incentive to work versus disincentive to invest: the case of china's rural reform, 1979–1984

JOURNAL OF COMPARATIVE ECONOMICS 22, 242–266 (1996)ARTICLE NO. 0029

Incentive to Work versus Disincentive to Invest:The Case of China’s Rural Reform, 1979–19841

CHONGWOO CHOE

La Trobe University, Bundoora, Victoria 3083, Australia

Received June 1, 1995; revised February 15, 1996

Choe, Chongwoo—Incentive to Work versus Disincentive to Invest: The case ofChina’s Rural Reform, 1979–1984

An institutional change from the communal system to the household responsibilitysystem in rural China brought about an increase in productivity during 1979–1984,but it has also opened up a set of new problems, including decreased investment. Iargue that the new responsibility system is effective in providing work incentives topeasants by rendering residual claims, but not so in internalizing positive externalitiesof investment, resulting in underinvestment. Remedies such as agricultural investmentsubsidies, investment tax credits, the roles of such institutions as township and villageenterprises in undertaking investment in agricultural infrastructure, and most funda-mentally, well-defined property rights are discussed. J. Comp. Econom., June 1996,22(3), pp. 242–266. La Trobe University, Bundoora, Victoria 3083, Australia.q 1996 Academic Press, Inc.

Journal of Economic Literature Classification Numbers: P27, P32.

1. INTRODUCTION

In the wake of a reform to the household responsibility system from tradi-tional collective farming, rural China has enjoyed a dramatic increase inoutput over the period 1979–1984. Many have attributed this success toimproved incentives that the new household responsibility system has

1 I thank Bob Ash, Harry Clarke, Sisira Jayasuriya, an anonymous referee, and the participantsat the International Conference: China’s Economy Towards 2000 held at La Trobe University,February 1995, for helpful comments. I gratefully acknowledge financial support provided bythe School Research Grant, School of Commerce and Economics, La Trobe University. Usualdisclaimer applies.

0147-5967/96 $18.00Copyright q 1996 by Academic Press, Inc.All rights of reproduction in any form reserved.

242

AID JCE 1364 / 6w07$$$$$1 05-07-96 09:51:08 ceas AP: Comp

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243DISINCENTIVE TO INVEST IN RURAL CHINA

TABLE 1

AVERAGE ANNUAL GROWTH RATES (%) OF AGRICULTURE, 1952–1987

Subsector 1952–1978 1978–1984 1984–1987

Crops 2.5 5.9 1.4Grain 2.4 4.8 00.2Cotton 2.0 17.7 012.9

Animal husbandry 4.0 10.0 8.5Fishery 19.9 12.7 18.6Forestry 9.4 14.9 0Sidelines 11.2 19.4 18.5

Agriculture (overall) 2.9 7.7 4.1

Source. Lin (1992), p.35.

brought.2 The seeming success of the reform, however, has been confrontedwith serious challenges in subsequent periods. Not only has output growthslowed since 1984, but rural China has to tackle a set of new problems tosecure sustainable growth in the future.3 Water conservation, soil erosion,decreased investment, and fragmentation of farmland are but a few (see Ash,1988; Kojima, 1988; or Chisholm and Jayasuriya, 1994). Table 1 shows adramatic change in output growth before and after the reform. Of particularsignificance is the decrease in grain production after the reform, which endan-gers the long-cherished goal of Chinese agricultural policy, food self-suffi-ciency.

Rather than providing a comprehensive discussion of these problems, Ifocus on one aspect of the problems in this paper: how the reform of thehousehold responsibility system has affected investment in agriculture. Thefollowing is quoted from Ash (1988), p. 552.

‘‘. . . recent years have seen agricultural investment in decline and the agriculturalinfrastructure deteriorating. Statistics provide eloquent testimony; during the Sixth Five-

2 Lin (1992) reports that the output growth during this period is largely due to the householdresponsibility system, some other factors including the increased use of fertilizers, an increasein the state procurement price, etc. McMillan et al. (1989) draw a similar conclusion. Althoughfavorable weather during the period has been also noted as an important factor (Zhang andCarter, 1994), there seems to be little objection to improved incentives that the householdresponsibility system has brought.

3 Lin (1992) ascribes the sluggish output growth during 1984–1987 to outflow of labor forcefrom the farming sector, a decrease in the state procurment price, and the completion of thereform to the household responsibility system among others.


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244 CHONGWOO CHOE

Year Plan period (1981–85), state investment in agricultural capital construction consti-tuted a mere 6 per cent of the state’s total outlay on capital construction, comparedwith an average of 11.9 per cent for the previous 29 years. Between 1980 and 1984,investment in water conservancy fell from 2.1 billion yuan to 1.1 billion. During 1981–85, the irrigated area declined by 9.33 million hectares so that it now embraces lessthan half of China’s cultivated area. That deficiency is particularly serious in thenorthern arid regions, where adequate water supplies are a critical condition of acceler-ated agricultural growth. The stock of farm machinery is old and the area under mecha-nized cultivation has fallen substantially in recent years. In general, the technical andmechanical base of agriculture remained low, with the supply of working capital fallingmarkedly short of demand.’’

The reasons for the decline of agricultural investment may be found in anumber of places. After the collapse of the rural commune, the ability ofrural China in mobilizing the mass labor necessary for investment in infra-structure has been, if not completely lost, weakened (Liu, 1994). Somewhatrelated to this point is the outflow of farm labor and capital to more lucrativetownship and village enterprises (Watson, 1989; Lin, 1992; Chisholm andJayasuriya, 1994). An extreme fragmentation of landholding after the reformcreates adverse conditions for further infrastructural investment (Kojima,1988; Liu, 1994).

I attempt to provide another, formal explanation for decreased agriculturalinvestment. Under collective farming without a well-functioning monitoring sys-tem, the production team faces the classical problem of free-riding as in Holm-strom (1982).4 The introduction of the household responsibility system is intendedto resolve this problem by making each peasant a residual claimant, therebyproviding incentives to work. However, I argue that the very household responsi-bility system opens up a room for another kind of free-riding. Under the house-hold responsibility system, each household works on a separate plot, sharingsuch common resources as water conservation systems, farm machinery, draughtanimals, and so on.5 The nature of this new kind of free-riding is, then, similarto that of the tragedy of the commons: a disincentive to invest in common

4 Lin (1988, 1990) argues that formal supervision was technologically impossible in Chinesecollective farms and that the only way to extract effort was to threaten shirkers with informalretaliation (i.e., exit from the team by honest workers). See also a special issue on Chinese RuralReform in Journal of Comparative Economics, 1993, on the debate over this point. Dong andDow (1993a) estimate significant monitoring costs in Chinese agricultural teams, while addingthat punishments on shirkers might not have been likely, possibly due to egalitarian considera-tions.

5 Although the privatization of farm machinery and draught animals was carried out ratherrapidly, Kojima (1988) reports that, at the end of 1984, for every 100 farms, there were only 47draught animals, three hand tractors, one diesel engine, three motors, and one pump. The owner-ship of all water resources rested with the state, the management taking various forms of thecollective contract system.


