Mathematics Economics

CHAPTER II

DISCUSSION

 A.History of Mathematics Economics

The use of mathematics in the service of social and economic analysis dates back to the 17th century. Then, mainly in German universities, a style of instruction emerged which dealt specifically with detailed presentation of data as it related to public administration. Gottfried Achenwall lectured in this fashion, coining the term statistics. At the same time, a small group of professors in England established a method of "reasoning by figures upon things relating to government" and referred to this practice as Political Arithmetick.Sir William Petty wrote at length on issues that would later concern economists, such as taxation, Velocity of money and national income, but while his analysis was numerical, he rejected abstract mathematical methodology. Petty's use of detailed numerical data (along with John Graunt) would influence statisticians and economists for some time, even though Petty's works were largely ignored by English scholars.

The mathematization of economics began in earnest in the 19th century. Most of the economic analysis of the time was what would later be called classical economics. Subjects were discussed and dispensed with through algebraic means, but calculus was not used. More importantly, until Johann Heinrich von Thünen's The Isolated State in 1826, economists did not develop explicit and abstract models for behavior in order to apply the tools of mathematics. Thünen's model of farmland use represents the first example of marginal analysis.Thünen's work was largely theoretical, but he also mined empirical data in order to attempt to support his generalizations. In comparison to his contemporaries, Thünen built economic models and tools, rather than applying previous tools to new problems.

Meanwhile a new cohort of scholars trained in the mathematical methods of the physical sciences gravitated to economics, advocating and applying those methods to their subject,and described today as moving from geometry to mechanics.These included W.S. Jevons who presented paper on a "general mathematical theory of political economy" in 1862, providing an outline for use of the theory of marginal utility in political economy.In 1871, he published The Principles of Political Economy, declaring that the subject as science "must be mathematical simply because it deals with quantities." Jevons expected the only collection of statistics for price and quantities would permit the subject as presented to become an exact science.Others preceded and followed in expanding mathematical representations of economic problems

B.The Meaning of Mathematical economics

Investopedia explains 'Mathematical Economics' is :

Mathematical economics relies on statistical observations to prove, disprove and predict economic behavior. Although the discipline is heavily influenced by the bias of the researcher, mathematics allows economists to explain observable phenomenon and provides the backbone for theoretical interpretation.

Definition of 'Mathematical Economics' is

Mathematical economics is a discipline of economics that utilizes mathematic principles and methods to create economic theories and to investigate economic quandaries. Mathematics permits economists to conduct quantifiable tests and create models to predict future economic activity.

'Mathematical Economics' is

Much of modern economics is expressed in terms of mathematical models. This program uses quantitative methods to understand and represent economical theories and to solve complex problems found in a wide range of economic systems. Mathematical economics uses differential calculus, differential equations, and mathematical optimization to understand economic behaviour and to prepare students for applications in banking, industry, and government.

Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. By convention, the applied methods refer to those beyond simple geometry, such as differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, and other computational methods.An advantage claimed for the approach is its allowing formulation of theoretical relationships with rigor, generality, and simplicity.

It is argued that mathematics allows economists to form meaningful, testable propositions about wide-ranging and complex subjects which could less easily be expressed informally. Further, the language of mathematics allows economists to make specific, positive claims about controversial or contentious subjects that would be impossible without mathematics.Much of economic theory is currently presented in terms of mathematical economic models, a set of stylized and simplified mathematical relationships asserted to clarify assumptions and implications.

Broad applications include:

    optimization problems as to goal equilibrium, whether of a household, business firm, or policy maker

    static (or equilibrium) analysis in which the economic unit (such as a household) or economic system (such as a market or the economy) is modeled as not changing

    comparative statics as to a change from one equilibrium to another induced by a change in one or more factors

    dynamic analysis, tracing changes in an economic system over time, for example from economic growth.

Formal economic modeling began in the 19th century with the use of differential calculus to represent and explain economic behavior, such as utility maximization, an early economic application of mathematical optimization. Economics became more mathematical as a discipline throughout the first half of the 20th century, but introduction of new and generalized techniques in the period around the Second World War, as in game theory, would greatly broaden the use of mathematical formulations in economics.

This rapid systematizing of economics alarmed critics of the discipline as well as some noted economists. John Maynard Keynes, Robert Heilbroner, Friedrich Hayek and others have criticized the broad use of mathematical models for human behavior, arguing that some human choices are irreducible to Mathematics.

1.       The Article of Mathematics Economics

MATHEMATICAL ECONOMIC

   Both neoclassical price theory and Keynesian income theory have been illustrated by theory mathematic of calculus, linear algebra, and other sophisticated techniques. The most powerful and popular-if not necessarily the most successful-alliance of economics with mathematics and statistics occurs in the specialty called econometrics. Econometricians are  model builders who link together hundreds or even thousands of equations that purport to explain the behavior of an entirtrie economy. As forecasting tools, econometric models generally are used by both corporations and government departments, although their record of accuracy is neither better nor worse than that of alternative ways of looking into the future.

      Operations research and input-output analysis are two additional specialities in which economic analysis and higher mathematics operate in tandem. Operations research stresses a systems approach to problems. Typical puzzles involve coordinating the functions of a multiple plant corporation, fabricating many products, and using equipment so as to minimize costs and maximize efficiency. Researches make use of the expertise of engineers, economists, industrial psychologists, statisticians, and mathematicians.

       In the words of its inventor, the Russian Amrican economist Wassily Leontief, input output analysis tables”describe the flow of goods and services between all the individual sectors of a national economy over a stated period of time.” Although constructing such a table is a challenge , this method has had a major impact on economic thinking. It is now widely used in socialist as well as capitalist countries.

C. Correlative Conjunctions

Correlative conjunctions are sort of like tag-team conjunctions. They come in pairs, and you have to use both of them in different places in a sentence to make them work. They get their name from the fact that they work together (co-) and relate one sentence element to another. Correlative conjunctions include pairs like “both/and,” “whether/or,” “either/or,” “neither/nor,” “not/but” and “not only/but also.”

Use either … or, neither … nor

The Formula :

Either  + noun + or + plural noun + plural verb

Either + noun + or + singular noun + singular verb

Neither + noun + nor + plural noun + plural verb

Neither + noun + nor + singular noun + singular verb

The Example :

Ø  Either….or

                        Either The students  or Toni is watching TV now

(para pelajar itu  atau Toni sedang menonton TV sekarang.)

Either  my friends or my mother sweeps the floor every morning

(Teman-teman saya atau ibu saya menyapu lantai itu setiap hari.)

Either the cats or the dog eats the fish.

(para kucing atau anjing makan ikan)

Either the dog or the cats eat the fish.

(anjing atau para kucing makan ikan)

Ø  Neither … nor

Neither the students nor Toni is watching TV now

(Tidak murid-murid itu, tidak juga Toni, sedang menonton TV sekarang)

Neihter my friends nor my mother sweeps the floor

(Tidak murid-murid itu, tidak juga Toni, sedang menonton TV sekarang)

Rina is neither smart nor stupid

(Rani tidak pandai dan tidak juga bodoh)

I will either play games nor sing a song tomorrow

(Saya tidak bermain game dan tidak juga bernyanyi besok)

Both/and
She won gold medals from both the single and group races.

Both TV and television are correct words.

Not only/but also
Not only red but also green looks good on you.

She got the perfect score in not only English but also math.

whether/or