coexistence of surplus labor and the lewis turning point in china: a unitary household...

J Econ Interact CoordDOI 10.1007/s11403-012-0095-4

REGULAR ARTICLE

Coexistence of surplus labor and the Lewis turningpoint in China: a unitary household decision-makingmodel study

Huai Yu Liu · Shinan Cao · Jing Deng

Received: 18 October 2011 / Accepted: 30 March 2012© Springer-Verlag 2012

Abstract This paper discusses the underlying relationship between surplus laborand the Lewis turning point in the duration of rapid economic growth in China.An agent-based model was proposed for studying the Lewis turning point and laborresource allocation, in which the decision-making interactions were made among themembers of a household. This model differs from traditional development economicstheory in which only an individual’s behavior is considered. How peasant householdsallocate their human capital to maximize the utility of a household unit was investi-gated on the basis of the unitary principle under the assumption of risk aversion. Theroles of living expenses, subsidies and income adjustment factors were also consid-ered. Our results revealed the paradoxical phenomenon that rural surplus labor andthe Lewis turning point coexist.

Keywords Lewis turning point · Surplus labor · Agent-based model ·Unitary model · Labor resource allocation

JEL Classification D13 · E27 · J22 · J24

1 Introduction

The Lewisian dual economy model (Lewis 1954, 1958) has been widely adoptedin development economics for understanding and modeling the labor market in

H. Y. LiuSchool of Environment and Natural Resources, Renmin University of China, Beijing, China

S. Cao (B)School of Finance, Renmin University of China, Beijing, Chinae-mail: [email protected]

J. DengSchool of Economics and Management, Beijing Forestry University, Beijing, China

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developing countries during the processes of urbanization and industrialization.According to this model, there is an income gap between the urban and rural sec-tors, which incentivizes surplus labor in the rural sector to move to the urban sector. Inthis way, at the early stage of development in a low-income country, there is no need toraise the wages of surplus rural laborers because these laborers are desirable to moveinto in the urban sector. As a result, the income gap between the two sectors shouldeventually be eliminated, and the dualistic urban-rural labor markets will be integratedinto a unified market whose manufacturing wage level reaches the Lewis turning point(LTP) (Minami 1973). The demographic dividend will also begin to taper off.

In practice, however, an integrated urban-rural labor market is unlikely to material-ize. The rural labor surplus has not been completely integrated into the urban sector,and the income gap remains. Cai and Wang (2010) found that China has alreadyreached the LTP at which more assertive workers and wage increases should emerge.That study found that a large number of peasant households did not suspend their agri-cultural production and work in the urban sector. At the same time, ordinary surplusrural laborer wages increased by nearly 60 % in recent years in China (Liu et al. 2008),which conflicts with the Lewis model’s prediction that the income gap determines howwilling individual farmers are to move to the industrial sector. Many empirical studiesof other East Asian countries also have not found support for the dual labor markethypothesis, which is built on the assumption that labor dynamics change according tothe wage determination mechanism between the two sectors. Japan in particular has aunique situation in which the rural household labor supply is stagnant in both the agri-cultural and industrial sectors (Hayami and Godo 2003). Korea’s labor market reachedthe LTP in the 1970s, when urban wages increased significantly, while the supply ofrural surplus labor remained the same. In terms of Southeast Asian countries, e.g., thePhilippines, Malaysia, Indonesia and Thailand, none has reached its LTP during the21st-century process of industrial development (Islam 2003), if the LTP is signifiedby the elimination of surplus labor. This situation has existed not only in developingcountries such as China but also in developed countries. A 9–13 % income gap betweenthe urban and rural sectors (Hatton and Williamson 1991) existed in the United States,a country that completed its industrialization process at the end of last century, and theflow of rural labor to higher wage industries did not occur instantaneously (Barkley1990). This is, we believe, because non-agricultural income is the main source of ruralresidents’ income even in a well-developed country (Gardner 2002).