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resources. Of course, this is not the problem inherent in the household responsibil-ity system per se, nor do I argue that these resources were entirely shared. Rather,what lies at the core of the problem is ill-defined property rights and/or thedifficulty of enforcing property rights. A peasant may secretly water his plot inthe still of the night from the irrigation ditch built by others, may freely adopta more productive seeding method developed through the efforts of the membersin his township, etc. Consequently, incentives to work under the householdresponsibility system may have been gained at the cost of reduced incentives toinvest. This would have a mixed effect on the output growth. In the short run,improved incentives to work may have caused the increase in productivity aswas the case during the period 1979–1984. Over time, this may have been offsetby the decrease in investment, resulting in sluggish output growth in subsequentperiods. How significant this effect has been requires empirical studies that,however, will not be carried out in the present paper. The purpose of this studyis to provide a simple formalization of the above idea that incentives to workvs disincentives to invest are the benefit and cost of the household responsibilitysystem.

The rest of the paper is organized as follows. Section 2 gives a brief,historical description of rural China before and after the reform leading tothe near-universal adoption of the household responsibility system. The prob-lem of underinvestment in agriculture during the first stage, 1979–1984, ofthe reform is then discussed. Section 3 describes the model, analyzing theindividual choice of labor and investment under the household responsibilitysystem, which is then compared with the choice under a team productionwith various work point systems. Section 4 discusses possible remedies tothe underinvestment problem and policy measures that have been taken inthe subsequent reform. Section 5 concludes the paper. Proofs of main proposi-tions in Section 3 are relegated to the Appendix.

2. A BRIEF HISTORY OF CHINA’S RURAL REFORM AND THEPROBLEM OF UNDERINVESTMENT

2.1. CHINA’S RURAL REFORM, 1979–19846

Prior to broad changes in rural policy initiated at the end of 1978, a typicalChinese rural commune consisted of three levels of units: the productionteam, the production brigade, and the commune. The production team wasthe basic accounting and production-organizing unit. Each team was givenannual production targets, sent through brigades and communes, based uponwhich it drew up its own plans, deciding how to organize production, when

6 This part closely follows Ash (1988), Lin (1988), and McMillan et al. (1989).


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246 CHONGWOO CHOE

to plow and plant and what types of fertilizer to use for which kinds of crops.At the end of a year, the net team income, after deductions for state taxes,the public welfare fund, etc., was distributed to team members according towork points that each one had accumulated during the year. Various systemsof work points were used. In essence, the quantity of work done was measuredby labor days, one labor day being assigned for each day a member appearedin the field. The quality of work done was measured by work points receivedper labor day, which were determined by peers’ evaluation, the assessmentby the team staff, and the preassigned grade into which each team memberwas classified. The number of labor days was multiplied to work points earnedper each day, yielding a member’s total work points for the year. Lin (1988)argues, however, that it is extremely difficult to supervize agricultural work,often leading each team member to receive fixed work points for a day’swork regardless of the quality of his work, hence a low incentive to work.

Ash (1988) pins down the central strategy of the reform in 1979–1984 asrestructuring rural economy through institutional change, based on decentral-ization of farming operations. Main policy issues during the reform summa-rized by him include the evolution of the household responsibility system,the reform of the commune system, diversification of the agricultural andrural economies, and the emergence of specialized households, and price, taxand quota adjustments (Ash, 1988, p. 530, Table 1). Although the householdresponsibility system was fully conceded by the central authorities only laterin the period, it must be regarded as the core of the reform.

The gist of the household responsibility system was two forms of output-linked contracts: baochan daohu (contracting output to the household) andbaogan daohu (contracting everything to the household). The former allocateda fixed amount of land to the household and specified a target level of output,while inputs were provided by the production team. The baogan daohu dif-fered from the baochan daohu in distributing draught animals, farm tools,and other equipment among the households. Moreover, once the specifiedquotas and taxes were paid to the state, it allowed the household to disposeof anything left, thereby rendering the residual claim to the household. Bythe end of 1984, virtually all agricultural households were switched to someform of output-linked responsibility system, with the proportion of baogandaohu well exceeding 95% (Ash, 1988, p. 538, Table 2). The evolution ofthe household responsibility system was also accompanied by administrativechanges with the gradual disbandment of the commune system and reemer-gence of townships as the basic unit of government administration (Ash,1988, p. 539, Table 3).

In short, the reform of 1979–1984 is characterized by the evolution of thehousehold responsibility system along with some other policy changes toencourage decentralization of farming operations. Such changes were obvi-


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ously intended to improve incentives of agricultural households, and, indeed,they have proven to be successful during the period. As it turned out, however,improved incentives were limited more or less to separate, fragmented plotsof each individual household only, presenting a new problem of decliningincentive to invest, a discussion of which follows in the next section.

2.2. THE PROBLEM OF UNDERINVESTMENT

While the main focus of this paper is on the underinvestment problem atthe level of individual peasants after the reform, it seems appropriate to havea broader picture of how patterns of investment changed after the reform. Asa number of studies (e.g., Watson, 1989; Ash, 1991; Feder et al., 1992; Tsangand Cheng, 1994, among others) already addressed this issue in some detail,the treatment in this section will be a brief review with details referred to theabove studies.

Four major sources for investment in agriculture are labor accumulation,direct and indirect state investment, investment by rural collectives, and in-vestment by rural residents. There is no dispute that mass labor mobilizedunder the communal directives before the reform was instrumental in theconstruction of agricultural infrastructure. During the 1960’s and 1970’s, itis estimated that some 80 million laborers were mobilized each year with anaccumulated total of 8 billion days of work (Watson, 1989, p. 95). Becauseof the dissolution of the commune system that followed the reform, masslabor no longer comes for free. Household labor mobilized for collective andstate projects has to be subsidized or paid. Moreover, rural cadres no longerhave the authority to command peasant labor. It is estimated that labor accu-mulation after the reform has dropped to only a quarter of what it used to be(Watson, 1989, p. 103).

Table 2 shows that state investment in agriculture had been declining until1986. Such trend is more dramatic when we look at the proportion of invest-ment in agriculture relative to total investment. Watson (1989) argues thatone of the reasons for the decline in the state investment is the rise in stateprocurement prices for agricultural products. Another reason can be found inthe gradual process of decentralization. As the reform progressed, more andmore autonomy was given to local governments in allocating budgetary reve-nues. It may be deemed a rational choice for local governments to investmore in lucrative industrial and commercial development than in agriculture.

