Mathematical analysis

Vilfredo Pareto (1848-1923) was an Italian economist, best known for developing the concept of the circumstance under which nobody need be made worse off, and nobody better off through wealth redistribution. When this situation exists, the economy is said to be "Pareto efficient". Pareto devised mathematical representations for this optimal resource allocation, which when represented on a graph would yield a curve. Different points along the curve represent different allocations, but each would be optimally efficient. Rather than using the persuasive language of classical economists like Mill, the Pareto efficient curve could be represented with a precise mathematical formula:

Alfred Marshall is also credited with an attempt to put economics on a more mathematical footing. He was the first Professor of Economics at the University of Cambridge and his work, Principles of Economics^[57] coincided with the transition of the subject from "political economy" to his favoured term, "economics". He viewed maths as a way to simplify economic reasoning, though had reservations, revealed in a letter to his student Arthur Cecil Pigou.

"(1) Use mathematics as shorthand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life. (5) Burn the mathematics. (6) If you can’t succeed in 4, burn 3. This I do often."^[58]

Coming after the marginal revolution, Marshall concentrated on reconciling the classical labour theory of value, which had concentrated on the supply side of the market, with the new marginalist theory that concentrated on the consumer demand side. Marshall's graphical representation is the famous supply and demand graph, the "Marshallian cross". He insisted it is the intersection of both supply and demand that produce an equilibrium of price in a competitive market. Over the long run, argued Marshall, the costs of production and the price of goods and services tend towards the lowest point consistent with continued production. Arthur Cecil Pigou in Wealth and Welfare (1920), insisted on the existence of market failures. Markets are inefficient in case of economic externalities, and the State must interfere. However, Pigou retained free-market beliefs, and in 1933, in the face of the economic crisis, he explained in The Theory of Unemployment that the excessive intervention of the state in the labor market was the real cause of massive unemployment, because the governments had established a minimal wage, which prevented the wages from adjusting automatically. This was to be the focus of attack from Keynes.