 /).26 0.23 0.09 /).31 curve ~ -11.76 -0./14 -(/.61 -0 .29 - 0 . 7 4 -(I.05

*See Table A1 for the identification of these groups. ?Wage figures are in rupees deflated by the food grain price index.

1092 W O R L D D E V E L O P M E N T

A P P E N D I X 13

1. a = 1,/3 = 1, 6 = 0 . 5

,o- t i l l / \

0 0 0.4 0 8 1.2 16 2.0

Physical rest

2. a = 5, ~O'= 5, 6 = 0.5

I0-

6-

0 j 0 OJ4 0:8 11.2 116 2.0

Physical rest

3. a = 0.2,~8 = 0 . 2 , 8 = 0 . 5

6-

4-

2-

O-

)I/\\\ \~

0.'4 018 112 116 210

Physical r e s t .

4. a = 5 , ~ = 0 .2 ,6 =0.5

'%11 /

21 '/ 0 0.4 018 122 1.6 2.0

Physical rest

Figure B1-4. Indifference maps and wage-consumption curves for different values of parameters of the utility function.

F O R W A R D - F A L L I N G L A B O R S U P P L Y 1093

5. a = 0 , 2 , / / = 3 , 8 - -0 ,5

lO-

Ill

4 - L//

o \ 1 I

0 0.4 018 112 1.6 2:0

6. a = 1 , ~ = 1 , $ = 0 . 2

1 0 -

2- /

0 0[4 ' j h I o o.s 1.2 1.6 2.0 Physical rest Physical rest

7, a = 1, 0 = 1 , 5 = 0 . 8 8. a = 0 .2 , B = 0.2, 8 = 0.7

0 0.4 0.8 1.2 1.6 2.0 0 0.4 .8 1.2 .6 2.0

Physical rest Physical rest

F i g u r e B 5 - 8 . Indifference maps and wage-consumption curves for different values of parameters of the utility function.