A similar trend is observed from the investment pattern of rural collectives.As Table 3 shows, investment in agriculture by rural collectives showed adrastic decrease both in absolute and in relative terms until 1986. This de-crease is partly due to the introduction of the household responsibility system,under which a growing proportion of agricultural and sideline output belonged


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248 CHONGWOO CHOE

TABLE 2

INVESTMENT IN FIXED ASSETS OF STATE-OWNED UNITS (UNIT: BILLIONS OF YUAN)

Total investment For agriculture, (B) asin fixed assets forestry, husbandry, % of

Year (A) and fishery (B) (A)

1981 66.75 3.47 (3.47) 5.21982 84.53 4.25 (4.18) 5.01983 95.20 4.18 (4.07) 4.41984 118.52 4.56 (4.31) 3.81985 168.05 4.46 (4.08) 2.71986 197.85 4.33 (3.84) 2.21987 229.80 5.49 (4.65) 2.41988 269.50 6.20 (4.56) 2.31989 253.54 6.22 (3.85) 2.51990 291.86 8.03 (4.75) 2.81991 362.81 10.14 (5.83) 2.81992 527.36 13.23 (7.37) 2.5

Source: Statistical Yearbook of China, 1993, p. 124. All figures except those in the bracketsare in current prices. Figures in the brackets represent the values deflated by the overall industrialproducts rural retail price index (Statistical Yearbook of China, 1993, p. 202) with 1981 as thebase year. See the Appendix (Table 6) for the price indices.

to the contracting households. Another culprit is the rapid emergence of morelucrative rural industries, township and village enterprises being a notableexample. Undoubtedly these enterprises have diverted resources away fromagriculture. According to Ash (1991, Table A3), the share of agriculturalloans of the Agricultural Bank of China declined from 22.84% in 1979 to11.77% in 1986, while that of rural credit cooperatives declined from 71.41%in 1979 to 53.23% in 1986.

The decrease in agricultural investment by the state and rural collectiveshas been offset partly by the increase in the investment by rural residents asTable 4 shows. Although the level of overall investment shows a steadyincrease, absolute figures are rather misleading in so far as what proportionof the increased investment was intended for the improvement of agriculturalproductivity. As Table 4 clearly demonstrates, peasants’ investment structurehas been biased toward residential housing.7 While purchases of productive

7 Feder et al. (1992) argue that possible reasons for the heavy investment in housing are:farmers view investment in housing as relatively risk-free because houses were allowed to beprivately owned; by building a house, a Chinese farm household in effect establishes permanentuse rights on the land on which the house stands; housing is a consumption item with relatively


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TABLE 3

INVESTMENT IN FIXED ASSETS BY RURAL COLLECTIVES (UNIT: BILLIONS OF YUAN)

Total investment For agriculture, (B) asin fixed assets forestry, husbandry, % of

Year (A) and fishery (B) (A)

1982 13.14 5.23 (5.15) 39.61983 11.07 3.34 (3.26) 30.11984 17.48 2.90 (2.74) 16.61985 19.92 2.07 (1.90) 10.41986 24.54 1.99 (1.77) 8.11987 36.57 4.25 (3.60) 11.61988 37.64 4.29 (3.15) 11.41989 38.44 4.38 (2.71) 11.41990 36.61 6.23 (3.69) 17.01991 49.40 7.20 (4.14) 14.61992 99.49 8.79 (4.90) 8.8

Source: Statistical Yearbook of China, various issues. All figures except those in the bracketsare in current prices. Figures in the brackets represent the values deflated by the overall industrialproducts rural retail price index (Statistical Yearbook of China, 1993, p. 202) with 1981 as thebase year.

assets increased until 1985, not all of these assets were used for agriculturalpurposes. For instance, a steady increase in the number of tractors is largelyexplained by their use in providing nonagricultural transport services. In fact,despite the increase in the number of tractors, the tractor-plowed area fellfrom 42.2 million hectares in 1979 to 34.9 million hectares in 1984 (Putt-erman, 1993, p. 38; also Table 5 below). Moreover, due to the nature ofprojects, peasants’ investments could not compensate for public, state andcollective, investments in larger projects such as agricultural infrastructure.Together with the decline in public investment, this has resulted in seriouslack of investment in agricultural infrastructure such as irrigation systems.

To account for the laxity in agricultural production, it is therefore necessaryto decompose the agricultural investment into two components: a productivecomponent and a nonproductive component, the latter including the invest-ment in residential housing. In a country like China, where full mechanizationof agriculture is still a remote possibility, the most significant inputs to agricul-ture are no doubt human labor and agricultural infrastructure. In what follows,

high income elasticity; the baby boom in the early 1960’s coupled with the fact that, in ruralChina, a new house has become a precondition for marriage eligibility of young males, etc.


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250 CHONGWOO CHOE

TABLE 4

INVESTMENT IN FIXED ASSETS BY RURAL RESIDENTS (UNIT: BILLIONS OF YUAN)

Total Forinvestment in purchases of (B) as Forfixed assets productive % of nonproductive

Year (A) assets (B) (A) constructiona

1982 19.85 (19.54) 3.00 (2.95) 15.1 16.85 (16.59)1983 30.51 (29.74) 6.10 (5.95) 20.0 24.41 (23.79)1984 37.91 (35.83) 11.33 (10.71) 29.9 26.58 (25.12)1985 47.84 (43.81) 12.83 (11.75) 26.8 35.01 (32.06)1986 57.48 (51.00) 7.18 (6.37) 12.5 50.30 (44.63)1987 69.53 (58.87) 9.21 (7.80) 13.3 60.32 (51.07)1988 86.52 (63.57) 12.40 (9.11) 14.3 74.12 (54.46)1989 89.20 (55.20) 9.79 (6.06) 11.0 79.41 (49.14)1990 87.65 (51.90) 9.93 (5.89) 11.1 77.72 (46.01)1991 104.26 (59.89) 13.01 (7.47) 12.5 91.25 (52.42)1992 100.55 (56.05) 6.80 (3.79) 6.8 93.75 (52.26)

Source. Statistical Yearbook of China, 1993, p. 182. All figures except those in the bracketsare in current prices. Figures in the brackets represent the values deflated by the overall industrialproducts rural retail price index (Statistical Yearbook of China, 1993, p. 202) with 1981 as thebase year.

a Nonproductive construction consists mainly of the investment in residential housing.

the focus will be on the productive component, in particular, on the investmentin agricultural capital construction.

3. INCENTIVE TO WORK VS DISINCENTIVE TO INVEST

Consider a production team consisting of n peasants. The model I study isa slight extension of Dong and Dow (1993b). Each peasant i supplies laborinput li § 0 and chooses the level of investment ki § 0. Rather than suchquantitative measures as hours worked or work days, the labor input is inter-preted as the quality of labor or the intensity of effort. Without doubt, thelatter is more significant in directly affecting output. A consequence of thisinterpretation, though, is that this type of input may be harder to monitor andmeasure, and thus to use to assess the reward to peasants, which may wellhave been the case in rural China under the collective farming system (Lin,1988). The investment variable is taken quite generally. It could be anymaterial inputs of peasants, including hours worked for agricultural capitalconstruction, repair and maintenance, and so on, which are easier to measurethan the labor input.


