## Friday, July 10, 2015

### “Rationality” in the Theory of the Firm... Part 1

Previously: Introduction

Turning now to Standish and Keen’s response, they first argue that I
completely failed to discuss... that the so-called profit-maximizing formula for an individual firm– of equating marginal cost and marginal revenue– provably does not maximize profits in any industry structure apart from monopoly.”
This is, to put it mildly, a not true. As I wrote in Section 5 (bold added)
There is no dispute as to whether or not profits would be higher at, say, the collusive result. Objectively, profits would be higher at that level than Cournot-Nash, and firms would be better off producing at that level. The neoclassical argument is that collusion is rational, but firms competing for the greatest profits will not forgo opportunities to increase their individual profits and so will over-produce (relative to the collusive level) even if that would result in lower profits for the industry on the whole. That is, competition hurts profits.
Far from discussing it, I address the specifics of this topic throughout my Comment. Each thread mustered in support this argument fails.

Returning to their response, they hide conceptual errors in their math, arguing
Standard Neoclassical pedagogy teaches that, regardless of market structure, an individual firm in an industry will maximize its profits by equating its marginal revenue... to its marginal cost... $$\frac{\partial\pi_i}{\partial q_i}=\frac{\partial\!\left(P\!\left(Q\right)\cdot q_i\right)}{\partial q_i}-\frac{\partial\mathrm{TC}_i\!\left(q_i\right)}{\partial q_i}\label{eq:sk1}$$
where $P\!\left(Q^d\right)$ is inverse demand and in the above equation is evaluated at quantity supplied. That is, price is assumed to be that which will clear the market ex post of firm production. Unfortunately, this is not necessarily true in the perfectly competitive model. Keen and Standish argue here that if a perfectly competitive firm were to expand output, that this would lower the price it would receive for its output. Hence the authors introduce market power where, by assumption, none exists. Their equation is simply wrong for perfect competitors. Textbooks teach that perfectly competitive firms maximize profits given a market price $p$ for their production. That is, lacking any power to change $p$ in the current period, the $i$th firm is left to maximize its profits $\pi_i$ by setting to zero $$\frac{\partial\pi_i\!\left(q_i;p\right)}{\partial q_i}=\frac{\partial\left(p\cdot q_i\right)}{\partial q_i}-\frac{\partial\mathrm{TC}_i\!\left(q_i\right)}{\partial q_i}=p-\frac{\partial\mathrm{TC}_i\!\left(q_i\right)}{\partial q_i}\label{eq:dr1}$$ Contrary to the authors’ claims, then, the textbook model implies that only if firms are given a specific price price will the market clear. According to such Econ 101 analysis of rent control statutes, the government forces the price of housing below the market-clearing price leading to a housing shortage. If firms supplied even less housing then– rather than raising the price of housing– this would lead to a more severe shortage.

Even for a monopoly the authors’ equation is wrong. A profit maximizing monopolist with power to price discriminate does not operate as they suggest. Rather, such a firm charges increasingly lower prices $P\!\left(q\right)$ for each next unit, expanding output to the point that $P\!\left(q\right)=\mathrm{MC}\!\left(q\right)$.

In short, their equation does not accurately reflect “Neoclassical pedagogy... regardless of market structure” because marginal revenues to the firm depend upon the choice of market structure. Keen and Standish are simply wrong.

In Part 2, I will consider their proposed example.

Read my original Comment (including Technical Appendix) at World Economic Review.