Introduction to Mathematical Economics : A Practical Guide for Second and Third Year Undergraduate Students

Economics is a social science that studies the interaction of individuals and organisations engaged in the production, distribution, and consumption of goods and services. The goal is to prevent or correct problems such as unemployment, inflation public deficit and market failures. Economics is the study of scarcity. The study of allocation of scarce resources to satisfy human wants. Human needs are unlimited. On the other hand, output is limited and restricted. The main economic problem faced by all societies is that of allocating the scarce resources of land, labor and capital. Scarcity is a fundamental problem for every society. The main problem is that the individuals that constitute the society are producing or inventing wrong services and products that in the long-term they create financial and spiritual problems. Governmental decisions should be made in such a way to facilitate the spiritual and financial effort of the households. Opportunity cost is what is sacrificed to achieve an alternative action. Microeconomics studies the economic behavior of individual decision makers such as consumers and business companies. Macroeconomics studies aggregate output, employment, and the general price level. The amount a consumer spends (C) is positively related to the disposable income Yd . Thus, the mathematical function is as follows: C = f Yd.The dependent variable, consumer spending is plotted on the vertical axis. The independent variable, disposable income, is plotted on the horizontal axis.To be able to take sound decisions in economics, economic agents have designed mathematical models based on differentiation of simple functions, integration of simple functions, matrix algebra, first order differential equations, second order differential equations, and optimization theory. The relationship between different cost and revenue curves such as marginal revenue, marginal cost, total fixed and variable cost could be better explained through mathematical notations. Supply and demand curve designed to find the equilibrium point and elasticizes are better explained through mathematical equations. Economics and mathematics are directly related as changes in quantities and variables affect the relationship and the direction of the consumer behavior to become better-off or worse-off