Ebooks

Five years ago, I came to know that there was not even a single book on the topic “Econometrics and Production Economics: Basics Concepts and Practicals” written by Indian authors for the “Post Graduate Ph.D. Scholars and faculties” of the “Department of Agricultural Economics and Pure Economics” of Indian post graduate colleges and Universities. To fill up this gap, the author took it as a mission to draft a book on this topic and it took approximately five years to complete the original draft of the manuscript, finally ending on October 2, 2021.

1.1 Common Logarithm Logarithms to the base 10 are called common logarithm. This system was first introduced by Briggs in 1615. The mathematician Napier was the inventor of logarithms and Briggs was a contemporary of Napier. From the equation 10x = N, it is evident that the common logarithm will not always be integral and that they will not always be positive. We have  3154 > 103 and 3154 < 104  Hence, log10  3154 = 3 + a fraction  Again we have 0.067 > 10–2 and 0.067 < 10–1  Hence, log10  0.06 = –2 + a fraction  = 2+ a fraction

2.1 Function A variable ‘Y’ is said to be the function of an other variable ‘X’ if for every value of ‘X’ there exists a corresponding value of ‘Y’. It is denoted as Y = f (X). The function f (X) is a relationship between two variables (Y, X) which associates any given number x with another number y. A function is a mapping or transformation of x into y and is denoted by y = f(x). The variable X represents the elements of the domain ‘D’ and is called the “independent variable”. The variable ‘Y’ represents the elements of the range ‘R’ and is known as the “dependent variable”.

3.1 Definition  Let f (x) be the function of a random variable ‘x’. If there exists a number ' ' ?  such that f(x) may be made as close to ' ' ? as we proceed to choose x close to  a given number ‘k’, then we say that the limit of f(x) as x approaches to k, is ' ' ?  and we write it symbolically as  x k  limf(x)  ?  ??  Example 3.1 : We are giving some examples as below:  Example 3.1.1 : A function f (x) may become infinite as x tends to a value ‘c’  and we write that  x c  limf(x)  ?  ??  Example 3.1.2 : Consider the function 1 f(x) x ? . Then we say that as x ??,  f(x) tends to zero and write it as :  x  1 lim 0

4.1 Introduction There are some mathematical tools that are applicable in solving the mathematical problems related to the subject matter on “Economic Theory”. Differential calculus is one of those mathematical tools. Hence the useful theory of differential calculus will be discussed in this chapter. 4.2 Differentiation The mathematical term “Differentiation” is involved in finding the rate at which a variable quantity changes. In the theory of “Differential Calculus” we are concerned fundamentally with the “Rate of Variation” in a function y = f(x) with respect to the change in other variable (Independent Variable X) on which the dependent variable ‘Y’ depends through a relation Y = f(x).

5.1 Introduction In many problems of economics, we may want to know how small or how large a certain quantity may become. In other words, we may want to know the minimum and maximum values of some functions of variables. The term ‘optimisation’ may be used in general, both for maximisation and minimisation. The term ‘optimal position’ is often applied to the ‘equilibrium position’ resulting from the balancing of the forces.

6.1 Introduction Let v : Represents the volume of a gas. p : Represents the pressure of a gas. t : Represents the absolute temperature. The law is represented by the relation writen as t v k. p ? where k is a constant. 1. Suppose the temperature varies and pressure remains constant then 2. Suppose the pressure varies and temperature remains constant then

7.1 Introduction The integral calculus is concerned with the opeartion of “integration” which is the reverse process of differentiation. If f '(x) represents the differential coefficient of f '(x), then the problem of integration is to find f(x) from f '(x). 7.2 Integration of a Function Containing a Constant If we integrate a function containing a constant factor, this factor must also be a factor of final integral.

8.1 Matrix An arrangement of m×n elements into m rows and n columns is called a matrix. A matrix is a rectangular array of numbers usually represented by enclosing the array in brackets. Order of a Matrix : The number of rows and columns is called the ‘dimension’ or ‘order’ of the matrix.  

9.1 Introduction and Definition Literally, econometrics means “Economic measurements”. Although measurement is an important part of econometrics, the scope of econometrics is much broader. Econometrics is an amalgam of economic theory, mathematical economics, economic statistics and mathematical statistics. It can also be stated that “Econometrics consists of the application of mathematical statistics to economic data to provide empirical support to the model constituted by mathematical economics and to obtain numerical results from such data.

10.1 Introduction Least square theory is a statistical technique used to estimate the parameters involved in the regression model in such a way that the sum of squares of errors (residuals) is minimum (least). We have generally two methods of estimation of population parameters. These are (i) Ordinary least square (O.L.S.) method and (ii) Maximum likelihood (M.L.) method. The method of ordinary least square (O.L.S.) is used extensively in regression analysis primarily because it is intutively appealing and mathematically much simpler than the method of maximum likelihood estimation (M.L.E.). In the context of lineaer regression analysis, the two methods generally give similar results.

11.1 Introduction The term “regression” literally means moving back towards the average. It was first introduced by the British biometrician Sir Francis Galton (1822-1911). in connection with the inheritance with the stature. a) Definition Regression analysis is a mathematical measure of the average relationship between two or more variables in terms of the original units of data. In regression analysis, there are two types of variables. The variable whose value is influenced and is to be predicted, is known as the dependent (or predicted/ response explained) variable and the variable that influences the values of the dependent variable or is used for prediction purposes, is known as the independent (predictor/explanatory/ auxiliary/ regressor) variable.

12.1 Introduction There is no other pair of words except the pair “Multi-Collinearity” which is more misused both in “Econometric Texts” and in “Applied Literature”. In many practical problems, many of our explanatory variables are found to be highly correlated among themselves. One of the assumptions of the “classical linear regression model (CLRM) is that there is no “Multicolinearity” among the regressor variables included in the regression model.  