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I assume a standard quasilinear utility function for each peasant. That is,peasant i’s utility function is expressed as

ui(yi , li , ki , ∑jxi

kj) Å yi 0 ci(li , ki , ∑jxi

kj), i Å 1, . . ., n, (1)

where yi § 0 is peasant i’s income and ci is the cost to peasant i of supplying(li , ki). The dependence of ci on the investment of all other peasants capturesthe positive externalities of investment. In the absence of well-defined prop-erty rights, peasant i may enjoy the reduction of his own investment costthanks to the investment taken by others. Consequently, ci is nondecreasingin li , ki and nonincreasing in (jxikj . More specifically, I assume a separablecost function,

ci(li , ki , ∑jxi

kj) Å £i(li) / wi(ki , ∑jxi

kj), i Å 1, . . ., n, (2)

with £*i § 0, £9i § 0, (Ìwi/Ìki) § 0, (Ì/Ìki)(Ìwi/Ìki) § 0, (Ìwi/Ì((jxiki)) £0.8 A final assumption on preference is the symmetry of wi : wi(ki , (jxikj) Åwk(ki , (jxikj) for all i, k. In other words, the cost of his own investment andthe benefit of the investment taken by others affect each peasant in the sameway.9 This assumption is for ease of analysis, in particular enabling us tofocus on the symmetric choice of investment at the equilibrium.

In order to focus on the incentive aspect of institutional changes that accom-panied the reform, I abstract away such factors as the state quota and variousprices and work directly with the net income that is represented by the produc-tion

F(L, K) Å u1L / u2K, (3)

where L is the aggregate labor input, K is the aggregate investment, and u1 ,u2 ú 0 are given parameters. An explanation for the form of the aboveproduction function is in order. It is decomposed into two parts: a temporarycomponent (u1L) that is dependent mainly on the labor input, and a persistentcomponent (u2K) that is dependent mainly on investment. Since the effect ofinvestment on output is expected to last for a certain period of time, the lattermay also be interpreted as the present discounted return from the investment.Thus a one-shot decrease (increase) in L will cause a temporary decrease(increase) in income, while one-shot decrease (increase) in K will be reflected

8 Positive externalities of investment may be expressed through individual production functionsas well. Separability of the cost function is for simplicity: along with the production functionspecified below, it allows separate analysis of the choice of li and ki .

9 Examples are wi(ki , (jxikj) Å f(ki) / g((jxikj) with f* § 0, g* £ 0; wi(ki , (jxikj) Åf(ki)/g((jxikj)) with f* § 0, g* § 0.


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252 CHONGWOO CHOE

by a decrease (increase) in income over a period of time, possibly with a lag.A formal dynamic analysis will be deferred to a later occasion. Again, theseparability of the production function is for simplicity.

We start by characterizing the Pareto-optimal allocation of labor and invest-ment as a benchmark. It is the solution to the program

Maximize(li,ki)iÅ1,. . . ,nu1 ∑

n

jÅ1

lj / u2 ∑n

jÅi

kj 0 ∑n

jÅ1

[£j(lj) / wj(kj , ∑ixj

ki)].

Denote the solution to the above program by (l*i , k*i )iÅ1,. . .,n . Then the first-order conditions are

u1 Å £*i (l*i ), i Å 1, . . ., n, (4)

u2 ÅÌwi

Ìki

(k*i , ∑jxi

k*j ) / ∑jxi

Ìwj

Ìki

(k*j , ∑lxj

k*l ), i Å 1, . . ., n. (5)

The second term on the right-hand side of (5) measures the marginal externali-ties of investment. By the linearity of the production function and the separa-bility of cost functions, the optimal choice of labor is independent of theoptimal choice of investment. Note also that, due to the symmetry of wi , wemay focus on the symmetric choice of ki . That is, k*i Å k*j for all i, j. Thiswill simplify the analysis to follow.

Although the household responsibility system followed various work pointsystems historically, we will first study the individual peasant’s choice oflabor and investment under the household responsibility system. It will beshown that the choice of labor is made at an optimal level while the choiceof investment is made at a suboptimal level. Work point systems will thenbe studied depending on two assumptions about the monitoring ability of theproduction team. In the first case, work points depend only on the investment,which I call the work point system with partial monitoring. The rationale forthis kind of partial monitoring is that the labor input as representing the qualityof effort is hard to measure, while the investment activity as is understood inthe current context is rather easy to assess. The resulting choice of labor isbelow the optimal level, while investment is above the level chosen underthe household responsibility system. As Liu (1994) emphatically argues, thisis what may have been the case in rural China under the communal system,whose high capacity for labor mobilization made possible the investment insuch agricultural infrastructure as irrigation systems. If this was indeed thecase, then the institutional change from the communal system to the householdresponsibility system has brought about an increase in labor supply and adecrease in investment. Impressive output growth during the early phase ofthe reform may be attributed to the former factor, which mainly affects the


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temporary component of the production function, while the subsequent stagna-tion may be imputed to the latter factor which exercises a persistent impactupon output. Next, team production in the absence of monitoring will bestudied, showing not surprisingly, that both the labor and the investment arechosen at suboptimal levels.

3.1. HOUSEHOLD RESPONSIBILITY SYSTEM

The household responsibility system I consider is the prevalent baogandaohu, under which each peasant is the residual claimant. Thus, peasant itries to maximize his own net benefit given the choice of investment byothers, denoted by (kh

j )jxi . Although the household responsibility system hasintroduced a set of new choice variables to peasants, such as investing inresidential housing or leaving farms for rural enterprises, I consider the prob-lem of a peasant who stays in agriculture. Moreover, investment in nonproduc-tive components, residential housing in particular, is precluded from the prob-lem since it adds an additional dimension, making the comparison of the twoinstitutional arrangements intractable. The objective function is then

u1li / u2ki 0 £i(li) 0 wi(ki , ∑jxi

k hj ). (6)

The Nash equilibrium will be denoted by (lhi , kh

i )iÅ1,. . .,n . The first-order condi-tions for maximization are

u1 Å £*i (lhi ), i Å 1, . . ., n, (7)

u2 ÅÌwi

Ìki

(khi , ∑

jxi

k hj ), i Å 1, . . ., n. (8)

As is clear from the comparison of the above conditions with the first-orderconditions of the Pareto-optimal problem, the equilibrium choice of labor isequal to the Pareto-optimal level of labor allocation. This is mainly due tothe linearity of the production function and the separability of cost functions,which furthermore ensure that the above choice of labor is also a dominantstrategy for each peasant. Thus the household responsibility system providesincentives to work to each peasant. The household responsibility system,however, results in underinvestment. Since it fails to internalize the externalbenefits of investment, we have a classical case of positive mutual externali-ties. More formally, we have the following proposition.

PROPOSITION 1. Under the household responsibility system, the equilibriumchoice of labor is made at an optimal level, but the equilibrium choice ofinvestment is made at a suboptimal level. That is, lh

i Å l*i , khi £ k*i for all i.


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254 CHONGWOO CHOE

3.2. WORK POINT SYSTEM

We study two cases of work point system depending on the team’s abilityto monitor. In the first instance, no monitoring is done. It is then natural toconsider a symmetric distribution of the net team income as a probable sharingrule. Namely, each team member has a share of 1/n of the net team income.10

The case of partial monitoring is considered next, under which the team baseseach peasant’s work points only on investment. The rationale for the partialmonitoring has been provided earlier.

