Mathematical Economics Case Solution And Analysis, HBR Case Study Solution & Analysis of Harvard Case Studies

Mathematical Economics Case Solution

In the similar manner, the constraint optimization,which is also called mathematical programming model, is widely used in economic analysis for providing a valuable information and deeper insights into the behavior of the economic agents and for preparing of decision support system for play makers and businessmen. The mathematical optimization is used as an instrument for the qualitative analysis and also for a wider range of applications in economies, which are as follows:

Efficiency analysis.
Industrial economics.
International economics.
Input-output economics.
Quantitative economics.
Environmental economics.(Pardalos, 2019).

In addition to this, one of the mathematical optimizations is the linear-optimization, which is used to achieve the best outcome,such as: lowest cost or maximum profit in the mathematical model, the requirements of which are represented by the linear relationship. There are various elements of the model, which include: the constraints, decision variables and the objective function. Thus, the linear programming helps the economists in making processes that are both cost effective and efficient. On the other hand, the non-linear programming optimization is another method of the mathematical optimization model in which some of the objective functions or constraints are non-linear. Hence, the mathematical optimization using both linear programming and non-linear programming,provide valuable insights and information base for the optimum allocation of the scarce resources and it also helps in analyzing and evaluating the profit and cost of various alternatives.

Game theory

The theory of game is one of the branches of the applied mathematics, which is widely used in economics. With the use of the theory of game; the real-world scenarios for various-situations, such as:product releases as well as pricing competition, could be laid out and the outcomes could be estimated. The economist often use the theory of game in order to understand the behavior of oligopoly firm, and it also help to easily predict the likely outcomes and results when the firm tends to engage in certain behaviors, such as:collusion and price-fixing.

In addition to this, the wider application of the theory of game in economics ranges from the analysis of economic competition to the economic phenomenon, such as:voting theory, bargaining mechanism design, political economy, behavioral economics and experimental economics.

Econometrics

The econometrics is the application of the methods of statistics to economic data for the purpose of giving an empirical content to the economic relationship. Econometrics is the use of the statistical methods and techniques to understand the test theories as well as economic issues. Modeling choices and preferences of customers with the use of the econometrics approach could improve the strategy of the firm, decision making and hence saves-resources and costs as well. Additionally, it helps in decision making in areas where the risk factor is high, thus the econometric modeling could help in reducing the risk exposure as well as in predicting the outcomes with some probability to make the process of decision making considerably easier.

Moreover, the prediction of the demand from the customers could help to appropriately allocate the staff resources, thus the efficient staff allocation facilitates in meeting the needs of customers with less delay and without resources wastage. Hence, the econometrics modeling could drive the business ahead, helping in optimization of cost, better or smarter decision making and better understanding of the customer and in the market.(Sarkar, 2020).

One of the methods of econometrics is the least square estimations, which is statistical procedures to find the best fit for the set of points of data by minimizing the sum of the residuals of point from the plotted curve. Another widely used method of the econometrics is the maximum likelihood estimation, which is used to estimate the parameters of the probability distribution by maximizing the function of likelihood. The reason of using the maximum likelihood estimate model is to get the robust parameter estimates.

Matrix algebra

Matrix algebra is used in statistics for the purpose of expressing the collection of data and it is the art of manipulating matrix in a way that is similar to manipulating the ordinary numbers in ordinary algebra. The matrix is the set of the elements that is organized in the columns and rows.

a b

c d

Whereas a and b are the diagonal elements and c and d are the off-diagonal elements.

One important application of the algebra matrix in economics is that it helps in handling the large system of equations, and it also helps in testing for the existence of a solution to the system of equations before attempting to solve them. The matrix algebra involves various problems that tends to demonstrate the foundation expressions of matrix algebra as well as the illustration of using algebra for a number of economic problems and issues.(Shayle( R. Searle, 2001).

Minimization and maximization

The cornerstone of the economic thinking is that the people are supposed to be rational, and the rational behavior of the people means minimizing the cost and maximizing the profits, thus the rational households tend to maximize utility and the rational firms maximize the profits. Both utility maximize as well as the profit maximizes need to minimize the costs. It is pertinent to note that the profit maximization objective could be achieved when the marginal revenue is equal to the marginal cost.

Profit maximization marginal revenue (MR) = marginal cost (MC)

Whereas, the rule of minimizing the cost of operations is that all the levels of the labor and capital, such marginalization of labor divided by wage is equal to the marginal product of capital divided by the capital rental price.....................

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Mathematical Economics Harvard Case Solution & Analysis