The Inconsistent Neoclassical Theory of the Firm and Its Remedy

Transcription

1 The Inconsistent Neoclassical Theory of the Firm and Its Remedy Consider the following neoclassical theory of the firm, as developed by Walras (1874/1954, Ch.21), Marshall (1907/1948, Ch.13), Samuelson (1965, Ch.4), Varian (1984, Ch.1), and many others. A firm, which operates with a Cobb-Douglas production function: β 1 β Y = AK L, (1) where Y is output, K capital and L labor, and faces the corresponding profit weighing: π = PY rk wl, (2) where P is output price, r rental price of capital and w wage rate, will employ the following profit-maximizing inputs: PβY K =, r (3) Y L =. w (4)

2 They are also known as the derived demands. In this particular Cobb-Douglas case, their own-price and income elasticities are all equal to one, and there is no cross-price elasticity. Given an exogenous output order, the prescribed demands can be worked out. Example 1 Given A=P=1, β=0.6, w=r=0.2 and Y 0 =20, according to (3) and (4) respectively K=60 and L=40, as also illustrated in Figure 1. However, with the resultant K and L the output according to (1) becomes Y 1 =51! This firm produces more output than what is ordered. Under different circumstances, it may produce less. <Insert Figure 1 Here> When the demands of (3) and (4) are substituted into (1), output becomes: β Y1 = AP r β 1- β w 1 β Y0. (5) Some conclude from this equation that output is indeterminate (Samuelson, 1965,

3 p.78-79), but such conclusion is misled by the assignment of identical notation to the two outputs, i.e. Y β = AP r β 1 β 1- β w Y. What (5) really indicates is that the inconsistency problem will persist, unless the bracketed term by rare chance happens to be equal to one. Even then output is not indeterminate; it does not exist at all, as shall be illustrated in the next section. Furthermore, when (3) and (4) are substituted into (2), profit becomes: PβY0 Y0 π 1 = PY1 r w. (6) r w Some also draw from this equation the zero profit conclusion (Varian, 1984, p.27; 1993, p.332), but it is again a wrong one. Zero profit would happen only by rare chance when Y 1 =Y 0, otherwise profit can be positive or negative. Consequently, the neoclassical notions of zero and maximum profit are meaningless. Hence, the neoclassical calculation is inconsistent and its conclusions invalid. Appendix I shows that the use of the CES function also produces the inconsistent calculation. For the same set of parameters as in Example 1, given a cost of C=20, the output-maximizing inputs are K PβC = =60 and r C L = =40, which will w produce an output of Y=51. Similarly, given an output of Y=20, the cost-minimizing

4 inputs are K (1 β ) βw (1 β ) r = Y =23.52 and L = Y =15.68, which means (1 β ) r βw β a cost of C=7.84. If P=1, both output maximization and cost minimization imply profit. However, for a different set of parameters, both of them may imply loss. Thus, these constrained optimization methods are also inconsistent. As the inconsistency is derived from (3) and (4), these demand functions are not trustworthy any more. Similarly, the other neoclassical conclusions about cost and market structure must also be invalid, as will be revealed step by step below. i The consequence of the inconsistent calculation could be catastrophic for real business firms, had they taken the neoclassical advices seriously. Such inconsistent mistake is too severe to be covered by the excuse that the analysis is for the short run. On the contrary, this is precisely the reason for the inconsistency. The neoclassical theory derives an input demand by holding output and the other input constant. It over-emphasizes, perhaps even abuses, the concept of short run. In practice, inputs and output are interdependent. Hence, only a simultaneous method can provide consistent results. i Earlier criticisms to the neoclassical theory include Hall and Hitch (1939), Lester (1946), and Gordon (1948), but after the defense by Machlup (1946, 1967) and

5 Friedman (1953) the heat of the dispute seems to have faded away. The theme of the dispute at that time, whether marginalism is valid or not, looks superficial now. That is why the dispute has ended in a draw (Machlup, 1956, p.3).