Those phenomena can hardly be explained by the theory of a dualistic urban-rurallabor market, and they cannot be ascribed to demographic or economic factors. Inthe Lewis theory, there are two important factors for assessing the LTP in developingcountries: a reduction in the supply of surplus labor from the countryside, and labormarket integration and rapidly increasing industrial wages. However, the above men-tioned literature showed there are significant amount of the surplus labors existingin neither the industrial sector, nor the agricultural sectors, and the current dualistictheory has not even identified a labor segment that is unemployed and not looking fora job (called voluntary unemployment; Pigou, 1933). These issues indicate that thegeneral framework of maximization determination mechanisms and the dynamics oflabor flows between the two sectors are not perfectly sufficient. First, the study focuseson the wage mechanism, which may be suitable for individual decision making but

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lacks the rationality for household decision making. Furthermore, considering wagesas the only factor that can maximize individual utility ignores the effect of interac-tions among the household members, living expenses, imputed cost and income, riskattitude, and so forth. It is therefore difficult to predict how individual utility drivesthe process of optimized allocation of household labor resources. In addition, whentaking attitude toward risk into account, individuals have different utility curves thatare always non-linear; these curves were assumed to be linear in the Lewis theory.

In development economics, some scholars study farmers’ economic behaviorthrough the unitary model, which views the household as a single unit rather thana simple aggregation of each household member. All household members have asingle utility function, share the household income and take on the risk together tomaximize the entire household’s expected utility (Becker 1965, 1973, 1974; Barro1974). Therefore, in this paper, we introduce an agent-based model based on a unitarymodel to analyze how peasant households in China allocate their labor capital to max-imize the utility of the household unit under the risk-averse assumption. Specifically,by considering the role of living expenses, subsidies, imputed costs and income, thispaper outlines the micro-foundations of surplus labor formation, presents the labordetermination mechanism of peasant households and uses simulation to clarify therelationship between surplus labor and the LTP.

The remainder of this paper is organized as follows. Section 2 offers a brief the-oretical background for the paper and introduces our model. Section 3 develops oursimulation hypotheses and presents the model in more detail. Section 4 describes oursimulation results. Section 5 concludes and summarizes our findings.

2 Basic theories

2.1 The unitary model

Traditional labor supply theory takes the individual as the basic unit of study. It assumesthat an individual’s labor supply and leisure consumption depend on the substitutioneffect and the income effect, which are caused by changes in an individual’s wages.Accordingly, each laborer must work and allocate time between work and leisure. Thehypothesis posted by this theory is based on the assumption that the differing utilitiesof individual household members lead to different individual labor behavioral pat-terns. This is also the basic assumption of scholars who support the collective modeland reject the unitary model on the basis of household income distribution inequalityin the study of household labor supply (Lucas and Stark 1985; Hoddinott 1992; Coxand Jimenez 1992; Altonji et al. 1992). In reality, in most households, some memberswith the ability to work, such as housewives and some young adults, prefer to enjoyleisure 24 h a day rather than to get a job. This phenomenon cannot be adequatelyexplained by traditional labor theory and indicates that income sharing does existamong household members. This pattern of labor supply has led to a contradictoryoutcome in China, in which labor shortages in urban environments coexist with laborsurplus in rural areas (Chan 2010; Liu and Ma 2011).

In fact, collective model supporters do not deny the household decision-makingmode of the unitary model. Thomas et al. (1997) and Thomas and Chen (1993) found

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that expenditure patterns of household members did not indicate unified action ofthe entire household. However, these studies do not upset the Pareto efficiency ofhousehold decision making. According to this finding, Doss (2006), Quisumbing andMaluccio (2003), Attanasio and Lechene (2002), Hallman (2000), Lundberg et al.(1997), Lundberg et al. (2003) and Chiappori (1988, 1992) proposed a cooperativegame model with some non-unified household decision-making patterns, in whichindividuals have their own preferences, different weights, and different bargainingpower to affect the output. Browning et al. (2006), key advocates of the collectivemodel, demonstrated that the unitary model can be used as long as the needs of thehousehold members meet the Slutsky conditions by introducing distribution factorsto the dependent unitary model. However, considering the depreciation risk of humancapital caused by policy choices during the accelerated process of industrializationand urbanization in developing countries, it is reasonable for households to diversifythe risk through kind of income pooling and risk sharing. On the basis of these results,we assume the patterns of household decision making can be measured through theunitary model. We take the household as the basic unit, and an individual householdmember makes the decision relying on not only his (or her) own income but also theincome situation of other household members, including factors such as income, unem-ployment risks and work intensity. Household members share the income and risksto maximize the total household expected utility. Thus, labor resources will be allo-cated between work and leisure based on intra-household interactions, and voluntaryunemployment is a possible choice. Household members will evaluate the outcomeof different choice combinations, and they will use the principle of household utilitymaximization to determine the labor allocation.

