Alfred Marshall, who was instrumental in promoting the use of mathematics in economics, also warned against its potential for misuse. He outlined his personal guidelines for applying mathematics in the discipline in correspondence with A. L. Bowley, who was also a mathematically-oriented economist.

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Alfred Marshall (1842–1924) was a highly influential economist and a key founder of the neoclassical school of economics, whose work was driven by a desire to improve the material conditions of the working class. His book, *Principles of Economics*, first published in 1890, became the standard introductory textbook in the English-speaking world for half a century; its eighth edition was published in 1920 by MacMillan & Co. in London. A talented mathematician, Marshall advanced the study of supply and demand by using calculus to explain the functions of markets and firms. This work helped to formalize crucial economic concepts, including marginal cost, marginal utility, consumer surplus, and producer surplus. He is also noted for introducing the foundational model of supply and demand, often using the corn exchanges in English towns as a practical example. Marshall emphasized the importance of facts, and his observation that large firms could achieve lower unit production costs than smaller ones was central to his analysis. [1, 3] However, this particular insight was largely overlooked by subsequent neoclassical economists.

Alfred Marshall (1842–1924)

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Developed by Alfred Marshall, this economic model explains how prices are determined in markets with numerous buyers and sellers of identical goods. The model posits a supply curve based on the prices sellers are willing to accept and a demand curve based on the willingness to pay of buyers. A core assumption is that all goods are homogeneous. Marshall argued that even though the market price might fluctuate—being ‘tossed hither and thither like a shuttlecock’ during the ‘higgling and bargaining’ process—it would always gravitate towards the equilibrium price, where the quantity demanded by buyers equals the quantity supplied by sellers.

Marshall's Model of Supply and Demand

Marginal cost (MC) represents the additional cost a firm incurs to produce more output. It can be viewed in two ways: for discrete changes, it is the cost of producing one additional unit. More generally, when quantity (Q) is treated as a continuous variable, the marginal cost is the derivative of the total cost function, C(Q), with respect to Q. This represents the instantaneous rate of change in total cost and corresponds to the slope of the total cost function. [1, 2]

Marginal Cost

Marginal utility is the additional satisfaction or benefit resulting from a one-unit increase in the consumption of a good. More formally, it is the rate of change in total utility as the quantity of the good consumed increases. In economic models, marginal utility is often calculated using partial derivatives.

Marginal Utility

Consumer surplus is the total benefit consumers receive when they purchase a good. It is calculated by adding up the individual surplus for every consumer who buys the product. An individual's surplus is the difference between their willingness to pay (WTP) and the actual price they paid for the good. The term 'consumer surplus' typically refers to this aggregate sum across all consumers.

Consumer Surplus

A producer's surplus on a single unit of a good is the difference between the selling price and the marginal cost to produce that unit. The total producer surplus, often simply called 'producer surplus', is the sum of these individual surpluses for all units sold. This total represents the economic rent a firm gains from selling its product over the alternative of not selling. It's important to distinguish total producer surplus from a firm's total profit, as the surplus calculation does not subtract fixed costs.

Producer Surplus

A key part of Alfred Marshall's economic analysis was his observation that larger firms were capable of producing goods at a lower cost per unit compared to smaller firms. [1, 3] This concept, central to his work, was not incorporated into the mainstream neoclassical school of thought that followed him. [2]

Marshall's Observation on Economies of Scale

Alfred Marshall, a key founder of the neoclassical school of economics, expressed strong disapproval of the *Homo economicus* model, which assumes individuals are driven solely by self-interest. He would have been distressed by this concept becoming central to the textbooks of his followers. Marshall argued that ethical considerations are crucial for economists to analyze. In his 1890 book, *Principles of Economics*, he stated: 'Ethical forces are among those of which the economist has to take account. Attempts have indeed been made to construct an abstract science with regard to the actions of an economic man who is under no ethical influences and who pursues pecuniary gain... selfishly. But they have not been successful.'

Marshall's Disapproval of Homo Economicus

Marshall's Cautionary View on Mathematical Economics

In his 1890 publication, *Principles of Economics*, Alfred Marshall outlined what he considered the primary objective of the field. He contended that the 'chief and highest interest' of economics is to investigate whether the existence of a 'lower class' is a societal necessity. This inquiry delves into whether it is unavoidable that a large segment of the population must endure poverty and toil to facilitate a cultured and refined life for others, while being excluded from participating in that life themselves. Marshall believed that economics, through the application of factual analysis and inference, was the essential discipline for addressing this fundamental question about poverty and social hierarchy.

Marshall's View on the Core Purpose of Economics

The provided image is a portrait of the economist Alfred Marshall (1842–1924). This visual representation corresponds to the person who founded the neoclassical school of economics and developed the foundational model of supply and demand.

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