Cost Minimization of a Competitive Firm

One of the economists’ missions is to predict the behavioral responses of consumers or firms on the assumption that optimizing continues. Once this capability is developed, economists try to manage “today” to optimize future economic return of the inputs. Techniques to predict future performance vary from an educated guess based on an appropriate analogy to very complex analytical and numerical calculations and approximations. However, what they all have in common is that they analyze performance in past to say something to obtain constrained optimal output in future. Considering Lagrange multiplier technique applied to a firm’s cost minimization problem subject to production function as an output constraint, an attempt has been made in this paper to apply necessary and sufficient conditions for optimal values. We gave interpretation of Lagrange multiplier and showed that its value is positive. Examining the behavior of the firm; that is, if the cost of a particular input increases, the firm needs to consider decreasing level of that particular input; at the same time, there is no effect on the level of other inputs; also that when the demand of product increases, the firm should consider increasing its level of inputs: capital, labour and other inputs, have been derived.Lagrange Multiplier, Optimization, Cost Minimization, Cobb-Douglas Production Function.

Preference of Social Choice in Mathematical Economics

Mathematical Economics is closely related with Social Choice Theory. In this paper, an attempt has been made to show this relation by introducing utility functions, preference relations and Arrow’s impossibility theorem with easier mathematical calculations. The paper begins with some definitions which are easy but will be helpful to those who are new in this field. The preference relations will give idea in individual’s and social choices according to their budget. Economists want to create maximum utility in society and the paper indicates how the maximum utility can be obtained. Arrow’s theorem indicates that the aggregate of individuals’ preferences will not satisfy transitivity, indifference to irrelevant alternatives and non-dictatorship simultaneously so that one of the individuals becomes a dictator. The Combinatorial and Geometrical approach facilitate understanding of Arrow’s theorem in an elegant manner.Utility Function, Preference Relation, Indifference Hypersurface, Social Choice, Arrow’s Theorem.

Output Maximization of an Agency

Considering Cobb-Douglas function in three variables as an explicit form of production function, in this paper an attempt has been made to maximize an output subject to a budget constraint, using Lagrange multipliers technique, as well as necessary and sufficient conditions for optimal value have been applied. We gave interpretation of Lagrange multiplier in this specific illustration, showing its positive value, and examined the behavior of the agency.Lagrange Multipliers; Economic Problems; Maximizing Output Function; Budget Constraints; Explicit Examples.

Methods of voting system and manipulation of voting

In this paper an attempt has been taken to describe various types of voting system and manipulation of them. French philosophers Marquis de Condorcet (1743-1794) and Jeans-Charles Borda (1733-1799) introduced modern voting system. Duncan Black first introduced the manipulation of voting in 1958 in his book “Theory of Committee and Elections”. Condorcet, Borda and even many modern politicians believe that elections are logically imperfect. In this paper this imperfection is analyzed in some detail. In this paper voting methods are discussed in very simple but in a detailed manner. Voting system is directly involved with Economics, Political Science and Social Science. So that if one has no proper knowledge of the voting system then he can not serve the society in proper way and cannot expect the economic development of the society. Some voting methods such as Arrow’s theorem, median voter theorem, randomized voting, Muller-Satterthwaite theorem and Gibbard-Satterthwaite theorem are apparently non-manipulable and are included in this paper

Output Maximization of an Agency

Considering Cobb-Douglas function in three variables as an explicit form of production function, in this paper an attempt has been made to maximize an output subject to a budget constraint, using Lagrange multipliers technique, as well as necessary and sufficient conditions for optimal value have been applied. We gave interpretation of Lagrange multiplier in this specific illustration, showing its positive value, and examined the behavior of the agency

Utility Maximization Subject to Multiple Constraints

Using method of Lagrange multipliers, an attempt has been taken in this paper to derive mathematical formulation to devise optimal purchasing policy in order to maximize utility function subject to multiple constrained, in this particular illustration, two constraints: 1) budget constraint, and 2) coupon constraint. An explicit example is provided in order to examine the behaviour of an individual consumer and to support the analytical arguments

Borda voting is non-manipulable but cloning manipulation is possible

This paper deals with Borda count which is sincere voting system and originally proposed by French mathematician and philosopher Jeans-Charles Borda. In Borda count a defeated candidate can manipulate the election result in his favor in sincere way by introducing a candidate which is a clone of him and voters ranked this clone candidate immediately below him. In this situation Borda rule is strictly follows but manipulation is possible. The paper shows that this type of manipulation is vulnerable. Both single and simultaneous vulnerabilities of cloning manipulations are discussed with detail calculations and easier ways

Political Economy and Social Welfare with Voting Procedure

Mathematical Economics, Social Science and Political Science are inter-related. In this paper, an attempt has been made to describe aspects of these subjects by introducing examples, definitions, mathematical calculations and discussions. Game Theory is included in this paper to study mathematical models in economics and political science especially to study Nash equilibrium. Success and failure of democracy are interpreted as different equilibria of a dynamic political game with cost of changing leadership. Unitary democracy can be frustrated when voters do not replace corrupt leaders. Federal democracy cannot be consistently frustrated at both national and provincial levels. Arrow’s theorem indicates that the aggregate of individuals’ preferences will not satisfy transitivity, indifference to irrelevant alternatives and non-dictatorship, simultaneously to enable one of the individuals becomes a dictator. In this paper both social welfare functions and social choice correspondence are considered in economical environments

Preference of Social Choice in Mathematical Economics

Mathematical Economics is closely related with Social Choice Theory. In this paper, an attempt has been made to show this relation by introducing utility functions, preference relations and Arrow’s impossibility theorem with easier mathematical calculations. The paper begins with some definitions which are easy but will be helpful to those who are new in this field. The preference relations will give idea in individual’s and social choices according to their budget. Economists want to create maximum utility in society and the paper indicates how the maximum utility can be obtained. Arrow’s theorem indicates that the aggregate of individuals’ preferences will not satisfy transitivity, indifference to irrelevant alternatives and non-dictatorship simultaneously so that one of the individuals becomes a dictator. The Combinatorial and Geometrical approach facilitate understanding of Arrow’s theorem in an elegant manner