2.2 Utility function and risk attitude

In a 1972 study of a village in Aligarh district in India, Tankha (2008) found that thepoor peasant households do not consider their labor opportunity costs in the initialsurvival stage, which means that they lack the concept of marginal return. However,once they meet a basic living standard, farmers begin to consider whether their extraincome can cover the cost of extra meals needed because of increased working hours.Later, the “non-poor” farmers begin to consider whether their extra income can allowthe luxury of non-work (or leisure) time without affecting utility; if not, they willchoose leisure over work time.

We therefore explain labor-related economic behavior in terms of attempts toincrease one’s utility. This explanation differs from the constant linear function ofwage in the Lewis model in that workers are assumed to have a different risk attitudewith non-linear dynamics in our model. Usually, risk attitude is represented by thesign of the second derivative of the utility function, where a positive sign denotes riskseeking, a negative sign denotes risk aversion and zero is risk neutral. According tothe law of diminishing marginal utility, individuals want to have more wealth, and aswealth increases, marginal utility decreases. Therefore, we assume that agents pos-sess risk aversion and have a concave utility function. There are three popular concaveutility functions: the quadratic utility function, the logarithmic utility function and

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the exponential utility function. The diminishing marginal utility of wealth was firstproposed by Bernoulli (1954/1738) in solving the St. Petersburg paradox. He alsoargued that the paradox could be resolved if decision-makers displayed risk aversionand had a logarithmic cardinal utility function. Because logarithmic utility functionshave a decreasing absolute risk-aversion coefficient and a constant relative risk-aver-sion coefficient, we adopted a logarithmic function to reflect the risk aversion of ruralworkers in this study.

3 The model

3.1 Modeling concepts

In this paper, each family member is modeled as an autonomous agent, which individu-ally assesses its situation and makes decisions on the basis of a set of rules (Bonabeau2002). Since agent interactions are heterogeneous and individual behavior is non-linear, agent-based modeling (ABM) method (Arthur et al. 1997) was adopted to con-struct a dynamic model of farmers’ economic behavior that describes how individualsdetermine the distribution of household labor capital. A unitary model, derived fromthe Becker’s theory of new household economics, was used. The utility of all house-hold members reaches Pareto efficiency through a cooperative game. In this model,the incomes of household members may be quite different, and the entire householdincome is not absolutely equally distributed. In order to simplify the calculation, wetake money income to evaluate utility. Considering different income utility function ofurban and rural work, the utility cannot be added simply for different works or use totalincome to calculate. Therefore, this paper hypothesized that each agent has a utilityfunction that can be added, which means that even agents’ behavior is non-linear thehousehold utility can be calculated as a linear combination of the utility of its parts.In the part 3.5 for Eq. (4), the calculation process will be further illustrated.

In our model, the behavior of each household member was dynamically modeled,representing an advance over most other unitary models. In particular, each worker’schoice of jobs in one period is able to affect the household income and labor alloca-tion decision in the next period. Examining this effect through computer-simulatedagent-based analysis reveals the influence of farming income, working income, riskpreference, and the cost of living in urban areas on the coordination of economicbehavior among household members.

3.2 Household structure

The International Labour Organization’s database of key labor market indicators showsthat, in 2006, 2007, and 2008, China’s labor participation rates (for the population aged15 and above) were 72, 72, and 71 %, respectively. Data from the 2000 national census,taken from China’s National Bureau of Statistics database, show that those aged 15–64account for 66.98 % of the total rural population; according to the 2005 national 1 %sampling census data, those aged 15–60 account for 65.51 % of total rural popula-tion, and those aged 15–64 account for 70.5 %. Normally, the labor force consists of

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everyone above the minimum working age (typically 16 years) and below retirementage (approximately 65 years). Most Chinese researchers define the labor force as thepopulation between 15 and 60 years of age. In China, excluding collective households,the average household size is 3.13 persons, and the average rural household size is 3.27persons; if we exclude provinces inhabited by ethnic minorities such as Hainan, Qing-hai, Xinjiang, Ningxia, Guizhou and Tibet, the average rural household size is 3.18.

