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Effects of Externality-Corrective Taxation on the Extent of the Market and Network Size of Division of Labor Yew-Kwang Ng and Email: kwang.ng@buseco.monash.edu.au
Applying the inframarginal analysis of specialization and the effects of external costs in production and their control through taxation, this paper shows that, on top of the allocational inefficiency on the input and/or output mix caused and alleviated, there is the organizational inefficiency on the level of division of labor and extent of the market. External costs may lead to either too high or too low a level of division of labor or a mixture of efficient and inefficient structures. Low-cost taxes directly on the variables causing external costs may remove the inefficiency but may not be feasible, as, e.g., home production may be difficult to observe. Sales taxes/subsidies are completely useless as the general-equilibrium adjustments yields zero effects. A tax cum income transfer scheme may be effective in alleviating the allocational and organizational inefficiencies within certain ranges of parametric values. With the other range of parameter values, the optimum tax rate is 0 since a positive Pigovian tax generates organization distortion that outweighs corrective effect of allocative distortion. Keywords: Organizational efficiency, external effects, division of labor, network, tax, specialization. I. Introduction There are two different research lines regarding external effects in public economics. The traditional line is represented by Pigou (1940). Pigou used partial equilibrium and marginal analysis to argue that a tax on the source of a negative externality may generate Pareto improving resource allocation. The other line relates to the theory of endogenous externality, represented by Coase (1960), Cheung (1970, 1974, 1983), and Barzel (1982, 1985, 1989, 1997). These authors criticize the traditional Pigovian theory of externality and public goods. They argue that for any good there is the tradeoff between measurement cost and distortions caused by imprecise measurement. The efficient degree of "externality" is determined by the efficient balance of the tradeoff. It is misleading to assume that externality is exogenously given. Great degree of externality of pollution in the market is an efficient tradeoff caused by high measurement cost of pollution. If such cost is low, property rights and liability to pollution will be well defined and therefore efficiently traded. If measurement cost outweighs the benefit of precise measurement, then the efficient tradeoff is associated with a great degree of externality, so that rights to pollution are not well defined and pollution is not traded in the market. Even for the trade of oranges, it is not efficient to eliminate all externality caused by imprecise measurement of quality and quantity of orange since precise measurement may require division of orange into more than one thousand grades with a unique price for each grade which has a slightly different taste from another grade (Barzel 1982). The theory of endogenous externality is formalized by Holmstrom and Milgrom (1987, see Milgrom and Roberts, 1992), Yang and Wills (1990), and Lio (1998). Coase (1946, 1960) critisizes Pigovian partial equilibrium analysis of externality as misleading. He suggests that an inframarginal analysis of general equilibrium may show that decentralized bargaining can sort out problem of externality. The inframarginal analysis allows non-marginal cost pricing and discontinuous shift of decisions between different organization structures. In the present paper, we take an eclectic
position between the two research lines. We extend Yang-Ng's (1993)
framework with endogenous network size of division of labor, economies
of specialization, and transaction cost to examine the effects of
external costs and taxes on them. We assume that the problems created
either by the measurement costs or the publicness nature of the relevant
external effects are so big such that external effects cannot be priced
and traded in the market. In addition, it is assumed that the government
cannot observe self-provided consumption and can therefore tax only
sales of goods. The sales tax will encourage self-provided consumption
and discourage specialization and commercialized consumption and production.
The equilibrium degree of externality can be endogenized by formalizing
the trade-offs between economies of division of labor, transaction
costs, and the distortions caused by externality. If each individual
chooses autarky where economies of specialization cannot be fully
exploited and aggregate productivity is low, she can internalize a
part of the externality by engaging in all lines of production. But
the division of labor implies that a specialist producer of a good
generating externalities completely ignores the effects of such externalities
on the specialist producers of other goods. In addition, sales tax
may distort the pattern of division of labor as well. We may then
consider the tradeoff between externality correcting effects of and
the distortions caused by tax and income transfer schemes. We shall
show that within a certain parameter subspace, no Pareto improving
sales tax and income transfer scheme exists since the distortions
caused by such a scheme more than offset its externality correcting
effects. Within other parameter subspaces, such Pareto improving tax
and income transfer schemes exist and they can improve not only allocational
efficiency of resources, but also organizational efficiency. Our paper relates closely to Chu (1997) and Chu and Wang (1998). Chu (1997) shows that in a model of endogenous network size of division of labor with transportation infrastructure as a public good, tax or an infrastructure use fee can be employed to expand the network of division of labor. In that model the equilibrium network size of division of labor is dependent on transportation efficiency which is dependent on tax revenue used to construct infrastructure. Tax revenue is dependent on per capita income which is dependent on productivity which is, in turn, determined by the level of division of labor. However, in that model, the problem of resource allocation is trivial: the model is symmetric, the equilibrium prices and consumption and production quantities of all goods are the same. Use-fees or taxes are the same for all individuals. Our model in the present paper assumes asymmetric physical externality between two goods. Hence, if the equilibrium tax is positive, it is asymmetric between different sectors. For instance, the sector which generates negative externality is taxed and the sector that suffers from the externality is subsidized. Chu and Wang's model (1998) is very
similar to ours. However, in their model the numbers of individuals
choosing different occupations are exogenously given integers. Zhou,
Sun, and Yang (1998) have shown that for such a model of endogenous
specialization with a finite set of consumer-producers, a general
equilibrium may not exist. We shall assume a continuum of consumer-producers
in the present paper and make sure that all conditions for the existence
of general equilibrium are met. Sections II and III will show that
the endogenization of numbers of individuals choosing different occupations
will generate predictions that are different from those in the Chu
and Wang model. We shall then discuss at the end of section III how
Nash bargaining may sort out the existence problem and generate Pareto
optimum resource allocation and network size of division of labor
in the absence of taxation. Inframarginal Economics Society www.inframarginal.com
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