Mathematical Economics - Alfred Marshall

Introduction

Born in 26th July 1842, Alfred Marshall stood out to be one of the economists who were influential during his days. This was later to be strengthened by his book, ‘The Principles of Economy’ which was published in the year 1890, and which became a prominent book that was widely used across England for several years. The main idea in Marshall’s book was the principles of demand and supply, costs of production and the marginal utility. He is among those referred to as being the founders of economy. After his inaugural book on economy, Marshall’s works further advanced when he wrote his second volume of the same book, this time dealing with matters of collectivism, taxation, trade fluctuations, money and foreign trade. However, this book was never published. Through his book, ‘Principles of Economy’, Marshal established a reputation globally as it appeared in eight different editions ranging from 752 to 870 pages. This book was instrumental in the shaping of economics across nations that spoke English. Other wide range issues that the book addressed include increasing and decreasing returns. A lot of these ideas were later developed by Jevons among other economists.

Marshall’s quest

Broadly, Marshall was interested in reconciling the modern and the classical value theories. Earlier, John Stuart Mill explored the relationship that exists between the cost of production of commodities and their values. This was based on the theory that the effort that is put on the manufacturing process affects the value of the commodity. Later, the Marginal Utility theorists like Jevons explored the theory that was founded on the relationship between value and maximizing of utility. Marshall in his work amalgamated both the two approaches but put more focus on the issue of cost. Marshall held onto the idea that supply cannot be altered and the market value is dependent on the demand. His main idea was that there is a possibility of expanding production through the facilities that are in existence. This can be done in an intermediate period of time. The facilities that can be used in this verge include machinery and the buildings but there is very little influence on the products’ sale price due to the fact that there is no need for renewing them in their costs intermediate time period. He further pointed out the fact that variable costs or prime costs recur constantly and influence the price of the sale in this period. The replacement costs of buildings and machines that wear out are usually replaced by high sale price of the product. Among Marshall’s main contributions towards the theory of economics was the classification of the costs into variables and fixed and the time element. In his work, the models of partial equilibrium were his commitment as opposed to the general equilibrium on the grounds that the former was more practical given the fact that economics is dynamic in nature. (Marshall, pg. 101-103)

Marshall and mathematics in economics

Marshall was keen in the improvement of the mathematical rigor in economic issues and in the transformation of economics into a more scientific discipline. This led to his writing about the protectionism and international trade tracts in the 1870s. These works were compiled in ‘The Theory of Foreign Trade and the ‘Economics of Industry’ together with his wife Paley. Despite the fact that Marshall viewed and contributed to the taking of economics to a level of rigorous mathematics, he was always keen to ensure that economics is not overshadowed by mathematics hence rendering economics an irrelevant discipline to the laymen. In most of his books, the mathematical contents were placed in the appendices and the footnotes for the professionals. This was further evident by a letter which he wrote to Bowley instructing him to apply shorthand while using mathematics and not to make it as an enquiry engine, to translate into English, to use illustrations from real life so as to make economics easier and to ultimately burn the mathematics.

Marshall’s contributions to economics

Marshall is far much accredited for the success he achieved in his books and teachings. These are overtly based on his successful use of diagrams, a fact that most economists emulated later in their various works globally. The development of the standard supply and demand graph is accredited to Marshall. He was the proponent of the graph in which he explicitly demonstrated various fundamental issues attributed to the aspects of supply and demand which includes the demand and supply curves too. In the same wake, Marshall also introduced the law of diminishing returns, producer and consumer surpluses and the marginal utility law. This contribution has led to a model that is widely used by several economists across the globe and the application of different forms by applying various variables in trying to demonstrate other several principles of economics. Through this model, Marshal proponed and made it possible for there to be a representation that is visual of the fundamentals of economics that were otherwise abstract and complex, making them a little bit more easier for anyone to understand. These models that he introduced have proven to be vital in the study and teaching of current economics as there is a concise and clear representation of the theories and the economic fundamentals that are explained. (Reisman, 199)

Microeconomics

The contribution of Marshall was vast and prominent. In the British economies, Marshall established himself as a force to reckon with as he ventured into the microeconomics. This was later to be his specialty. In this aspect, he was able to study and inherently analyze the industries and individual markets as opposed to studying economy as a whole. The concept of the elasticity of demand is accredited to Marshall.

His other contribution was the consumer surplus concept, in which he noted that he each unit of commodity typically has the same price that a consumer buys but there is a decline in the additional units and the value of the consumer. Further, this concept indicates the fact that the consumer is set to buy units again and again until that point when the value and the price will be at par. Therefore, among all the units that are previous to that last unit, the consumer is bound to reap a benefit by a payment that is lower than the original value of that good in question. It further asserts the fact that the difference that exists between the value of the consumer and all the units and amount paid is equal to the benefits therein. This is what Marshall referred to as consumer surplus. The product surplus concept was also a brain child of Marshall. This he said referred to that actual amount that the producer is paid less the amount that the producer would in normal circumstance accept. These concepts were used by Marshall in the measurement of the various well being changes in the government taxation. This approach by Marshall has since been refined by various economies and is currently referred to as welfare economies.

Marshall also made a contribution towards the understanding of how the markets adjust to the various changes in the demand or supply over a period of time. This culminated to his introduction of the three periods. These include the market period which is the time amount in which a commodity is fixed stock wise. His second period was the time period and is the shortest according to him. This refers to the period in which there can be an increase in the supply through the addition of inputs and labor but not the addition of capital. The third period according to Marshall was the amount of time that a capital takes before it is increased. (Marshall, 77)

Conclusion

In his work, Marshall always ensured that he expressed qualifications, used footnotes and exceptions before attempting a statement. He established himself as a prominent and accomplished astute mathematician having studied Math at the St. John’s College in Cambridge. However, he ensured that he was limited in the used of quantitative expressions so that he could appeal and be understood by the layman. There is no doubt that Marshall has been and will continue to be a key player in the field of economics. His neoclassical analysis of economics and veering of the usually classical economics path is a testimony to his acquaintance and deep understanding of economics issues. The current and the future economists have and shall continue to use a lot of Marshall’s works as references and foundation to the development and understanding of economics issues.

  

References

Marshall, A. (1996). The Correspondence of Alfred Marshall, Economist, Volume 3. UK: Cambridge University Press, Feb 23, 1996 pg.77

Marshall, A. (Principles of Economics: Abridged Edition). New York: Cosimo, Inc., Apr 30, 2010 –pg 101

Reisman, D. (2013). Alfred Marshall's Mission (Routledge Revivals). New York: Routledge, Jan 11, 2013 pg 199