From the above statistical results, we can estimate that the average household sizeis approximately 3, and the ratio of the non-labor population to the labor force isapproximately 1:2. Therefore, our model assumes that each household has 3 members(agents), 2 of whom are labor suppliers.

3.3 Household income and variables

In our model, N families were considered. As outlined in the previous section, eachhousehold has approximately 3 members, 2 of whom are working, so that there are2N labor suppliers in total (we have labeled them interactive agents in our model).The labor suppliers in the i th (i = 1, . . ., N ) household are denoted as Ai , Bi . Weinvestigate and denote the following factors: cost of living non-labor income, expectedincome, income adjustment factor, and pure income.

Living cost Lewis’ basic idea is that the unlimited supply of labor from the rural sectorkeeps wages in the urban sector at the subsistence level. Considering the subsistencecost, Ci denotes the average cost of living per person of the i th household, and thetotal cost of living of the household is 3Ci .

Non-labor income The portion of farmers’ income that originates from investments,transfer payments (payments from governments to individuals) and other sourcesunrelated to employment is called non-labor income, and it is denoted by Ii,0.

Expected income At period t , agents predict the expected wages they will earn in thenext t + 1 period. Each agent has three options: farming, non-farm labor (working asmigrant worker labor), and leisure. Choosing a certain option at period t among farm-ing (F), non-farm labor (W = working) and leisure (L) results in expected incomes inthe next period of E F

t , EWt , E L

t , respectively

Adjustment factor and pure income The expected income consists of income fromthe agricultural sector and from the industrial sector, and non-labor income, in whichdifferent associated costs are disbursed. These costs must be reduced to accuratelydetermine the corresponding expected pure income. Thus, pure income is the incomeafter adjusting for relative cost, imputed income, and inflation.

Because farmers in China have not yet completely discarded the self-sufficientsmall-scale peasant economy, a portion of the agricultural output of peasant house-holds is retained for their own household consumption. This imputed income, a portionof which also cannot be included in expected income, should not be evaluated on thebasis of the selling price of the agricultural output but with reference to the urbanretail price. Hence, pure income from farming may have been underestimated. Interms of migrant workers in urban areas, their cost of living, e.g., consumer goods,

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medical care, education, and housing, is significantly higher, particularly with regardto housing prices. In comparison, housing is nearly free in the countryside. Therefore,compared with the income of farmers, the exact working income of migrant workerstends to be overestimated.

To address this issue, this study introduced an income adjustment factor to morerealistically evaluate the pure income of all agents. At time t , the adjusted pure income(I ) of each option (F , W , L) is expressed as the corresponding expected income (E)times the associated adjustment factor (μ), which are denoted as I F

t , I Wt , I L

t , respec-tively.

3.4 Utility function

Each household has a unique utility preference, which leads to differences in the utilityof income among different families, even where the farming and working incomes ofthe families are the same. To account for this situation, a utility function is proposedin the form of a logarithmic function, denoted as UF (I ), UW (I ), UL(I ) for farming,working, and leisure, respectively:

UF (I ) = logai(IF ),

UW (I ) = logbi(IW ), (1)

UL(I ) = logci(IL)

We let r ai , bi , ci denote the risk attitude factor for the i th, (i = 1, . . . , N ) house-hold, which depends on a different risk preference for each strategy where a > 0, a �=1; b > 0, b �= 1; c > 0, c �= 1.

