Increasing Returns and Efficiency.

Yoon, Yong J.

"Increasing returns" is an active area of research in economics now. But economists use "increasing returns" in at least three different ways. The most traditional concept of increasing returns comes from Adam Smith, Marshall, and Allyn Young (see Buchanan and Yoon). The idea is elegantly expressed by the Smithean proposition that "the division of labor is limited by the extent of the market." On the other hand, Brian Arthur and others |1; 3~ understand increasing returns as positive feedback of technology in economic dynamics.

The book is about neither of the two. This monograph is a formal analysis of natural monopoly, another concept of long history, in which the firm produces by falling average cost.

There is an extensive literature on partial equilibrium analysis of natural monopoly, but few works have been done on general equilibrium analysis. The economy consists of two sectors: a private sector with competitive firms with decreasing (or constant) returns and a public sector consisting of regulated firms producing with increasing returns.

The general equilibrium analysis of a competitive market introduced by Walras excludes the possibility of increasing returns. The Arrow-Debreu theory of general equilibrium exclude increasing returns in production, externalities, and entry of new firms. Thus the task is not a straightforward extension of Arrow-Debreu general equilibrium. The tradition of Debreu's theory of value is a topological approach. The "differential" approach taken in this book is more useful for the analysis of non-convex production sets.

The author discusses the origin of ideas and controversies on increasing returns and marginal cost pricing in the introductory chapter. The falling average cost proposed a dilemma since the production of each additional unit will cost less and increase the profit. This is incompatible with competitive market. Marshall introduced the internal and external economies of the firm to overcome this difficulty.

The debate whether increasing returns are compatible with competitive equilibrium sort of petered out because monopolistic competition can handle both increasing and decreasing returns conditions of production. The necessity to sell the output as a monopolist may determine the price rather than rising marginal cost determining the price.

After the turn of the century, Pigou, Lerner, Lange, and Hotelling all advocated marginal cost principles as a necessary condition for an efficient allocation of resources. However, Maurice Allais was against Hotelling's proposal because firms will have no incentives for cost minimization in the absence of budget restriction.

The author defines marginal cost pricing equilibrium in Chapter 3. Marginal cost pricing will not recover the cost under such technology conditions, thus the deficit has to be financed somehow. This requires a rule for distribution of incomes, which is a new feature that does not appear in Arrow-Debreu theory of general equilibrium. Having defined the concept of equilibrium, the book continues, in the tradition of general equilibrium theory, to prove the existence and the efficiency of the "equilibrium." Assumptions are made so that a version of Kakutani fixed point theorem applies.

Chapters 2 and 3 provide a foundation for marginal cost pricing for non-convex economies by introducing income map. Marginal cost pricing equilibrium is a natural extension to non-convex economies of the competitive equilibrium.

In general, the problem of efficient allocation of resources is difficult to solve when production set is non-convex. Arrow and Hurwicz pointed out a pathological case of non-convex economy: Efficiency (Pareto optimal allocation) does not always require cost minimization. The example indicates that organization (i.e., planning) matters for the economy. Such a problem does not appear in convex economies.

The author considers the decentralized organization by which non-convex firms can be run. This research strategy seems to reflect the spirit of the time. As Hayek warned, and as the fall of socialism in this century has shown, it is not possible to achieve efficient allocations through central planning. The firms have no incentive to reveal the relevant information to the planning board.

Question: Does the arrangement lead to an efficient resource allocation for the economy?

The two-part tariffs have advantage over Hotelling's lump-sum income taxation. If the taxes are presented as fixed fees that give agents the option to buy the goods at their marginal costs, then the taxes become more acceptable. Two-part tariffs are particularly appropriate for public utilities (telephony, electricity, water, etc.). The question is sharpened now.

Question: Can an efficient allocation be supported by a two-part tariff?

The author examines the compatibility of two-part tariffs with first best optimality. He assumes that the fixed charges are to cover the deficit of the whole public sector. I think this assumption is too restrictive. More appropriate assumption would be to require each regulated firm to cover its deficit (earmarked). The example by Guesnerie and Quinzii is instructive for finding conditions under which a Pareto optimum can be decentralized by a two-part tariff. A sufficient condition is that the surplus derived from buying each good at the equilibrium price must be larger than the fixed cost. This is what the author calls the "Surplus condition." This justifies the relevance of my suggestion above that requires each regulated firm to finance its own deficit.

Production and exchange normally generate a surplus of welfare. If an allocation is such that a subgroup of agents using only their own resources can obtain better allocation for each of them, then the allocation cannot be the outcome of voluntary production and exchange. The allocation fails to be in the core.

Every competitive equilibrium of a convex economy is in the core. If one sector of the economy produces by increasing returns, it seems that a grand coalition would exploit the potential increasing returns most effectively. The results in the book show that this intuition needs to be refined. This will depend on the way of financing the deficit created by marginal cost pricing, because some agents may not agree with the allocation determined by a given income map. Chapter 6 discusses the problem of finding acceptable ways of financing the deficit by a standard cooperative game theory.

The formal theory in this book does not discuss other issues of great concern to economists, such as incentive problems and information and knowledge in the market mechanism as emphasized by Hayek.

References

1. Arthur, Brian. "Competing Technologies, Increasing Returns, and Lock-in by Historical Events." The Economic Journal, 1989.

2. Buchanan, James and Y. Yoon. The Return of Increasing Returns. Ann Arbor, Michigan: University of Michigan Press, 1993, forthcoming.

3. Waldrop, M. Complexity. New York: Simon & Schuster, 1992.