13.1 Meaning of Dummy Variables In econometrics, particularly in regression analysis, a dummy variable is also known as “Indicator variable or Binary variable or qualitative variable”. It is one which takes the value (0 or 1) to indicate the absence or presence of some categorical effect that may be expressed to shift the outcome, e.g. i) Literate (1) and Illiterate (0)  ii) Male (1) and female (0) iii) Farmers in a cross sectional data in terms of year with normal weather condition (1) and year with abnormal weather condition (0).

14.1 Introduction In this chapter, we have to present the review matters related to the theory of the “Classical Linear Regression Model (C.L.R.M.) and Testing of Significance of Statistical Hypothesis”. Here, I have to provide the references about the topics and the names of the books from where the readers can refer about the availability of the subject matters (preliminaries, procedures and interpretations) of numerical results obtained through the statistical analysis carried out for the empirical studies considered there in.

15.1 Agricultural Economics and Definition As a separate subject, agricultural economics emerged in the beginning of 20th century when the economic issues related to agriculture aroused interest at various educational centres. The depression of 1890s which wrecked have in agriculture at many places and it forced organised farmers groups to take keen interest in farm management problems. The study and teaching of agricultural economics was started at Harvard University (U.S.A.) in 1903 by Professor Thomas Nixon Carver. Agricultural economics may be defined as the “Application of Principles & Methods of economics to study the problems of agriculture to get maximum output and profits from the use of minimum in but for the wellness of society in general as well as the farming industry in Particular.

In production one or a combination of the following relationship are commonly observed: 1. The law of constant marginal returns (productivity)  2. The law of increasing marginal returns (productivity)  3. The law of decreasing marginal returns (productivity)

17.1 Introduction Factor-factor relationship is concerned with the possibility of substituting one input factor (X1 ) for another input/factor (X2 ) for producing a given level of output. It answers the crucial question of finding out the optimum or least cost combination of two or more resources in producing the given amount of output. The two fold objective of factor-factor relationship is:  

18.1 Introduction The farmers have limited resources and a number of enterprises/or enterprise combinations of crops and livestock to choose from. So, the question is how much of what to produce and with what technology. In other words, what combination of enterprises should be produced is expressed as.

19.1 Introduction The farm management comprises of two words: ‘farm’ and ‘management’. Literally ‘farm’ means a piece of land where crops and livestock enterprises are taken up under a common management and has a specific boundaries. ‘Management’ means the act or art of managing, the agricultural production or enterprises etc.

20.1 Introduction The farm management is the science which concerns with making decisions and choices about combining different enterprises and the optimal utilisation of resources available. It is necessary to understand the typical farming decisions. Decisions can be classified into agricultural management decisions, administrative management decisions and marketing management decisions which are discussed below: 20.2 Organisational Management Decisions These are further sub-divided into operational management decisions and strategic management decisions.

21.1 Cost Principle  We know that  TC = VC + FC  and Net Revenue = TR-TC. In the short run, gross revenue (G.R.) must cover the V.C. The maximum net revenue is obtained when MC = M.R. If GRs VC, the guiding principle should be to keep increasing production as long as MR > M.C. In the short run, MC = MR point may be at a level of input use that may involve a loss instead of profit. Yet at this point, the loss will be minimised.This situation of operating the farm when MR > AVC but    

22.1 Farm Planning It refers to setting the objectives and actions to be taken in directing or controlling the organisation of farm business and it precedes all other managerial functions on the farm to achive the desired results. It is deciding in advance to the production management problems viz. what to produce, how to produce, when to produce, financial management problems viz how to borrow, how much to borrow, when to borrow, from where to borrow and marketing management problems viz, where to buy, and sell, when to buy and sell, how to buy and sell ete. Farm planning governs the survival progress and prosperity of farm organisation in a competitive and dynamic environment. It is a continuous and unending process. Farm planning is as old as farming itself but mainly it uses the farmal planning.

23.1 Introduction The following Frank Kright, the knowledge situation can be classified into the following logical possibilities: 23.2 Perfect Knowledge There would be no need for farm management experts if knowledge was perfect. If there were so technology, prices and institutional behaviour would be known with certainty for any period of time in the nature. But the concept of perfect knowledge is a fallacious one and does not represent the real world situation.

24.1 Introduction Linear programming is a budgeting technique which is more refined and systematic than conventional budgeting in determining the optimum combination of enterprises or inputs so as to maximise the income or combination of enterprises or the income or minimise costs within the limits of available resources. It may be defined as “The analysis of the problem in which a linear function of a number of variables is to be maximised or minimised when these variables are subject to a number of restraints in the form of linear inequalities”, In linear programming models, the objective of the typical farm i.e maximisation of net profit or cost minimisation is achieved through an optimal plan generated from its solution.

25.1 Introduction Farmers must be able to take appropriate decisions at appropriate time. Incorrect judgement and decisions will return in failure of execution of farm plan and in turn economic loss. The farm management decisions can be broadly categorised into two ways.

26.1 Introduction In a single equation model, the dependent variable Y is expressed as a linear function of one or more explanatory variables (say X1 , X2 , ... XK ). In such models, an implicate assumption is that the cause and effect relationship between (Y, Xs) is unidirectional. Here explanatory variables are the cause and the dependent variable Y is the effect. However, there are some situations where two way flow of influence among economic variables exists. Thus one economic variable affects other economic variables and in turn is affected by them. Thus, in the regression of money M on the rate of interest r, the single-equation method assumes implicitly that the rate of interest r is fixed and it is tried to find out the response of money demanded when the level of interest rate is changed.

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