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Endogenous Specialization and Endogenous Principal-agent Relationship

Xiaokai Yang
Monash University
and Harvard Center for International Development
Yeong-nan Yeh
Academia Sinica, Taiwan

This version: October, 2000

*Thanks to Ken Arrow, Paul Milgrom, Yingyi Qian, the anonymous referee, and the participants of the seminars at Stanford University, Hong Kong University of Sciences and Technology, and Monash University for comments and criticisms. We are solely responsible for the remaining errors.

Abstract

The paper develops a general equilibrium model with endogenous principal-agent relationship within a framework of consumer-producer, economies of specialization, and transaction costs. It is shown that if transaction efficiency is low, then autarky is chosen as the general equilibrium where no market and principal-agent relationship exists. As transaction efficiency is improved, the equilibrium level of division of labour increases, comparative advantage between ex ante identical individuals emerges from the division of labour, and the number of principal-agent relationships increases. The following features of the model distinguish it from other principal-agent models in the literature. The principal-agent relationships are not only endogenous, but also reciprocal between different specialists. In a general equilibrium environment, choice between pure pricing and contingent pricing is endogenized. In the paper, the implications of endogenous transaction costs caused by moral hazard for the equilibrium extent of the market and related degrees of market integration, production concentration, trade dependence, diversity of economic structure, and productivity are explored. The model predicts two interesting phenomena: a man might work harder for the market with moral hazard than working for himself in the absence of moral hazard; a market with moral hazard might be Pareto superior to autarky with no moral hazard.

I. Introduction
The purpose of the paper is to endogenize the principal-agent relationship and transaction costs in a general equilibrium model with consumer-producers, economies of specialization, and transaction costs. Two phenomena that cannot be explained by existing models of principal-agent motivate this research. From our daily experience, we can see an interesting phenomenon that when an individual works for himself in the absence of moral hazard, he may be not as diligent as working for the other in the market with moral hazard. Why, under a certain condition, does an individual choose a higher effort level when moral hazard is present than when moral hazard is absent? If specialization and transaction costs are simultaneously endogenized in a general equilibrium model, we can then predict this phenomenon as follows. In the present paper we call a departure of equilibrium from the Pareto optimum endogenous transaction cost and refer to exogenous transaction costs as a kind of transaction costs that can be identified before individuals have made decisions. Endogenous transaction cost cannot be identified before individuals have made decisions and the economy has settled down in equilibrium. The trade offs between positive network effect of division of labour, endogenous transaction costs caused by moral hazard, and exogenous transaction costs imply that interactions between two types of transaction costs are crucial determinants of the equilibrium level of division of labour. If an exogenous transaction cost coefficient for each unit of goods traded is very large, the transaction cost outweighs productivity gains from the division of labour. Hence, individuals choose autarky where there is no transaction and related exogenous and endogenous transaction costs. Because of each person's limited time, each person has a narrow scope for trading off positive contribution of effort in reducing low productivity risk against leisure in autarky. Thus, the efficient trade off between the positive contribution and the disutility of the effort may end up with a low effort level in autarky. As the transaction cost coefficient falls, individuals will choose a higher level of division of labour, which implies a higher aggregate productivity, so that the scope for trading off the positive contribution against disutility of risk avoiding effort is enlarged by the higher level of specialization. This is because each individual has more time for both leisure and working in the activity that he chooses when he increases his level of specialization (reducing the number of production activities that he undertakes). Also, the decrease in the exogenous transaction cost coefficient enlarges the scope for trading off economies of specialization against moral hazard. Hence, he may choose a higher level of effort in reducing risk when he chooses to work for others in a larger network of division of labour where endogenous transaction costs are present due to moral hazard. In other words, individuals can afford a higher endogenous transaction cost when aggregate productivity increases as a result of a larger network of division of labour. We may refer to the phenomenon as that a man works harder for others in the presence of moral hazard than working for himself in the absence of moral hazard.

The second phenomenon that motivates the paper relates to the first phenomenon. We can see that in a large and very commercialized city (or with a very sophisticated network of division of labour), a greater interdependence between individuals and a larger number of transactions create more scope for endogenous transaction costs caused by moral hazard and adverse selection than in a remote countryside village in a poor country where the number of transactions is small and no much scope for moral hazard to take place. As a general equilibrium phenomenon, we may observe that residents in that large city are more opportunistic than village folks. But yet people in the city are Pareto better off than those in the poor country. In other words, an equilibrium with moral hazard, which is not Pareto optimal, may be Pareto superior to an equilibrium with no moral hazard under different exogenous transaction conditions. This phenomenon may be referred to as Pareto improvement associated with an increase in moral hazard.

