# Applying modern economics to Edgeworth's Hedonical Calculus

## Preface

The late 1800s was a genesis for many economic theories. As math spilled over into the social sciences, one of the more obscure applications of measurement was: Hedonical Calculus, developed by Edgeworth. Of course, centuries later, some of these Victorian Age studies aged better among modern academic communities than others. Hedonical Calculus gained little traction and faded to the periphery as modern economic thinkers steered the field away from quantifying everything. On the notion that if one cannot measure something one does not have a satisfactory understanding of the matter, Frank Knight sarcastically interjects:

If you cannot measure a thing, go ahead and measure it anyway.

## Hedonic Calculus

The work tackles several broad areas of study, and to keep my question within a reasonable scope, I will limit the focus to capital formation / efficiency. With that in mind, I will try to unpack the basics of Hedonical Calculus:

Objective: To find the distribution of means ($$α$$) and labor ($$β$$), the quality ($$γ$$) and number of population (δ), so that there may be the greatest possible happiness

• Pleasure: The term includes absence of pain. Greatest possible happiness is the greatest possible, integral of the differential: Number of "enjoyers" × duration of enjoyment × degree thereof
• Means: are the distributable proximate means of pleasure, chiefly wealth as destined for consumption
• An individual has a greater capacity for happiness than another, when for the same amount whatsoever of means he obtains a greater amount of pleasure; and also for the same increment (to the same, amount) whatsoever of means a greater increment of
• An individual has more capacity for work than another, when for the same amount whatsoever of work done he incurs a less amount of fatigue, and also for the same increment (to the same amount) whatsoever of work done a less increment of fatigue.

With this framework, Edgeworth proposes we may allocate human capital in such a way that we minimize pains of production. Pains of production may include blood and sweat, but could be negative if we suppose the thrill one may get from being a pilot (especially during the first few flights). Formally, by finding the largest possible value of:

$$\int_{x0}^{x1} n\left [ F(xy)-p \right ]dx$$

• n = number of each section
• F(xy) = a unit's pleasure of consumption (x=capacity for pleasure, y=means for living up to his capacity)
• p = pains of production

Fully aware of the black box limitations and pitfalls of attempting to quantify the sentiment and decisions of a human being capable of exerting his/her own free will, I am still very curious about the impact on long-term capital formation and efficiency of such a system

## Question

Assuming complete omniscience on measurements such as "units of pleasure" and "pains of production," would modern economic theory expect differences in long-term capital formation from a pleasure maximizing economy than that of a profit/utility-maximizing economy of today (or whatever you want to call our economy)? If so how, if not why?

Reference:

https://babel.hathitrust.org/cgi/pt?id=njp.32101063551350&view=1up&seq=414