Whether the communal system was exercising effective monitoring is aquestion of empirical nature. While Dong and Dow (1993a) estimate, apartfrom the effectiveness of monitoring, the monitoring cost of about 10–20%of overall labor time during the period 1970–1976, Lin (1988) emphasizesthe extreme difficulty of supervising agricultural work due to the spatialdispersion and the sequential nature of agriculture, establishing a case for nomonitoring. However, it will be shown within the context of current modelthat the case of no monitoring results in the undersupply of labor as well asthe underinvestment, not being able to explain why investment has stagnatedafter the reform in favor of the household responsibility system. This leadsus to suspect that partial monitoring is the case that, at least theoretically,will give us the desired result that a shift from the work point system withpartial monitoring to the household responsibility system results in an increaseof labor effort and a decrease of investment.

Throughout this subsection, I maintain a simplifying technical assumptionabout the sign of cross-partial derivative of the cost function, wi :(Ì/Ìki)((Ìwi/Ì (jxikj)) § 0 for all i Å 1, . . ., n. This assumption means that themarginal external effect is nondecreasing in one’s own investment, implying akind of complementarity in investment.

3.2.1. Work Point System with No Monitoring

Since each team member has a share 1/n of the net team income in theabsence of monitoring, peasant i has the objective function

1n

[u1(li / ∑jxi

l nj ) / u2(ki / ∑

jxi

k nj )] 0 £i(li) 0 wi(ki , ∑

jxi

k nj ), (9)

10 The case of no monitoring is an abstraction. Even if resources have actually been used forthe purpose of monitoring (Dong and Dow, 1993a), all that matters is whether the monitoringsuccessfully rewarded hard-working peasants. Lin (1988, 1990) argues this was not the case,which is rejected by Kung (1993). This case of symmetric distribution is also the one studiedby Dong and Dow (1993b).


Econ


where (l nj , kn

j )jxi is peasant i’s expectation of others’ choice. Denote the Nashequilibrium by (l n

i , kni ), i Å 1, . . ., n. Then from the first-order conditions for

individual maximization,

1nu1 Å £*i (l

ni ), i Å 1, . . ., n, (10)

1nu2 Å

Ìwi

Ìki

(kni , ∑

jxi

k nj ), i Å 1, . . ., n. (11)

Comparing the above with (7), (8) shows that both the labor and theinvestment chosen under the work point system without monitoring are belowthe levels chosen under the household responsibility system. In the absenceof monitoring, each peasant chooses labor so that the marginal disutility oflabor (£*i (l

ni )) is equated to the fraction 1/n of the marginal return (u1) under

the household responsibility system. Since the marginal disutility is nonde-creasing in labor, we have ln

i £ lhi for all i, recalling that (lh

i )iÅ1,. . .,n is the laborchosen under the household responsibility system. Also due to the symmetryof wi , we have kn

i Å knj for all i, j as can be verified by inspecting (11). Noting

again that (khi )iÅ1,. . .,n is the investment chosen under the household responsibil-

ity system, we have (Ìwi/Ìki)(kni , (jxik

nj ) £ (Ìwi/Ìki)(k

hi , (jxik

hj ) for all i Å

1, . . ., n. Since it was assumed that (Ì/Ìki)(Ìwi/Ì(jxikj) Å(Ì/Ì(jxikj)(Ìwi/Ìki)) § 0 for all i Å 1, . . . , n, kn

i £ khi for all i Å 1, . . . , n

follows from the fact that kni Å kn

j , khi Å kh

j for all i, j. The reason for theunderinvestment is again the same: each peasant’s marginal investment isrewarded only by a fraction of his marginal cost. Proposition 1 then allowsus to conclude the above argument in the following proposition.

PROPOSITION 2. Under the work point system without monitoring whereeach peasant has an equal share of the net team income, both the labor and

the investment are chosen suboptimally. That is, lni £ l*i , kn

i £ k*i for all i Å1, . . ., n.

The point made in the above proposition is by no means new: in teamproduction, the piece rate contract fails to provide incentives for efficientbehavior. Such observation has been made by numerous authors, Meade(1972) and Holmstrom (1982) among others. Moreover, what has actuallyhappened during the reform seems to vitiate the conclusion of the proposition.If we take the work point system without monitoring as what prevailed undercollective farming, then Propositions 1 and 2 imply a counterfactual conclu-sion that both investment and labor effort have increased after the reform,contrary to an ample evidence of underinvestment that has already beendocumented. This begs the question of whether the collective farming indeed


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256 CHONGWOO CHOE

suffered from the absence of monitoring. In the least, it was the case thatwork points were assessed for each peasant based on such observable variablesas work days or tasks (Putterman, 1990). This leads us to the work pointsystem with partial monitoring.

3.2.2. Work Point System with Partial Monitoring

Let (li , ki), i Å 1, . . ., n be the choice of labor and investment of teammembers. Under the assumption of partial monitoring, work points are as-sessed based only on investment. Thus total work points are (n

jÅikj . The shareof peasant i out of the net team income is then (ki/(

njÅ1kj). Peasant i then

chooses labor and investment to maximize his net benefit given the expecta-tion of others’ choice, denoted by (lp

j , kpj )jxi . The objective function is

ki

ki / (jxikpj

[u1(li / (jxi lpj ) / u2(ki /∑

jxi

k pj )] 0 £i(li) 0 wi(ki , ∑

jxi

k pj ). (12)

Denote the Nash equilibrium by (lpi , kp

i ), i Å 1, . . ., n. Then from the first-order conditions for individual maximization,

kpi

(njÅ1k

pj

u1 Å £*i (lpi ), i Å 1, . . ., n, (13)

(jxikpj

(njÅ1k

pjSu1 (n

jÅ1lpj / u2 (n

jÅ1kpj

(njÅ1k

pj

D / kpi

(njÅ1k

pj

u2 ÅÌwi

Ìki

(kpi , ∑

jxi

k pj ),

i Å 1, . . ., n. (14)

Equations (13) states that the marginal disutility of labor is equated to afraction of the marginal return, with the fraction equal to each peasant’s workpoints divided by total work points. A similar argument as in Proposition 2then shows that the labor chosen under this regime is below the level under thehousehold responsibility system. The marginal cost of investment, however, isequal to the weighted average of the average return from investment ((u1

(njÅ1l

pj / u2 (n

jÅ1kpj ) /(n

jÅ1kpj ), and the marginal return (u2), where each peasant’s

work points share is used as the weight. Since the average return from invest-ment is higher than the marginal return, we may conjecture that the level ofinvestment chosen under this regime will be higher than under the householdresponsibility system where the marginal cost of investment is equated to themarginal return from investment.11 More formally, we have the followingproposition.

