eChapters

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.

Prologue: The Issues

Farmers lose a significant portion of their income when their crops and products become infested with various insects, diseases and weeds, resulting in much lower crop productivity and lower actual yields than the attainable yield of crops. Yield losses due to pests, pathogens and weeds are responsible for 20-40% losses in global agricultural productivity. India reports crop losses of 20-25% annually due to pest infestations. Without the use of crop protection solutions, there could be a 78% loss in fruit production, 54% loss in vegetable production and 32% loss in cereal production. According to the Ministry of Agriculture, India loses INR 1.48 billion worth of agricultural production annually due to pests, weeds and plant diseases.

Disease is one of those terms that are very difficult to define. It is realized that disease (literally dis-ease) implies lack of ‘comfort’and therefore, involves deviation from normal functioning. From time to time several definitions which have been proposed, in fact descriptive but not simultaneously exclusive. The definitions for the term disease are.

History of plant pathology records chronological account of important events, contributions of persons who significantly influenced the thinking of their era and interpretation of the observed facts or phenomenon over a period of time. Historical writings help us to understand systematic development in plant pathology, and there problems faced by certain outstanding workers whose view points were unacceptable to majority of opinion makers, simply because it was new and against the established norms of the day. History of plant pathology is a must read for the students of this discipline. The historical accounts will unfold the stories that may motivate the new generation to think and interpret the findings in their own way, without fear of established theories and dogmas carried from the past.

Plant Pathogen

Pathogen is an inducer of disease.

A pathogen can therefore be defined as any factor that induces unresolved impairment or disruption of one or more important plant functions.

Some plant functions such as nutrient uptake, are highly localized. Others, such as respiration, occur in all living tissues. Still others, such as photosynthesis and photorespiration, are extensively coordinated. Pathogen effects therefore range from very local to very general.

1. Growth of plant pathogens

Various plant pathogens, namely fungi, bacteria, nematodes, viruses, viroids, mollicutes, fastidious bacteria, and protozoa, grow in different ways.

1.1 Fungi and parasitic higher plants

Fungal pathogens and parasitic higher plants usually invade and infect tissues by growing on or in them from the first point of inoculation.

Most of these pathogens, whether they cause small lesions or large infected areas on the plant, grow, branch, and spread to more and more plant tissues until the infection stops spreading or the plant dies.

Plant diseases are a recurring threat. Everywhere they appear in a certain cycle. Chains of infection (pathogenesis) initiated by primary inoculums comes spontaneously at the end of the harvest season or at host death due to the production of various types of pathogenic reproductive organs/propagules. These propagules must find ways to bridge the gap between harvest times to ensure continuity of infection. Therefore, plant pathogen survival is a critical step in a successful pathogen disease cycle. Pathogen spread is another important phenomenon in plant disease recurrence and epidemiology. Effective spread/diffusion of virulent propagules is critical for initiation of chains of infection and further progression of the disease in time and space.

Disease development depends on three factors: host, pathogen, and environment.

Host must be susceptible.

The pathogen must be virulent to cause disease.

The environment must be conducive to disease development.

Role of environment on disease development 

Environment

 

 

Host -Pathogen Interaction

Most often, plants become diseased when attacked by living (biotic) or affected by non-living (abiotic) pathogens.

In the first case, at least two components viz., host and pathogen must come into contact and interact for plant disease to occur.

Then, for disease to develop, a third factor, a favorable range of environmental conditions, must also occur.

The interaction of the three disease factors was often visualized as a triangle called the “Disease Triangle".

Each side of the triangle represents one of three components.

Enzymes, toxins, growth regulators, and polysaccharides are much more common and perhaps more important in the development of plant diseases. The pathogen produce these substances when grown on certain substrates (inducible). Let’s talk carefully one by one

Enzymes in plant diseases.

Toxins in plant diseases.

Growth regulator in plant diseases.

Polysaccharides in plant diseases.

Philosophy of defence in plants

Plants cannot move and must resist or tolerate co-located pathogens.

Plants have evolved very powerful preformed defense systems in the form of structural and toxic barriers.

Plants cannot keep intruders out, they can only limit (contain) them.

Plants can tolerate more nutrient runoff. They often sacrifice a piece of tissue to contain pathogens.

Introduction

Plant pathogens include fungi, bacteria, viruses, viroids, phytoplasma, and nematodes.

They have evolved different strategies for invading, feeding on, and reproducing inside plants.

Biotrophic pathogens require living tissue to grow and reproduce.

Necrotic pathogens kill host tissue at the onset of infection and feed on the dead tissue.

Viruses generally require living tissue for survival.

1. Genes and Disease

When various plants such as rice, wheat, tomato and apple are infected with pathogens and cause disease, pathogens are generally different for each host plant type.

Venturia inaequalis, the fungus that causes apple scab, only affects apples. Fusarium oxysporum f. sp. lycopersici which causes tomato wilting, only affects tomatoes and so on.

It is the presence in the pathogen of one or more genes of pathogenicty, specificity, and virulence to the respective host that enables disease development in the host.

 

Genetic variations

Genetic variation is the presence of differences in gene sequences between individual organisms of a species.

Enables natural selection, one of the major forces driving the evolution of life.

When an individual’s offspring exhibit mutations in the traits of their parents, such offspring are called variants.

Introduction

Most common improvement of host resistance to almost any pathogen is brought about by improving the genetic resistance of the host, that is by breeding and using resistance varieties.

Genetic engineering technology made possible the isolation of individual resistance (R) genes from resistant plants and the transfer of such genes into susceptible plants in which they induce the hypersensitive resistant response.

Thus, genetic engineering technology combined with Conventional plant breeding, will provide one of the most effective tools for controlling plant diseases.

