 # The Relevance of Mathematics to Economics

THE RELEVANCE OF MATHEMATICS TO ECONOMICS

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Introduction

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It is obvious that, what makes it different is its use of mathematics and statistics to prove theories and concepts while still incorporating other subjects, such as politics, philosophy, and geography. Economics as a social science does not just describe what goes on in the economy. It attempts to explain how the economy operates and to make predictions about what may happen to specified economic variables if certain changes take place, e.g. what effect a crop failure will have on crop prices, what effect a given increase in sales tax will have on the price of finished goods, what will happen to unemployment if government expenditure is increased. It also suggests some guidelines that firms, governments or other economic agents might follow if they wished to allocate resources efficiently. Mathematics is fundamental to any serious application of economics to these areas.

The major development of the second quarter of 20th century in the field of economics was the mathematization of economics. An economist of 19th century cannot even understand the economic journals of present times. Starting from the microeconomics theory, macroeconomics, international trade, economic development, public finance and all the other branches of economics have been changed into a number of equations. The Relevance of Mathematics to Economics

The versatility of the roles that mathematics carries out in economics-such as technique, analysis and rhetorical tool-implies that it is to be considered by all means a professional requisite indispensable to the modern economist. Here is P.A. Samuelson’s advice to a youth with modest mathematical background who wishes to study economic analysis in depth. Apparently, therefore, there is more mathematics in economics then in any of the other social sciences and even than in more traditional scientific disciplines. The need for mathematics in economics is more that obvious.

## The Relevance of Mathematics to Economics

• Mathematics is an integral part of understanding economics because it is necessary in the construction and explanation of economic models, which is how we understand how the economy works.
• The general relevance of mathematics in economics is to build strong mathematical background needed to aid students develop analytical skills required to solve economics problems.
• It helps in the understanding of elementary matrix algebra in a form suitable for application to econometrics and optimization.
• It also helps in the understanding of calculus of several variables, including optimization of functions of several variables, and be able to apply their knowledge to simple economic problems.
• Understand simple first order differential and difference equations and be able to apply their knowledge to simple problems in economic dynamics.
• Mathematics in economics acquaint students with basic mathematics concepts and operations
• Mathematics in economics express economics terms in a more precise manner
• Use Mathematical models to preset simplified versions of how economies work
• ·Show the difference between the product rule and chain rule of partial derivative as well as showing the difference between differentiation and integration.
• Help train the students’ mind to be analytical.
• Empirically measure the costs, benefits and effects of competing options when faced with the issue of scarcity and choice.
• Mathematics allows economists to express their ideas very precisely as formulas. Moreover, formulas can be manipulated, revealing relationships that might have been far more difficult to spot had the concepts been described in prose.
• Economic Models: In planning models, sect oral targets are fixed only with the help of mathematical models like input –output model and linear programming. Determinants and matrix Algebra of Mathematics are of immense use in such techniques.  Mathematics is indispensable to calculate “capital formation” and interest rates. thus, in all most all fields of economics, mathematics is useful.
• Math in Decision-Making: Economists are hired to determine the risk or probable outcome of an event. For example, hospitals want to know what the risks are of dying from an operation and if the benefits are worth it. Economists working for pharmaceutical companies make similar math computations to assess if the risk of taking a drug outweighs its potential benefits.
• Economic Facts: Economic analysis often uses quantitative methods when reviewing specific information in an economy. Quantitative methods are mathematical or statistical calculations that provide economists with indicators for comparing the current economic analysis to those of previous periods. Economists often use various types of math to ensure their personal judgments, inferences or theories are supported by meaningful calculations.
• Calculus: Calculus is the most common type of math found in economics. Calculus includes the use of various formulas to measure limits, functions and derivatives. Many economists use differential calculus when measuring economic information. Differential calculus is the specific measuring of a derivative that relates to a specific function. In basic terms, a function usually represents a straight line known as a tangent. This represents a functions normal operation. The derivative is any change in the tangent that represents a deviation (up or down) in the original line.
• Economic analysis and business plans: Economic analysis in a business is an important management tool when making business plans and decisions. Business owners do not usually require the heavy use of technical math concepts when breaking down economic information. Owners can use the information provided by economists and make basic decisions regarding business operations from these economic models.
• Functions: In economics Demand is a function of price and production is a function of factors of production. Likewise, utility, cost, Revenue, profit, supply, savings etc., are the functions of some related variables. This functional relationship is a mathematical concept. In usual language we say that demand(D) depends on the price, in mathematical terms we would say that demand is function of price while in symbolic notations we would write ; D=f(P) where ‘f’ stands for functional symbol. Similarly, if the utility of a commodity (U) depends on the quantity of the commodity consumed or used (q), we write; U=f (Q) or many a times this is written as U=f(Q). In the case of production function, one variable is determine by a group of variable means one dependent variable is depends on group of independent variables. Qx=f(Px,Py,Pz,L,T,i…..n).
• Straight Line: Linear function is another mathematical concept. The linear function is usually represented in a graph as a straight line. This function is also used in economic analysis, especially in demand and supply analysis. For Example: the demand curve under perfect competition is a straight line, which can be expressed as ‘Linear Equation’ The demand can also write as D=f(P) & D=7-p. Here ‘P’ is the independent variable and ‘D’ is dependent variable, and with a unit fall in price, demand rises by a unit.
• Parabola: Quadratic Function or second Degree function is yet another mathematical concept. The graph of this function is a “parabola” i.e U shaped. This technique is applied in Economics in cost “functions” since, cost curves in economics are U shaped.
•  Differentiation: Rate measurer: most of the economic decisions are based on mathematical concepts “Derivatives” this process is called “marginal analysis”. The concept of “margin “is a basic concept in economics. For example if the total utility function U= f(Q) then the marginal utility is the first older derivative of the total utility function. i.e. du/dq Similarly all marginal concepts such as marginal productivity, marginal revenue, marginal cost, marginal rate of substitution (MRS) ,marginal propensity to consume (MPC), marginal propensity to save (MPS) are the first older derivatives of the relevant functions .in short, differentiation is helpful to derive the marginal functions from the total functions .e)Slope: Graphically the value of dy/dx is the slope or gradient of a curve. This technique is used in economics, to know the” rate of change” or the ‘ slope’ of the curves like demand curves ,revenue curves, cost curves , indifference curves and isoquants . If the slope is negative, then the curve will be a falling curve and if the slope is positive, then the curve will be a rising one.
• Maxima: In economics, we are interested in analyzing the consumer equilibrium and Firm’s equilibrium. The optimization in Calculus is helpful in the study of Consumer’s equilibrium and Equilibrium of the Firm. Consumer is in equilibrium only when his utility is maximum. Hence, with the help of optimization technique, we can calculate the maximum utility of the consumer and in turn the consumer’s equilibrium. Likewise, firm is in equilibrium only when its profit is maximum.

Conclusion

In mathematical application of economics, assumptions and conclusions are stated in mathematical symbols  and  equations,  whereas  in  literary  economics,  assumptions  and  conclusions  are  stated  in words and sentences. The Relevance of Mathematics to Economics.

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