11 This is reminiscent of what Sen (1966) dubbed the overallocation of labor in a cooperativeenterprise.


Econ


PROPOSITION 3. Under the work point system with partial monitoring, laboris chosen below the level under the household responsibility system, whileinvestment is chosen above the level under the household responsibility sys-tem. That is,

lpi £ lh

i , kpi § kh

i for all i Å 1, . . . , n.

The novelty of Proposition 3 is that when monitoring is only partial in ateam production, a team member has an incentive to oversupply only thatinput that is monitored while undersupplying the input that is not monitored.One one hand, it is contrasted with the observation of Meade (1972) that ateam member has an incentive to undersupply effort when the team incomeis equally shared among the members. On the other hand, it is contrastedwith Sen (1966) who showed that a team member oversupplies labor in acooperative enterprise with a proportionate-to-labor-supply sharing rule.

In view of the above proposition, the stagnant output growth following theinitial success of the reform to the household responsibility system may beascribed in part to the reduced incentive to invest. Initial increase in productiv-ity in 1978–1984 may be reflected in the temporary component of the produc-tion function, which has been augmented mainly by the improved incentiveto work. In fact, the estimate of McMillan et al. (1989) implies that Chinesepeasants supplied only about 56% as much effort under the communal systemas under the household responsibility system. Subsequent stagnation may bedue to the effect of reduced incentive to invest upon the persistent componentof the production function. Such a trend was clearly demonstrated in Table1. Moreover, in an empirical study of China’s grain sector for the period1966–1988, Tsang and Cheng (1994, Table 8) found that 88% of outputgrowth during 1978–1984 was attributed to the household responsibility sys-tem, while the fixed capital accounted for only 7% of output growth duringthe same period. They also found that the decrease in fixed capital accountedfor 97.5% of the decrease in grain output during 1984–1988. Aside fromthis, the household responsibility system is nevertheless an effective institu-tional device that brought about an increased incentive to work.

The following section discusses several measures that could be taken tocomplement the household responsibility system to alleviate the problem ofunderinvestment, which will then be followed by a discussion of subsequentreforms.

4. DISCUSSION OF REMEDIES AND SUBSEQUENT REFORM

4.1. Discussion of Remedies

We first discuss possible remedies to the underinvestment problem fromthe perspective of individual peasant’s incentives. The nature of the problem


Econ

258 CHONGWOO CHOE

is the positive externalities of investment that are not internalized under thehousehold responsibility system. Economic theory has taught us several waysof circumventing this problem: create markets for the external benefits; letthe involved parties bargain over the external benefits; and subsidize thosewho emit positive externalities. Considering the fact that the main point ofChina’s rural reform, which still has a long way to go, is introducing marketforces, the first option seems a remote possibility. Neither does the secondoption seem feasible, in particular in the absence of well-defined propertyrights, which are a crucial prerequisite for any efficient bargaining. This leavesus the option of an investment subsidy or tax credit. In what follows, theproblems involved in the use of an investment subsidy will be discussed withthe derivation of optimal investment subsidy relegated to the Appendix.

Two problems can be raised regarding the use of investment subsidy. Thefirst one, as is the case with any Pigouvian subsidy or tax, is the informationalrequirement. In order to determine the size of the subsidy, the knowledge ofindividual cost functions, preferences, and the production functions of eachteam is a prerequisite, which may be a daunting task for the state, especiallyin a huge, populous country like China. A role may be played by localadministrative units of each township and village. They may gather informa-tion, compute the amount of subsidy needed for each township to which theybelong, and report to the central authorities who, then, determine the size ofthe actual subsidy to give. While the role of information gathering by townshipand village governments may be feasible, this arrangement is subject to vari-ous transactions costs. For the subsidy scheme to work, accurate and impartialinformation gathering is essential. This process may be quite costly if itwere to successfully defeat peasants’ incentives to misrepresent their privateinformation to their advantage. Each township and village government mayalso have the incentive of misrepresentation simply to increase the size ofsubsidy allocated to its township and village. Finally, influence costs at variouslevels could be expended to affect the decision process as well as the imple-mentation of the subsidy scheme. Another, obviously harder, problem is thefeasibility of such a policy, especially when we consider the huge financialburden that already presses the Chinese government. In view of this, thesuccess of investment subsidy or tax credit directly aimed at individual peas-ants seems questionable, or, at least, may come at additional costs that maydefeat the intended purpose.

Another possible remedy may be found by reviewing the era of the commu-nal system when the investment in agricultural infrastructure was made possi-ble by the high capacity of the commune for labor mobilization. While I donot argue that the return to the communal era is desirable, nor does theChinese government endorse such retreat, it seems imperative that initiativesbe started at some collective level. At this point, the role of township and


Econ


village enterprises may be considered.12 They have two main advantagescompared to central authorities or local governments in undertaking invest-ment in agricultural infrastructure. The first one is the informational advantagethat enables them to make decisions as to which investment to make andhow, and which may better suit specific townships. Another advantage comesfrom their competitive nature and the proclivity to follow, more or less closely,a profit motive, in contrast to other institutions. What could be imagined isan institutional framework in which township and village enterprises emergeto undertake investment in agricultural infrastructure. The control, manage-ment, and maintenance of the infrastructure are given to the enterprises, whilethe state stipulates, in a way consistent with the overall interest of the public,minimal regulations to which these enterprises should adhere. For this scenarioto be attractive to the enterprises, at least two conditions must be met. Thefirst of these is the profitability of investment. With more lucrative industrialand commercial projects present, the state may have to subsidize those enter-prises undertaking agricultural investments. The second, and obviously morefundamental condition, is the guarantee of property rights. For it is needlessto say that the most powerful incentive of all is the alignment of control andownership.13 This last point deserves further comment.

In an afterthought, both at the level of individual incentives and at the levelof broader institutional aspect, the problems that followed initial success of thereform could have been expected. While the basic pillar of the socialist systemstill prohibits the private ownership of land, granting land usage rights only couldvery well have made peasants myopic. In the absence of confidence about thestability of the system, peasants may likely be interested only in a temporaryincrement to their own income, causing possible soil erosion, early depletion ofirrigation systems, etc. The absence of well-defined property rights acts as adisincentive to invest in infrastructure. The impossibility of land trading, althoughsubleasing was possible, together with peasants’ reluctance to relinquish usage

12 Township and village enterprises are collectives typically with close links to local administrativeand state structures, but are not subject to centralized state control. They have evolved as profit-oriented, dynamic entrepreneurial organizations in response to the opportunities created by the re-forms. In 1993, they accounted for 40% of the nation’s total industrial product and employed nearly112 million workers. See Chang and Wang (1994) or Chisholm and Jayasuriya (1994).

13 Chang and Wang (1994) note that the township and village enterprise is owned by localcitizens and controlled by the township and village government, thereby providing a solution tothe central government’s problem of improving citizens’ welfare subject to the constraints thatthe current political system be preserved and that local agents be provided with incentives.Although political constraints may be significant, these enterprises, as they stand, are also subjectto the problem of misalignment of ownership and control in so far as the control rights of theseenterprises rest with the township and village government. It thus seems necessary that theenterprise reform and the rural reform must proceed in a complementary way.