1. Markers: Easily identifiable features are called markers or marker features.

2. Types of marker

These markers are three types

2.1.Morphological markers: These relate to the size, shape, color and surface area of different parts of the plant.

2.2.Biochemical markers: Such markers refer to changes in protein structure. For example, isozymes and storage proteins.

Introduction

Genetic engineering is the process of using molecular techniques to add, modify and delete genes of interest to the DNA strands of recipient cells or recipient plants. Genetic engineering is also called genetic technology, transgenic technology, transformation technology and recombinant DNA technology. Genetic engineering consists of tools and techniques used to study, identify, or modify the genes of living organisms. It is also defined as a technique for developing transgenic organisms. The key points of genetic engineering are briefly listed below.

Disease Control vs. Disease Management

The word control evokes the notion of finality, the final elimination of problems .

It is impossible to exclude , eliminate or prevent diseases.

Control is ecologically and practically not possible.

Although disease control is an established and widely understood concept, there are compelling reasons to replace control with management .

Changes in philosophy about plant disease management

To achieve reasonable and sustainable results crop disease management philosophy should shift focus from

Management of pathogens (or insect vectors) to managing host plants.

A single goal of high productivity to multiple goals of high yield, efficiency, quality and safety.

Introduction

It is becoming increasingly difficult to find workers to work in agriculture.

Younger generations do not want to work in plant protection.

We can see that the average age of farmers is getting older.

This leaves the fields unprotected from disease and insects and greatly reduces yields.

Fortunately, this gloomy situation has changed since 2015 thanks to modern technology.

Digital tools are among the most innovative crop protection tools in modern agriculture.

India’s agricultural accomplishment is a global success story

Post Green revolution; Some of the most pertinent questions that humanity faces

Can we sustain our food production ecosystem, while feeding 9 billon people?

Can we improve farm economics without reversal of soil biodiversity loss and carbon content?

Can agriculture play an important role in reducing carbon footprints and mitigating the current climate crisis?

Answers to abovementioned questions do not lie in the currently dominating chemical intensive farming practices, which rely too heavily on

1.1 An overview of biomass

Biomass is an abundant and renewable energy source that has the potential to meet the growing need for clean and sustainable energy solutions. This chapter provides an overview of biomass, its potential, and conversion technologies, which include various techniques for transforming biomass into useful forms of energy such as heat, electricity, and biofuels.

Biomass is an organic substance that can be obtained from agricultural crop waste, forest waste, animals, and microorganisms. It can be used as an energy source or a primary material in various applications. The energy in biomass is derived from photosynthesis, in which plants convert sunlight, carbon dioxide, and water into organic matter.

Biomass, a diverse and renewable resource, holds immense potential as a source of energy, feedstock, and environmental solutions. However, effectively harnessing its benefits necessitates a systematic approach. This chapter introduces the concept of Biomass Management Techniques as a pivotal framework for optimizing the utilization of biomass resources. With a focus on sustainable practices, this chapter delves into various techniques to handle, process, and utilize biomass efficiently. From collection and transportation to storage, conversion, and beyond, Biomass Management Techniques encompass a wide array of methods that ensure the seamless integration of biomass into energy generation, industrial processes, and environmental conservation.

3.1 Overview

3.1.1 Rice straw: What is it?

When harvesting paddy rice, rice straw is produced as a by-product. Approximately 0.7-1.4 kilograms of rice straw can be obtained for each kilogram of milled rice, depending on the variety, moisture content during harvest, and cutting length of the remaining plant stems. The rice straw is separated from the grains after the plants are threshed manually using stationary threshers or with modern combine harvesters, as shown in Figure 3.1.

Rice straw is a type of lignocellulosic biomass comprising cellulose, hemicelluloses, and lignin. Figure 3.2 illustrates that pretreatment can be used to separate these components. Unlike lignin, which is found in the cell wall, cellulose and hemicellulose are organic fibers.

4.1 Introduction

Baling biomass is a crucial technique in efficiently managing and utilizing agricultural crop residue. This chapter explores the process of baling, which involves compacting biomass materials into standardized bundles for easier handling, storage, and transportation. From agricultural residues to forestry waste, the chapter delves into various types of biomass suitable for baling, the equipment used, and the benefits of this technique. It also discusses the environmental impact, economic considerations, and emerging trends in baling methods. Through in-depth analysis and practical insights, this chapter offers a comprehensive understanding of how baling contributes to sustainable biomass management and resource optimization.

5.1 Introduction

The densification of biomass involves transforming loose and low-density organic materials, such as wood residues, agricultural waste, and plant-based materials, into compact and energy-dense forms. This process is necessary because natural biomass can be challenging to handle, transport, and store. Densification uses mechanical, thermal, or chemical processes to increase the material’s density and energy characteristics. The resulting products, such as pellets, briquettes, or cubes, offer several advantages, including higher energy content per unit volume, efficient storage and transportation, reduced moisture content, and improved combustion efficiency. These products are utilized in various industries, including energy production, residential heating, waste management, and industrial applications. Biomass densification promotes sustainable practices by effectively utilizing biomass resources, reducing waste, and promoting the use of renewable energy sources while mitigating environmental impacts.

The utilization of biomass presents a promising avenue for addressing the challenges of resource scarcity, waste management, and environmental sustainability. This book chapter delves into the multifaceted applications of biomass, with a particular focus on the processing of straw, a versatile agricultural residue. From providing essential bedding material for animals and enhancing agricultural practices to playing a pivotal role in horticulture, cushioning, mulching, and composting, this chapter examines the diverse roles that processed straw assumes. Furthermore, it explores its significance in paper and cardboard manufacturing and its emergence as a renewable fuel source, underscoring how thoughtful biomass utilization paves the way toward a more environmentally conscious and resilient future.