Keynes postulated that nominal wages and real wages are inversely related apropos unemployment; one would then expect the opposite to be observed today in the Phillips curve. Common sense dictates that less available positions for employment equates to downward pressure on wages, with a downwardly concave GDP function suggesting on the microeconomic level an opportunity for companies to participate in auspicious projects. In sum, prosperity for the owner of the means of production and the consumers, though bi-conditional in their economic functions are not isomorphic in their relations. Scholars will disagree on the notion of whether this is what primarily belays the dialogue between that of Keynes’s partial reaction to the Austrian school (not least of which from a psychosocial perspective) or Hayek, with Friedman’s commentary “Inflation is always and everywhere a monetary phenomenon” still maintaining effervescence.

Some closure may be found in Keynes seminal work The General Theory of Employment, Interest, and Money, chapter 3: “The Principle of effective demand” (Keynes, 1936). Aggregate real income, when increasing, does so at a marginally greater rate than aggregate consumption, which informs the employers current investment differential. Nota bene, this follows the structural nature of foreign sovereign debt crises, including the Argentine debt restructuring circa 1990’s and Turkey’s recent debt crisis, especially characterizable by Mundell’s Trinity and reliance upon foreign direct investment (FDI). The corollary is that the equilibrium level of employment is a function of current investment, which is a function of inducement to invest, further a function of the relationship between the schedule of marginal efficiency of capital and structural interest rates. The conclusion is that the propensity to consume and the second derivative (gamma) of new investment will necessitate a singular level of employment which agrees with equilibrium.

In decomposing the complex partial differential equation above, it is recognized that the equilibrium level of employment can be conceptualized to utility functions re: indifference curves, namely:

Perchance, evolutionary biologists and economists may agree on one thing.

It is uncontroversial with these claims that if the indifference curves of the consumer do differ with respect to the marginal rates of substitution/transformation for the employer which is built into these equations, and considering that points of undulation are not reliably maintained throughout the multivariate transformation of z and thus follow a predictable pattern, the values of sigma squared — — would have to be isomorphic such that the 4th central moment and kurtosis could reliably explicate the third derivative[j(t)] of these equations. The Taylor series:

might be the differential under the curve, but the predictive power is nullified partly because the indefinite integral:

is (suspiciously) alluded to as opposed to the definite integral’s use of the differential as defined in the preceding definition of the causal chain, with the definite integral formally as:

What is mathematically thought of as the inverse eigenvalue or point of inflection may instead manifest as a saddle point for z=f(x,y,n…). “Equilibrium” may not have extrema but could have critical points, but in any case fail to appear bijective.

Allocative efficiency is a core tenet of Pareto efficiency (or Kaldor-Hicks efficiency) and need not only be applied on the macro level (think market making re: finance and performance agreements). The utilitarian, boundedly-rational actors working in the theory above cannot comport with the concept’s meaning vis-a-vis contract theory, for it is assumed that “counterparts” have unique outputs, and thus inputs. Contract theory is instructive here given that a social contract is entered into by actors and employers. If the condition of information asymmetry is satisfied, it is difficult to infer whether the state in such a system fully eludes a Markov process — and thus the system itself as a Markov chain — in which case will make it difficult to argue that error terms are encompassed in the equilibrium model rather than that of skewness contributory to residual terms. Using Keynes’ notation in the chapter:

where:

Z=aggregate supply price of output forthcoming from N actors’ labor

D=aggregate demand proceeds from receipt of N actors’ labor

N=employed actors

Z=phi(N)=aggregate supply function

D=f(N)=aggregate demand function

Regards to set theory, equality here does not map to equivalence, and instead represents a point of intersection. Thus beholden is the earlier proposition that this could just as well represent a saddle point rather than extrema. This is indeed supported by recent affirmed literature in endogenous growth theory (Romer, 1994). Moreover, the conceptualization of insurance contracts placed by counterparties in moral hazard literature is illuminative. The actuarial assumption related to Keynes’ conception of “hoarding” can be thought of as encompassing the opportunity cost of not lending the capital out at an interest rate potential that maintains the tangent line of the indifference curves for the respective parties. This would be an interval on a linear line adhering to the fundamental theorem of calculus:

which seems self-defeating since gamma would=0 and would hence be self-fulfilling. While this agrees with the behavior of monetary policy reactions that guide the reaction functions of banks in the examples above concerning sovereign debt crises (historically) and may even encompass the cyclicality of business cycles, wouldn’t the point of intersection become a point of undulation? Alas, it isn’t palpable that addition of stochastic slack variables is any less nihilistic.

Friedman’s helicopter money

Hearkening back to the disutility of a transaction used in the methodology of classical economics, the Grossman-Hart-Moore theory indeed posits a similar framework in ex post “disagreement payoffs”. The theory of choice has been professed as the following equation:

If opportunity costs for both parties continue in a space — the disagreement payoff structure — , the surplus does not cede merely to the owner of the means of production. This evinces that the definition of supply was not given sufficient taxonomy in its expounding as reactionary to demand.

The logic of this argument appears to be acted out in the scope of the legal field. The application of the reasonable person standard can be thought of as encompassing a similar epistemology as the counterparties in the economic examples. At the origin, each form a market, and stakeholders can be thought of as having active (implicitly or sometimes explicitly) options or futures contracts on the outcomes. This expands to the (much criticized) calculus of negligence, the “Hand Test” in United States v. Carroll Towing Co. Furthermore, the primacy of allocative efficiency has been deemed overestimated in recent times in its application to antitrust and contract law (see previous post), and incompatibilism has gained reception in criminal law (LSAC, 2019). While not inherently insoluble, examples above lend criticism to a self-evidentiary, absolutist application of the concept of law. Einstein’s relativity interacts in a peculiarly Hohlfeldian manner with the late Oliver Wendall Holmes’ claim “The life of the law has not been logic: it has been experience.”

References:

Keynes, J.M. (1936). The principle of effective demand. In The general theory of employment, interest, and money. UK: Palgrave Macmillan.

Law School Admission Council. (2019). The official lsat prep test 86. Newtown, PA: LSAC

Romer, P.M. (1994). The origins of endogenous growth. Journal of Economics Perspectives, 8(1). Retrieved from: https://pubs.aeaweb.org/doi/pdf/10.1257/jep.8.1.3