Econ

260 CHONGWOO CHOE

rights leave farmland fragmented at the cost of forsaken scale economies. Whatseems to be at the heart of the problem is the misalignment of ownership andcontrol. However, a sweeping change in the structure of property rights in Chinamay be both infeasible on political grounds and undesirable as we learned fromthe experience of the East European countries. What should happen, though, isa gradual, but definite establishment of well-defined property rights encom-passing, of course, land and enterprises.14

4.2. SUBSEQUENT REFORM

The Chinese government did recognize the problem of underinvestment inagriculture, and these concerns echo repeatedly in various central documents.15

This section reviews some of the major policy measures that have beentaken in subsequent periods and assesses their implication for agriculturalinvestment. These measures include further rationalization of the agriculturalproduct procurement system, policies on land use and land tenure, agriculturalsubsidies, and increases in agricultural investments and loans.

Given the institutional framework of the household responsibility systemprepared by the initial reform and seeming success of the newly introducedresponsibility system, it may be natural to expect that subsequent reformpolicies should be geared toward further strengthening of the responsibilitysystem. Such direction is reflected in Central Document No. 1 of 1985 andDocument No. 1 of 1986. The first of the 10 policies formulated in theformer is aimed at largely abolishing the state’s monopolistic procurementof agricultural products. For cotton and grain, monopolistic procurement wasreplaced by negotiated contractual procurement, with the contracts drawn upbefore the sowing season based on a ‘‘reverse 30–70 ratio,’’ meaning that30% of the contracted amount would be purchased at the state’s listed priceand 70% at the above-quota price. After meeting the contractual quotas, theremaining crops could be sold at the free market price, but with the provisothat the state would purchase all available crops at the listed price, shouldthe market price fall below the listed price. For other agricultural products,fixed procurement quotas were to be abolished and replaced by market trade.Document No. 1 of 1986 further reduced the total volume of contractual grainpurchases and guaranteed priority in obtaining loans and a fixed amount of

14 As Brada and King (1993) argue, it is needless to say that such a change should be accompaniedby general reshaping of the entire economic system in which socialist agriculture is embedded.

15 Such documents include Central Document No. 1 of 1985, Document No. 1 of 1986 on RuralWork, and Draft 1987 Plan for Economic and Social Development. For an English translation, seeBrithish Broadcasting Corporation, Summary of World Broadcasts. Part 3. The Far East, March27, 1985, February 16, 1986, April 15, 1987.


Econ


free chemical fertilizer proportional to the amount of contracted grain. Despitethese policies intended for introducing market forces to make agriculturemore profitable, agriculture still fell short of other sectors in profitability.16

Moreover, with falling grain production, the state retreated to mandatoryprocurement of grain in 1990. Although the introduction of market forces inagriculture may no doubt render higher productivity to agriculture, the marketforces per se cannot be a direct solution to the problem of underinvestment.Any rational decision on investment depends on returns from all other alterna-tives. While other sectors enjoy higher profitability and property rights remainunclear except for residential housing, it is not surprising that rural residentscontinue to direct their investment funds to nonproductive construction suchas residential housing. Such trend is shown clearly in Table 4.

The fragmentation of farmland and the uncertainty of land tenure are be-lieved to inhibit long-term investment in agriculture. In this regard, the natureof the relationship between the rural household and its contracted land wasreviewed in various policies. Peasants’ reluctance to invest in agriculture dueto uncertainty of land tenure may have been reduced, although not entirely,by Document No. 1 of 1984 that extended land tenure to 15 years or more,but, in effect, permanently as long as peasants stay in agriculture. This policy,however, could not prevent farmers from using land for purposes other thanagriculture such as house-building, forestry and husbandry, and so on. To-gether with the occupation of farmland by public enterprises and soil erosion,the decline of China’s arable area was substantial throughout the 1980’s.17

In this context, a land tax was proposed in 1987, which was designed torestrict encroachment on arable land by imposing a tax on units or householdsusing the land for nonagricultural purposes. The fragmentation of farmland,however, continues to be a problem. Although various proposals have beenmade to encourage more land concentration, it appears that specific policieshave yet to be worked out.18

Several agricultural subsidy programs have also been instituted for twopurposes. One was termed a ‘‘blood transfusion’’ (yigong bunong) that di-rectly allocates part of enterprise profits and tax remittances to peasants toreduce income differentials between peasants and their counterparts in ruralindustries. The other, called ‘‘blood making’’ (yigong jiannong), directs enter-prise income to rural collectives to cover costs of such things as irrigation,fertilizers, and farm machinery. For the purpose of improving agricultural

16 In 1986, the net output per employee in agriculture was only 15% of those in mining, 14%of those in manufacturing, and 37% of those in services (Watson, 1989, pp. 111–112).

17 During 1981–1985, about 2.5 million hectares were lost, and in 1986 and 1987, a further0.67 million hectares disappeared (Ash, 1988, p. 553).

18 See Watson (1989), pp. 121–122, on this.


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262 CHONGWOO CHOE

investment, there is no doubt that the latter is an effective measure. Neverthe-less, this free transfer can impinge on ownership rights and may underminethe incentives to promote rural enterprises.

The State Planning Commission’s Draft 1987 Plan for Economic and SocialDevelopment included medium and long-term plans for agricultural invest-ment. The draft emphatically stressed the plan to increase the state budgetallocation for direct investment in agriculture, forestry, and water conservationespecially for the construction of key projects designed to harness big rivers.The draft also emphasized the role of indigenous investment from within therural sector, especially investment by local authorities in capital constructionprojects and the mass mobilization of peasants for the maintenance and con-struction of such projects. To this end, the Agricultural Bank of China has beenencouraged to take the lead in extending more loans to support investment incapital and new technology. At least in absolute terms, such plans seem topay off, albeit very slowly, as we see in Table 2.

While the recognition of the underinvestment problem by the Chinesegovernment is clear, such recognition seems to have materialized only slowlypartly due to mismanagement of policies and partly due to policies not targetedat the core of the problem. This slow recovery is well reflected in Table 5.Although tractor-ploughed areas increased steadily since 1985, recovery ofthe irrigation system is slower, despite the government’s continued emphasison irrigation systems as the key aspect of agricultural investments. It is equivo-cally stressed by scholars and observers alike that the institutionalization ofcomprehensive property rights must be the ultimate and most fundamentalsolution to the underinvestment problem. What form of ownership solutionis suitable for rural China thus invites further research, although whether orhow such solution will be implemented remains to be seen.

5. CONCLUDING REMARKS

In this paper, I study a simple model of a production team to address thequestion of why agricultural productivity in China has stagnated after theinitial, seeming success of the reform from the traditional collective farmingto the household responsibility system. I seek the answer from the unwelcomeby-product of the reform: the disincentive to invest.