In China, farmers obtain rural land ownership through collective ownership ratherthan market transactions, and the agricultural tax was abolished in 2006. The riskrelated to land-based farming income is thus relatively low in the economic system ofrural areas, which remain partially self-sufficient. Thus, the self-consumed portion ofagricultural output can sometimes be treated as a risk-free asset. In this regard, the riskof farming in rural areas is less than working in urban areas, although the increasedcomfort and convenience of living in urban areas is another source of differing incomeutilities. The utility of working for same wage is relatively low because it is merelythe most direct way for migrant workers who suffer a year-round high overtime loadto access cash. The logarithms in the utility functions should differ because of thelower risk of farming, the lower utility of working, and the higher utility of leisure.Therefore, for the same income, the utility should be ranked as below:

UL(I ) > UF (I ) > UW (I ). (2)

3.5 Implementation of strategies

To maximize household utility, the household will make decisions according to itsunit utility. The initial market state is derived randomly. Some farming households

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use information sharing among household members at the same time that all majordecisions are made. Each household member at a given point in time will choose astrategy that is consistent with the general laws of household decision making, in linewith the basic constraints of the unitary model.

At each period t , agents Ai and Bi from the i th household choose a strategy s A(B)i

from strategy set S = {F, W, L}:

Si =⎧⎨

⎩

F, if choose farming jobL , if choose leisureW, if choose working (non-farming) job

⎫⎬

⎭. (3)

N Ft , N W

t , N Lt represent the number of agents who choose a farming, working or leisure

strategy at step t separately, whereN Ft + N W

t + N Lt = 2N . At each time t , agents

will evaluate each strategy according to the expected utility they will earn in the nextperiod. Agents are assumed to operate on the principle of utility maximization andconsider the results of cooperation with other household members. To show the inter-active influence in the process of household decision making, we presume that agentAi makes a decision first, and agent Bi then chooses an option based on the resultof Ai ’s decision. For each period, non-labor income is an important factor in deci-sion making. If non-labor income is sufficient to pay all of the household expenses,household members will tend to choose more leisure and less work.

For Ai , who chooses first, taking into account the existence of non-labor income,each strategic decision will be influenced by the difference between the household’stotal cost of living 3Ci and non-labor income Vi . If Ii,0 < 3Ci , which means thatnon-labor income cannot cover all of the household’s costs, Ai will spend his humancapital to gain money and make decisions according to his own utility maximization; ifIi,0 > 3Ci , which means that non-labor income can cover all of the household’s costsand yield some extra savings, Ai will select leisure with probability p and choosefarming or working with probability 1 − p. The decision-making process of Ai isshown in Fig. 1 below.

For Bi , who makes a decision based on Ai ’s choice, taking Ai ’s pure incomeinto account, each strategic decision will be influenced by the difference betweenthe household’s total cost of living 3Ci and non-labor income plus Ai ’s pure incomeIi,0 + Ii,A. If Ii,0 + Ii,A < 3Ci , Bi needs to earn money to support household expen-ditures. Bi will compare the utilities of different decision-making strategies whencombined with the decision of Ai to maximize the utility of the household as one unit;if Ii,0 + Ii,A > 3Ci , Bi will select leisure with probability p and choose farming orworking with probability 1 − p, as shown in Fig. 1.

In Eq. (4), utility function is measured by money income. The rate of change in totalutility per unit change in income and the utility of a marginal unit are both differentbetween urban and rural work, which is determined by the cost of living and purchas-ing power in the urban and rural areas. In a family, when all its members are engagedin urban or agricultural work, the family has a unified utility, which means its utility canbe calculated by taking logarithm after summing up all the income, rather than multi-plying. When family members are engaged in different kind of works between urbanand rural area, due to different purchasing power and cost of living in relative areas,

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iA

,0 3i iif I C>

AiS W=

AiS L=

AiS F=

,0 3i iif I C<

iB

,0 , 3i i A iif f I I C+ >

AiS W=

AiS L=

AiS F=

,0 , 3i i A iif I I C+ <

Fig. 1 Decision-making strategies for each agent

the utility function of each member is different. In this case, according to the basicassumption in unitary model, the overall utility of family is the sum of each member’sutility.

Thus, the overall utility Ui can be described as:

Ui

{if s A

i = s Bi , Ui = logs A

i

(Ii,A + Ii,B

)

if s Ai �= s B

i , Ui = logs Ai

(Ii,A

) + logs Bi

(Ii,B

) . (4)

4 Simulation and results

4.1 Description of model variables

Our program simulated the reactions of 100 individuals from 50 peasant householdsfor different variables. The variables are listed below in Table 1.

