Application of Mathematics in Economic Theory
Rakesh Sharma
Assistant Professor of Economics, Govt. Degree
College, Khad, District Una, H.P. – 177207
*Corresponding
Author E-mail: jagjitsinghpatial@gmail.com
Abstract:
Application of Mathematics into Economic Theory is a formal
description of certain relationships of economic variables; some of these relationships
are derived from empirical observations while other ones are deduced from theoretical
axioms based on a Rational Economic Agent. Mathematization of Economic Theory broadly
started in the second quarter of the 20th Century due to shift of emphasis from partial to general equilibrium analysis, economic
dynamism, growth theories and technical progress. In present scenario, it is being widely accepted as
a tool in improving Economic Theory and corrective measures for the formulation
of Economic Policy; Fiscal and Monetary Policies.
Economic
reasoning based on mathematics, in the form of a set of equations and simplified mathematical
relationships has been a fundamental factor in the development of Economic Theory
as a Science approximating to reality
sufficiently closed. Having a fair idea of economic problems with expert knowledge supplemented
by appropriate mathematical techniques do provide a better formal insight into the
problem and promotes understanding in a systematic and consistent form. Empirical
support and mathematical logic makes the theory easily understandable and to form
meaningful and testable propositions. That is why Mathematical Methods are being recognized
as a rational approach in solving Economic Problems; rational decision making, understanding
cause and effect relationship between economic variables, utility and profit maximization,
optimum allocation of resources, least cost-combination subject to budget constraint,
factor price determination, distribution aspect of the Gross National Product (GNP)
and growth path of the economy.
Mathematical
Equations in Economic Theory:
While
applying Mathematics into Economic Theory, equations can be distinguished in to
three parts;
1.
Definitional Equations e.g. Profit Maximization behaviour of a Firm or a Producer
Profit (π) =
Total Revenue (TR) – Total Cost
(TC)
2. Behavioural Equations e.g. Consumption Behaviour in an Economy C = 40+0.75
Y
3. Equilibrium Equations e.g. determination of Market Equilibrium with Demand and Supply Functions
Demand Function Qd = a - b
P
Supply Functions Qs = c +
g P
Differential Equations provide
solution to Demand and Supply functions resulting in Equilibrium Price. First Order
Difference Equations provide solution to Dynamics of the Equilibrium i.e. how fluctuations
converge or diverge to Equilibrium and paves the way for understanding a Business
Cycle over a period of time.
Prof.
Cournot, mathematically developed equilibrium market condition in view of
competition between two sellers referred as Cournot Duoploy. Differentiating
the profit function with respect to quantity supplied for each firm, Cournot
deduced a system of linear equations, the simultaneous solution of which gave the
equilibrium price, quantity and profit under Duopoly.
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