The main feature of the model is that each peasant chooses both labor andinvestment and that there are external economies of investment. Under thecommunal work point system with partial monitoring where each peasant’sinvestment is rewarded not only by an increase in his work points but by anincrease in net team income, the level of investment is higher than that underthe household responsibility system. For, under the latter, each peasant doesnot take into account the external benefits of his investment. Nonetheless, the


Econ


TABLE 5

AREA UNDER TRACTOR PLOUGHING AND IRRIGATION (UNIT: 1000 HECTARES)

Percentage ofArea under irrigation power-

irrigated areaTractor- Total Power- to total

Year ploughed area area irrigated area irrigated area

1978 406,700 449,650 248,950 55.41979 422,190 450,030 253,210 56.31980 409,900 448,880 253,150 56.41981 364,770 445,740 252,310 56.61982 351,150 441,770 251,450 56.91983 335,720 446,440 252,650 56.61984 349,220 444,530 250,620 56.41985 344,420 440,360 246,290 55.91986 364,280 442,260 250,320 56.61987 383,930 444,030 248,250 55.91988 409,140 443,760 260,830 58.81989 425,930 449,172 261,070 58.11990 482,552 474,031 271,483 57.31991 501,904 478,221 276,285 57.81992 514,690 485,901 282,828 58.2

Source. Statistical Yearbook of China, 1993, p 314.

household responsibility system induces the choice of labor at an optimallevel. Thus the benefit of the reform, the incentive to work, must be weighedagainst its cost, the disincentive to invest. Assuming that labor mainly exerts atemporary effect upon output while investment has a persistent effect, stagnantoutput growth after the initial success of the reform is imputed to underinvest-ment. Policy measures such as agricultural investment subsidies or agriculturalinvestment tax credits directed at individual peasants may not prove successfuldue to the informational requirements and transaction costs involved in thedesign and implementation of such schemes. It appears that the initiativeshould come at some collective level, where the roles of institutions such astownship and village enterprises are called into attention. It is needless tosay, however, that the remedy to the underinvestment problem at the mostfundamental level is the establishment of well-defined property rights.

The model has several restrictions. Aside from quasilinearity of preferencesand the way external economies are introduced, the seperability of the produc-tion function may not be warranted. Suffice it to say that the separability isfor the sake of decomposing the production function into temporary and


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264 CHONGWOO CHOE

persistent components, which much simplifies the matter as well. Perhaps, amore serious question may be whether the kind of partial monitoring I consideris a sensible one, a question that obviously invites further empirical studies.

The problem of stagnant investment is only one among many problemsthat plague current rural China. Fragmentation of farmland following thereform may have sacrificed scale economies. Early soil erosion and the deple-tion of irrigation systems are other factors explaining sluggish output growth.The current model is too simple and static to address these issues. However,I conjecture that a dynamic extension of the model could elucidate some ofthe environmental issues.

APPENDIX

TABLE 6

OVERALL INDUSTRIALPRODUCTS RURAL RETAIL PRICE INDEX BASE YEAR: 1981)

Year Price index

1981 100.01982 101.61983 102.61984 105.81985 109.21986 112.71987 118.11988 136.11989 161.61990 169.01991 174.11992 179.4

Source. Statistical Yearbook of China, 1993, p. 202.

Proof of Proposition 1. lhi Å l*i is clear. For kh

i £ k*i for all i, note thatu2k

hi 0 wi(k

hi , (jxik

hj ) § u2k*i 0 wi(k*i , (jxik

hj ) for all i by the definition of

khi . Summation over i yields u2(kh

i 0 (wi(khi , (jxik

hj ) § u2(k*i 0 (wi(k*i ,

(jxikhj ). By the definition of k*i , however, we also have u2(k*i 0 (wi(k*i ,

(jxik*j ) § u2(khi 0 (wi(k

hi , (jxik

hj ). Combining the two inequalities,

(wi(k*i , (jxik*j ) £ (wi(k*i , (jxikhj ). Moreover, due to symmetry of wi , we

have k*i Å k*j k hi Å kh

j for all i, j. Then khi £ k*i for all i follows from the

assumption thatwi is nonincreasing in its second argument. j

Proof of Proposition 3. To see lpi £ lh

i for all i Å 1, . . ., n, note that£*i (l

pi ) Å (kp

i /(njÅ1k

pj )u1 £ u1 Å £*i (l

hi ) for all i Å 1, . . ., n. Since £*i is nondecreasing


Econ


its argument, we have lpi £ lh

i for all i Å 1, . . ., n. Next I show kpi § kh

i forall i Å 1, . . ., n. An algebraic manipulation of the first-order conditions (14)yields (Ìwi/Ìki)(k

pi , (jxik

pj ) Å u2 / (u1(

njÅ1l

pj (jxik

pj /((

njÅ1k

pj )

2 for all i Å 1,. . ., n. Thus (Ìwi/Ìki)(k

pi , (jxik

pj ) § (Ìwi/Ìki)(k

hi , (jxik

hj ) Å u2 for all i Å 1,

. . ., n. The above first-order conditions also tell us that for each i, the choiceof kp

i depends only on others’ investment and the aggregate labor. Then fromthe symmetry of wi , we must have kp

i Å kpj for all i, j. Recalling kh

i Å khj for

all i, j, we have kpi § kh

i for all i Å 1, . . ., n by the assumption that the crosspartial derivative of wi is nonnegative. j

Derivation of optimal investment subsidy. The effect of subsidy given toeach unit of investment taken and that of investment tax credit can be analyzedin the same framework. Let si be the investment subsidy or tax credit givento peasant i for taking a unit of investment under the household responsibilitysystem. Then peasant i maximizes a new objective function

u1li / (u2 / si)ki 0 £i(li) 0 wi(ki , ∑jxi

k*j ), (A1)

where (k*j )jxi still denotes peasant i’s expectation of others’ investment. Corre-sponding first-order condition for the choice of investment at the Nash equilib-rium, (l*i , k*i )iÅ1, . . . ,n is

u2 ÅÌwi

Ìki

(k*i , ∑jxi

k*j ) 0 si . (A2)

All we need to determine now is the size of subsidy si that makes the Nashequilibrium equal to the Pareto-optimal level of labor and investment thatwas denoted by (l*i , k*i )iÅ1, . . . ,n . Note that the subsidy does not affect thechoice of labor; hence, l*i Å l*i for all i Å 1, . . ., n. Recall that the first-orderconditions for the choice of investment in the Pareto-optimal problem were

u2 ÅÌwi

Ìki

(k*i , ∑jxi

k*j ) / ∑jxi

Ìwj

Ìki

(k*j , ∑lxj

k*l ), i Å 1, . . ., n. (A3)

Comparing (A2) and (A3), the choice of si becomes obvioussi Å 0(jxi(Ìwi/Ìki)(k*j , (lxjk*l ). Recalling that k*i Å k*j for all i, j, and so eachpeasant faces the same amount of unit subsidy, it is easy to see that theNash equilibrium with subsidies determined in this fashion coincides withthe Pareto-optimal allocation. Note that the new Nash equilibrium is alsosymmetric.

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266 CHONGWOO CHOE

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Econ

incentive to work versus disincentive to invest: the case of china's rural reform, 1979–1984

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