The utility of the agents is calculated by the actual adjusted income. For farm-ing, this is farming income multiplied by alpha, and for working the calculation

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Table 1 Description of model variables

Variable Definition Notes

1 N Number of agents Each household has laborers A and B

2 IF Farming income Numerical value [0, 100]

3 α Adjustment factor for farming income Numerical value [0, 1]

4 IW Non-farming income Numerical value [0, 100]

5 β Adjustment factor for working income Numerical value [0, 1](urban work)

6 Subsidy Subsidy Numerical value [0, 10]

7 γ Living expenses Numerical value [1, 100]

8 p Probability of choosing leisure Numerical value [0, 1]

9 u Risk attitude factor Numerical value [0, 10]

is working-income multiplied by beta. The larger the alpha, which reflects the individ-ual’s living cost and quality of life when engaged in agricultural production in ruralareas, the greater is the effectiveness of the farming job. The larger the beta, whichrepresents the individual’s related imputed living costs and quality of life in the indus-trial sector, the greater is the effectiveness of working. In developing countries, as thedifference in income and living standards between rural and urban areas continuesto grow, the imputed cost of urban living is much higher than that of rural areas. Toaddress this issue, some migrant workers who are former peasants choose to reducetheir living standard to reduce urban living expenses. This phenomenon explains whyslums exist in developing countries.

In this case, to simplify the calculations and to obtain a more intuitive expression,we set the maximum for farming and working income at 100 (the real income can alsobe used). For subsidies, agricultural subsidies in China normally should not exceed10 % of agricultural income. Therefore, we set the maximum for subsidies at 10. Thevalues of alpha and beta can range from 0 to 1, α, β ∈ (0, 1). Variable alpha, with aselectively chosen value based on the conditions, is kept fixed during each simulationprocess, while the value of variable beta adaptively changes from 0 to 1, which rep-resents the relative gap between rural and urban living costs. Gamma represents theaverage household living expenses of farmers and can range from 1 to 100. Gammaincreases when the average living expenses rise.

The program compares the subsidy amount plus A’s actual income, which is farm-ing income multiplied by alpha or working income multiplied by beta, with total livingexpenses, which is 3 times the farming income multiplied by gamma. When the firstvalue is larger than the latter value, B will choose leisure with probability p and willchoose the farming or non-farming job with probability 1 − p. When the first value issmaller than the latter one, B must choose either the farming or the non-farming jobto maintain the basic household living standard. In addition, B will add the incomeutility from A to his own to obtain the household utility, and B will choose to work orto enjoy leisure to maximize the household utility.

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Table 2 Values of the parameters in the simulation

IW IF γ u α β p

CASE 1 60 20 10 5 1 * 0.5

CASE 2 60 20 20 5 1 * 0.5

CASE 3 60 20 6 5 1 * 0.5

CASE 4 60 20 16 1 1 * 0.5

CASE 5 * 20 16 0 1 1 0.5

CASE 6 * 20 6 5 1 0.4 0.5

* Value of the parameter varies during the simulation

4.2 Description of major results

First, to determine the effects of urban imputed living expenses on peasant households’labor allocation; we observe the results from changes in adjustment factor for workingincome(urban work) β. In this process, beta increases from 0.1 to 1.0. Some variablesare fixed, the adjustment factor for farming income αis 1, and the farming income IF is20. We use different values of other variables in different verification processes. Thesevalues are the average peasant households’ living expenses _γ , and the households’risk attitude coefficient_u. Here, we report the results of several conditions (Table 21).

Figure 2 presents the simulation results for case 1, in which we set IW = 60, IF =20, γ = 10, u = 5, α = 1, p = 0.5. At the beginning, agents tend to choose farm-ing in rural areas, even though the working income is much higher than the farmingincome. But when beta increases and the utility of the working income improves, someagents leave farming to work in urban areas; this indicates that urban living expensesas well as working income are major variables. As the pure working income increases,more peasants tend to choose leisure rather than going to work in urban areas. Evenwhen beta is 1 and working income is 3 times that of farming income, there are stilla significant number of peasants who stay in rural areas because of the pattern of riskaversion.

