Xiaokai Yang & New Classical Economics (3)

(Part 1 | 2)

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

In the previous post of this series I described how the author outlined a schemata for representing the emergence of proto-firms from a hypothetical universe of self-employed workers, all autonomous but for the price system. The interesting point about this section is Prof. Yang’s determination to represent as an endogenous part of the model the emergence of an optimal firm size. He begins with the simplest possible production functions (Yang, 2001, pp.196-202),

Production function of final good y:  y + ys = (x + txd)clya	where y is the usable good and x is an intermediate good; ys is output supplied to the market (y without a superscript = share of the good retained by the producer for own use); t is the transaction efficiency coefficient for the intermediate goods; c and a are exponents representing the productive contribution of the x-supply and labor supply ly, respectively. As one can see, higher values of t are better though it cannot exceed 1.1
Production function of intermediate good x: x + xs = lxb	lxb is labor used in the production of x; b is an exponent on labor indicating its productive contribution to x.
Labor Budget: lx + ly = 1	y, ys, x, xd, xs, lx, ly ≥ 0

and derives formulas for the likely price of y relative to x; the number of specialists (subject to population M;  and real income per capita.

In Part 2, I mentioned that the production functions for individuals always compell the same conclusion, that agents are best off if they specialize in the production of a single good; this is logically obvious, given the premise that no good is essential (in other words, there is no need to insure against the lack of a supply if other agents fail to produce it, or if the sole supplier requires an unacceptable price). The production curves for the good always include increasing returns to scale and increasing returns to specialization. Because we are looking at a classical production possibilities curve for each representative agent, specialization is always the answer.

FINDINGS

The structure in which the employer is the producer of y (Structure E) cannot be the general equilibrium if the intermediate good transaction efficiency coefficient s is low compared to t. Both t and s relate to the production of the intermediate good x, but s relates to the labor used in production and t relates to the good itself. If the transaction efficiency of labor is lower than that of the good itself then, then a firm like case E that specializes in the production of x^s will not be viable. Put another way, if the transaction efficiencies for the final and intermediate good are high (i.e., if k and t are high relative to s), then the structure producing x cannot be the final equilibrium since F must trade labor employed to produce the final good.

If, on the other hand, s is high relative to t, then there will be a tendency towards F (i.e., a firm that produces x and y, the latter with labor hired from outside.

FURTHER EXPLORATION

Generally speaking, this form of equation leads to an interest by future economists to explaining further levels at which firms would consolidate out of condition F. In other words, if we are interested in explaining the existence of firms employing more than one or two people, we could treat firms as if they were people, and merge them until we had hypothetical firms employing thousands of workers and using thousands of intermediate goods. Additional complexity could be introduced in the form of different types of fixed and circulating capital, or the introduction of time periods.

Let us suppose that the methods of economic modeling were able to adapt to very rich models that included the passage of time, different factors of production, and localized attributes such as peculiarities of geography or history. Such models might exist as computer programs with a fairly opaque operation, rather than visible systems of necessarily homogeneous linear equations.

Then I would like suggest that economists would use such models to explore the trajectories of production functions and the trajectories of t, s, r, and k to produce actual models of what Ronald Coase, Allyn Young, and Xiaokai Yang wanted to model.

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NOTES

1. In addition to a transaction efficiency coefficient on intermediate goods (t), there is also a transaction efficiency coefficient on the labor (l_x) employed to produce intermediate goods (s) and on the labor (l_y) used to produce final goods (r). In the subsequent system of equations, there is a trading efficiency coefficient k (Yang refers to 1 - k as the “iceberg transaction cost coefficient”); see Yang (2001), p.133. All of these coefficients are used about the same way. These coefficients t, s, r, and k ∈ (0, 1) and convey the share of the full value of x^s, l_x, l_y, and x^d respectively.