Xiaokai Yang & New Classical Economics (2)

(Part 1)

Xiaokai Yang, Economics: Neoclassical Framework versus New Classical, Blackwell Publishers (2001)

The normal economic system works itself. For its current operation it is under no central control, it needs no central survey. Over the whole range of human activity and human need, supply is adjusted to demand, and production to consumption, by a process that is automatic, elastic, and responsive..

J.A. Salter, Allied Shipping Control, p.16; quoted in D.H. Robertson (p.84)

Here and there, it is true, we have found islands of conscious power in this ocean of unconscious co-operation, like lumps of butter coagulating in a pail of buttermilk.

D.H. Robertson, The Control of Industry, Harcourt Brace (1923) p.84

For purposes of comparison, Prof. Yang explains the concept of neoclassical equilibrium (which he thinks is conceptually inferior to new classical analysis).  The system of equations consists usually of a single representative agent who can chose between two goods, each of which has a representative production function.  The need for a mathematically coherent solution imposes a lot of constraints, so that the production function nearly always takes the same form (these conditions, by the way, are known as the Sonnenschein-Mantel-Debreu conditions (Yang 2001, pp.101-103; see Rizvi 2006 for online explanation).¹

Usually, when neoclassical textbooks introduce utility functions, they go on to explain how students can derive demand functions from them. This textbook is not neoclassical, and it does not separate out consumers from producers (Yang, 2001, p.38).  Instead, each consumer is also a producer who faces multiple possible production functions (for each possible good).  In fact, Yang’s outline is a simplified version of Sraffa’s [classical] general equilibrium, although Yang includes the production functions so students have something to solve.



To be honest, it’s pretty obvious that Prof. Yang sets up his production functions to have a format such that there’s always a corner solution.²  This means that representative agents (the standard sample producer-consumer) always have to choose, at the same time, what to produce (and sell), and what to buy. It becomes abundantly clear that everyone always needs to produce one good as long as there’s any returns to scale or specialization at all.

This leads to “endogenous comparative advantage” (Yang, 2001, p.53), where agents are not different in their initial endowments, but are motivated to specialize in one product or another, leading to at least one agent in the general population becoming more productive than others in a particular field, and runners-up turning to other lines of production.  Eventually everyone becomes the most efficient available producer.³

The system of equations is not significantly affected by having representative agents making consumption and production decisions concurrently.  I think Yang mostly ignores the scenario in which there are only two people in the two-good economy and production choices decisively influence the price of each good, because in that case there would exist scenarios in which agents were not in a corner solution: it would make sense to produce some amount of each good in case your neighbor makes exactly the same production choices you do, and you both have ample burlap, but no food.

FIRMS

Part IV of Prof. Yang’s book addresses the existence of the firm.  Yang is very impressed by the approach taken by Coase (1937), which perceives firms as reflecting a peculiar subdivision of the productive system into units that are planned, as opposed to relations among the firms, which are determined through the price mechanism.

There is therefore point in Mr. Durbin’s answer to those who emphasize the problems involved in economic planning that the same problems have to be solved by business men in the competive system... The important difference between these two cases is that economic planning is imposed on industry while firms arise voluntarily because they represent a more efficient method of organising production. In a competitive system, there is an “optimum” amount of planning!

Coase (1937), p.389, fn.3

This is the key point to “The Nature of the Firm.”  Coase implies that having the whole economy as part of a single (socialist) economy is probably too much, and having every individual worker self-directed and contracted─that’s probably too little.

Coase estimates that the optimal amount of planning is determined by the costs of using the price mechanism all supplies and labor used. Having affiliated employees produce many parts of a completed good under one roof eliminates the risk that some of the parts will be unavailable, or incompatible with a special design, or that skilled works in adequate numbers will not turn up.  “The operation of a market costs something and by forming an organisation and allowing some authority..to direct the resources, certain marketing costs are saved” (p.392).

As the firm gets bigger, market costs diminish (more activities are carried out without the challenges of searching, doing without inventory, and so on) while management costs increase.  Eventually, the latter because greater than the savings of the former, and the firm no longer increases in size (much).

Click on image to enlarge

Prof. Yang (2001, p.196) formalizes this beginning with the idea of intermediate goods.  Each consumer-producer has a new production-income function that incorporates goods bought for the purpose of producing another good for sale.  Each person sells at most one good; no one buys and self-provides the same good (so, for example, I make brown sugar; I am assumed to never buy brown sugar. I might sell it, but I certainly meet all my own needs for brown sugar.)  He describes all the possible nodes in a network of exchange (or non-exchange), with the production functions taking on exponents to reflect increasing/diminishing returns to scale (see figure).

Structure A is autarky; under this arrangement, no one buys or sells anything; y, a finished, consumable good, is supplied by the agent to themselves. Under structure D, persons exchange goods for goods, but there is no firm. Instead, people produce x^s and supply it to y/x, who consumes it in the production of y^s, some of which used domestically, and some of which─x^s─is supplied to x/y.

In Structure E, the lower unit (l/y) supplies labor for the production of x  to the upper unit (y/l_x), which then supplies y^s in exchange for labor.  As before, some y is retained for own use. At this point, we notice the upper unit qualifies as a firm because it employs labor.

In Structure F, the firm x/l_y  is a producer of x who hires labor for the production of y from own output of x.  This is a bit strange as models go, but the model logically requires proto-firms to originate with a single agent who individually produces one good, while hiring another worker to produce the other.

(Part 3)

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NOTES

1. The SMD conditions include a requirement that preferences be homothetic. This means that, if utility is a function of goods x and y such that U = U(x, y), and we multiply the supply of goods by a, then U(a∙x,a∙x) = a∙U(x,y).
   
   The requirement that preferences be homogeneous of degree zero means that, if prices of both x and y are multiplied by a, and income is multiplied by a too, then the goods consumed will be the same. The latter sounds totally reasonable, except that various effects in welfare economics that are supposed to be explained by the shape of the utility curve cannot exist.  This utility function, for example, violates the rules.
   
   However, as Prof. Yang points out (2001, p.101), the SMD conditions are assuredly sufficient, but not necessarily necessary.  It’s conceivable that a Walrasian solution set of linear equations describing a neoclassical economy does include non-homothetic preferences.


2. Corner solution: suppose your utility is a function of three goods: U = U(a,b, c) subject to a budget p_aa + p_bb + p_cc = Y (viz., your total income; p_a = the price of a, and p_aa = the total amount spent on a).  If, for any value of Y, you always maximize U when one or more of the available goods is 0, then you are sitting on the corner of your indifference curve, wishing you could just get more of the other good.  In neoclassical economics, a corner solution is frustrating because you will never get an adequate supply of the items you want, and  prices will not reflect an efficient allocation of resources.


3. Most efficient available producer: my description of comparative advantage.  Michelle may be more productive at a and b than I am, but she is most productive in a and so she specializes in that while I focus on b.  Put another way, she’s more efficient at both a and b than I am, but she’s much more efficient at a, or perhaps a is just a more valuable activity than b.  In either case, it’s ideal for me to focus on b, so I have a comparative advantage in b.

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SOURCES 🙵 ADDITIONAL READING

S. Abu Turab Rizvi, "The Sonnenschein-Mantel-Debreu Results after Thirty Years" (PDF), History of Political Economy 38 (annual suppl.) (2006)

Ronald H. Coase, "The Nature of the Firm" (PDF), Economica, New Series, Vol. 4, No. 16 , pp. 386-405 (Nov 1937)