In case 2, we change gamma to 20 and keep the other variables unchanged (asshown in Fig. 3). We observe that the majority of rural laborers rapidly migrate to

1 For the values of farming income and working income, 20 and 60 are used to reflect the income gapbetween farmers and workers. Of course, other values can also be used, such as 30 and 90. Three times waschosen to reflect a relatively larger income gap between farmer and worker (the gap can also be 2.5 timesor 3.5 times), and then the changes in the curve can be more easily observed. The living costs in rural andurban areas vary greatly, which reflects the difference between developing countries (especially in China)and developed countries. Even if not working in cities would still maintain a basic living requirement,the value of gamma is less than or equal to that for farming income. For gamma, 6, 10, and 16 representdifferent living levels. In developing countries, the living standards in urban and rural areas are different,especially in China, where people living in rural areas can still maintain a basic living standard. Normally,the household member who is working in an urban area makes the money that the entire household spendsmainly in the rural area. Therefore, we set the gamma to be always less than or equal to farming income. Incase 6, β is chosen as 0.4 to reflect the fact that the living cost in an urban area is relatively high comparedwith urban working income and the living cost in rural areas. The value of p is set at 0.5 in all cases tosimplify the calculation.

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Fig. 2 Simulation results for case 1: IW = 60, IF = 20, γ = 10, u = 5, α = 1, p = 0.5. Asterisk β isexpressed as a percentage in horizontal axis

Fig. 3 Simulation results for case 2: IW = 60, IF = 20, γ = 20, u = 5, α = 1, p = 0.5. Asterisk β isexpressed as a percentage in horizontal axis

urban areas, and the increased working income does not lead to more leisure untilβ reaches 0.9. In this case, not all farmers from the countryside tend to move intothe cities for higher working income or to choose leisure. On the contrary, householdmembers staying in rural areas do not give up their land, and they may still invest in

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Fig. 4 Simulation results for condition 3: IW = 60, IF = 20, γ = 6, u = 5, α = 1, p = 0.5. Asterisk β

is expressed as a percentage in horizontal axis

agriculture under the risk constraints. Only when the real income in urban areas gradu-ally increases to a relatively high level do few peasants choose leisure (in Fig. 3, whenβ exceeds 0.9 there are 10 agents who choose leisure). In the traditional dual labor mar-ket hypothesis, leisure is not considered a behavioral choice for workers but instead isfactored into the individual labor hours supplied. Our experimental simulation resultsshow that complete leisure can exist in situations of “voluntary unemployment.” Aslong as the external market environment does not change, in theory, such behaviorand this pattern of household labor supply will continue in the long term, as distinctfrom short-term voluntarily unemployment enabled by individual savings or long-termvoluntary unemployment enabled by other sources of income (property, heritage).From the perspective of social welfare and efficiency, this is a negative externality.

In Fig. 4, when we adjust gamma to 6, the total household living expenses are 18.These expenses can be covered by farming income alone, with the result that morepeasants choose leisure. The Figure also shows that there are a significant numberof workers who remain in rural areas enjoying leisure, which means that increasingthe pure working income or the utility of income in urban areas cannot drive farminglaborers to become urban workers. This result is similar to our actual situation in thatthe Lewis turning point coexists with surplus labor.

To verify the effects of the risk management of agents, we set u to 1. As the result,Fig. 5 shows that as long as some risk exists, no matter the size, some agents willalways stay in rural areas, and some individuals will choose leisure. With the increasein working income, the number of those choosing farming dropped significantly but

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Fig. 5 Simulation results for condition 4: IW = 60, IF = 20, γ = 16, u = 1, α = 1, p = 0.5. Asterisk β

is expressed as a percentage in horizontal axis

still not all turn into workers, while the number of those choosing leisure increasedsignificantly. As the value of beta increases to a certain value, in this case ∼71, thenumber of free agents suddenly jumps to 20 from zero. We observed that under therisks, even if the actual working income increased significantly, it is unlikely that allof the available farming laborers will transfer to urban areas with consideration andawareness of the risks. Conversely, as long as there is a self-sufficient economy, farm-ers cannot be completely divorced from the land, which has practical significance forthe small Chinese peasant economy in the current situation of a large population withrelatively limited land area.