This interesting phenomenon can be predicted by our general equilibrium model with endogenous level of division of labour and the trade offs between endogenous comparative advantage and endogenous and exogenous transaction costs. If the exogenous transaction cost coefficient for each unit of good traded is large, then exogenous transaction cost outweighs endogenous comparative advantage, so that the Pareto optimum as well as the equilibrium is autarky where there is no transactions and moral hazard. As the exogenous transaction cost coefficient falls the scope for trading off endogenous comparative advantage against transaction costs is enlarged, so that the Pareto optimum shifts to a higher level of division of labour which involves more interactions and transactions between individuals. The transactions must involve endogenous transaction cost caused by moral hazard, so that the equilibrium is not Pareto optimal. But as long as endogenous comparative advantage that can be exploited is sufficiently large compared to endogenous and exogenous transaction cost such that individuals can afford the moral hazard caused by the division of labour, the division of labour with more moral hazard occurs at general equilibrium and is Pareto superior to autarky. Hence, productivity, welfare, and moral hazard are simultaneously increased by the fall of the exogenous transaction cost coefficient.
In the existing literature of moral hazard, the principal-agent relationship is exogenously given. The principal cannot take care of his own business and he has to ask an agent to do the job, while the agent cannot have his own business and he has to work for others. Since individuals' levels of specialization and related principal-agent relationships are not endogenized in this literature, the implications of the endogenous transaction costs caused by moral hazard for the equilibrium level of division of labour are not explored. Hence, the above two phenomena cannot be predicted by the existing models of principal-agent.

The literature of endogenous specialization has endogenized individuals' levels of specialization and the level of division of labour for society as a whole on the basis of the trade off between economies of specialization and exogenous transaction costs. But it has not endogenized transaction costs. Hence, this literature cannot explore the implications of endogenous transaction costs for the level of division of labour and related number of principal-agent relationships either. The current paper introduces moral hazard into the general equilibrium model of endogenous specialization and develops a general equilibrium principal-agent model with endogenous specialization to explore the implications of endogenous transaction costs caused by moral hazard for the equilibrium level of division of labour.

The concept of division of labour is in essence a general equilibrium concept. Hence, an individual's level of specialization and level of division of labour can be endogenized only in a general equilibrium framework. The equilibrium level of division of labour is dependent on endogenous transaction costs (for instance an individual will not choose specialization if it involves too high endogenous transaction cost), while the endogenous transaction costs are determined by the level of division of labour (for instance endogenous transaction cost does no occur if all individuals choose autarky where no transaction takes place). Hence, a general equilibrium mechanism that simultaneously determines the interdependent variables should be used to explore the implication of endogenous transaction costs for the equilibrium network size of division of labour. But in the existing literature, endogenous transaction costs are investigated for a given pattern of division of labour between the principal and the agent. As shown in the literature of endogenous specialization, the extent of the market, trade dependence, the degree of market integration, production concentration, the degree of diversification of economic structure, the number of markets, the degree of endogenous comparative advantage, the number of traded goods, the degree of interpersonal dependencies, productivity, and individuals' levels of specialization are associated with the level of division of labour which is determined by the efficient trade off between economies of specialization and transaction costs. Also, it is shown that emergence of money, business cycles, and unemployment can be explained by evolution in the level of division of labour. In a general equilibrium model with endogenous comparative advantage and exogenous and endogenous transaction costs, complicated trade offs among the three counteracting forces may generate much richer stories than told by the existing literature of principal-agent and by the existing literature of endogenous specialization.

Yang (1994) has drawn the distinction between endogenous and exogenous comparative advantage. The endogenous comparative advantage are positive network effect of division of labour that can be exploited only if different individuals, who might be ex ante identical in all aspects, choose different levels of specialization in producing different goods. Endogenous comparative advantage is much more important than exogenous comparative advantage since it is determined by individuals' decisions and level of division of labour. A general equilibrium model that can predict endogenous emergence of principal-agent relationship from evolution in division of labour can then be used to explore the implications of endogenous transaction costs for exploitation of endogenous comparative advantage. In most existing principal-agent models, exogenous comparative advantage which is based on ex ante differences between individuals is the driving force of the principal-agent relationship. The principal is ex ante different from the agent before decisions have been made. Hence, the existing literature has not explored the implications of endogenous transaction costs for exploitation of endogenous comparative advantage.

Endogenous transaction costs will affect in important way the equilibrium pattern and level of division of labour which generate some concurrent phenomena (evolution in endogenous comparative advantage, in the degree of market integration, in the degree of diversity of economic structure, and so on) which cannot be predicted by standard marginal analysis of principal-agent models. Hence, the implications of endogenous transaction costs and contingent pricing for productivity progress and for all of the above economic phenomena can be explored using our general equilibrium model of principal-agent.

In our general equilibrium model, players' choices between contingent pricing and pure pricing is endogenized. Within a certain parameter subspace, individuals may prefer pure pricing to contingent pricing in general equilibrium. This feature of our general equilibrium model may be motivated by casual observations. We can see contingent pricing as well as pure pricing in real world under different conditions. The condition might not be as simple as the presence or absence of moral hazard. Our model will be used to identify the dividing line between contingent and pure pricing when moral hazard is present.

Section 2 specifies the model, section 3 solves for corner equilibria in six market structures, section 4 solves for the general equilibrium and its comparative statics. In section 5, the implications of endogenous transaction costs for the equilibrium level of division of labour are explored. The final section concludes the paper.

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