In Fig. 6, we set u to 0, which means that farmers are no longer aware of the risks, andthe price of labor is the only key factor. The impact of price changes on farmers is nolonger a gradual process but has mutations and can jump to another balance suddenly,which contradicts the hypothesis in Lewis’ theory and urban-rural dual structure theory(in which risk factors are not considered) that urban migration continuously changeswith the increase in working income in urban areas. We also found that almost all ofthe agents choose to work in urban areas initially, and as the working income increases,more agents change to the other two strategies. However, leisure agents and farmingagents still exist, regardless of how high the income becomes. Because of urban livingexpenses, agents would rather have leisure or enjoy the low costs of rural life.

To further clarify the effect of the working income variable, we assume that theurban living expense is fixed and relatively high, where beta is 0.4 (Fig. 7). In this case,

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Fig. 6 Simulation results for condition 5: IF = 20, γ = 16, u = 0, α = 1, β = 1, p = 0.5

Fig. 7 Simulation results for condition 6: IF = 20, γ = 6, u = 5, α = 1, β = 0.4, p = 0.5

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with the increasing working income, the amount of people choosing leisure is steadyat approximately 33, even if the working income rises to 5 times farming income. Con-sidering the combined effect of the unemployment risk factor and the urban imputedcost, rather than working to obtain cash income directly from an urban manufacturingjob, a larger number of farmers still choose to remain in rural areas.

These results indicate that, normally, certain household members will stay in ruralareas because they are risk averse, even where the urban working income is 5 timesthat of the farming income. Moreover, more working income will enable more house-hold members to enjoy leisure, which indicates that the increasing utility of incomedoes not induce the majority of peasants to move to urban jobs but instead reduces thelabor supply for both rural and urban jobs. The results indicate that, as long as risksexist for urban employment and the self-sustaining lifestyle persists in rural areas,farmers will not completely migrate to urban areas because of increasing workingincome in the industrial sector. Rather, they will migrate only if that income is highenough to cover all of the risk costs, a condition that is fairly difficult to achieve indeveloping countries. Therefore, it cannot truly reflect the rural and urban migrationsituation by simply demonstrating that the Lewis turning point occurs as workingincome increases. The increase in an individual’s income is not the only key factor insurplus labor migration decisions. We can also observe a significant level of leisure inrural areas in our simulation when the working income is sufficiently high.

5 Conclusion

In summary, several new ideas have been put forward in this paper. First, farmers’economic behavior is considered in an interactive way, which means that they makedecisions based on the utility or strategy of others and not only based on their ownutility or strategy. Second, the roles of agricultural subsidies, imputed living cost andincome are discussed. Third, we introduce an adjustment factor to obtain pure income.Fourth, a dynamic determination model of household labor allocation based on utilitywith a nonlinear function is proposed, and fifth, scenarios for a surplus labor evolutionprocess are presented.

In the present work, we use the agent-based unitary model to analyze peasants’ eco-nomic behavior. Peasant households have complex characteristics of risk attitude, util-ity comparison and labor allocation methods that are ignored by the Lewis model. Thetraditional urban-rural dual structure theory relies on research on individual behavior,which ignores the interaction among household members. Such a theory also ignoresthe imputed urban living expenses and risk factors for farmers. Therefore, the the-ory fails to analyze real-world issues that affect labor migration in certain developingcountries. As a consequence, the urban industrial labor shortage does not necessarilymean that the Lewis turning point is reached because of the existence of low-incomerural labor and voluntarily unemployed peasants. However, our model, by introducingan interactive decision-making process, which includes risk attitude, can explain andsimulate the paradoxical phenomenon that surplus labor coexists with the Lewis turn-ing point and labor shortages in urban areas. This finding has important implicationsfor empirical studies.

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Acknowledgments This research work was supported by Program for China Postdoctoral Science Foun-dation (33110044).

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