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1 ​Terminology of Agricultural Production Economics by Gourav 1 Terminology of Agricultural Production Economics by Gourav Kumar Vani for course of ​ AgEcon 504 & Agecon 604 Last updated on 07-04-2020 at 16:34 PM Variables: Any quantity which can have different values in the production process. ​ Decision Variables: These are the quantities which are under control of the decision maker. Some variables are fixed in the short run while the rest are free to vary in the short run. These are the variables of interest in any optimization problem. Predetermined Variables: The quantities of variables which are known to the decision maker, but ​ he/she is unable to exercise control over their levels but can use the information regarding the same for better decision-making. Uncertain Variables: The quantities or levels of such variables are unknown to the decision maker ​ who is unable to exercise any control over their use. Constant: A quantity that does not change its value in a general relation between variables. ​ Dependent variable: A variable the level of which is governed by the level of other variables. This ​ is treated as the variable of interest in most of the functions. Independent variable: A variable the level of which does not depend on the level of other ​ variables in the system. Function: A function is a rule that describes a relationship between two or more variables. ​ Functions are sometimes referred to as transformations. In general, it is denoted as Y = f (X) where ​ Y is dependent variable while X is an independent variable. ​ Single Valued Function: A function satisfying a unique property that any X value uniquely ​ determines a Y value. Correspondence: A correspondence describes a relationship between two variables. Usually a ​ correspondence means multi-valued function. All functions are correspondences but not all correspondences are functions. Domain: The set of all possible values or permissible values that X can take in a given context is ​ known as the domain of the function. Range: The set of all values that Y variable can take. ​ ​ Slope: The rate of change of a function can be interpreted graphically as the slope of the function. ​ Mathematically, it is the first order (partial) derivative of the function dY when the function is dX ​ defined as Y = f (X) and is the partial derivative when there are more than one independent ∂Y th variables in the function as for i independent variable when function is Y = f (X1, ..., Xn) . ∂Xi ​ ​ Slope remains constant at every point on a straight line while it changes on every point on the curve. Equation: An equation is a function set equal to some particular number (usually zero). In general, ​ ​ it is denoted as f (x) = 0 . Upon solving the equation we get value of variable X that satisfies this ​ equation. Gourav Kumar Vani, Assistant Professor, Department of Agricultural Economics and Farm Management, JNKVV, Jabalpur First draft created at 12:43:16 AM on 09/18/18 2 Terminology of Agricultural Production Economics by Gourav Kumar Vani for course of ​ AgEcon 504 & Agecon 604 Last updated on 07-04-2020 at 16:34 PM Identity: An identity is a relationship between variables that holds for all values of the variables. ​ ​ ​ Often an identity is true by definition. Instead of an equal sign, an identity involves ≡ sign. Optimization: It is a mathematical technique of finding the extreme values of an objective function ​ with or without constraints. Objective Function: An objective function is the function which is the principal focus of the ​ investigator and represents the aim of the investigation. This function is to be either maximized or minimized. A set of decision variables decides the value of the objective function. Constraint: It places limits on level of variable(s) either through an equation or an inequality. ​ Lagrange Multiplier Method: this method is a mathematical technique to find the local maxima or ​ minima of a function f (X1, ..., Xn) subject to equality constraints M − g (X1, ..., Xn) = 0 . Lagrange multipliers are also used very often in economics to help determine the equilibrium point of a system because they can be interested in maximizing/minimizing a certain objective function. Here, instead of using f (X1, ..., Xn) Lagrange function is used as an objective function. Lagrange function is set up as shown below: L(λ, X1, ..., Xn) = f (X1, ..., Xn) + λ[M − g (X1, ..., Xn)] where λ is called Lagrange multiplier which is interpreted as the change in the value of Lagrange function due to an infinitesimal change in constraint amount M . Lagrange multiplier is sometimes referred to as dual value, shadow price or real worth of resources in different contexts. ​ ​ ​ ​ Production: The process which converts inputs (goods and services) into outputs. ​ Assumptions of Production Function Analysis: 1. Non-negative input and output quantities; 2. ​ Non-vanishing first and second order derivatives of the single valued, continuous production functions; 3. Concave production function to input axis; 4. Convex isoquants; 5. Concave PPC; 6. Decreasing returns to scale; 7. Perfect divisibility of products and factors 8. A set of technical decisions taken by a producer determines the exact shape of the production function of the firm. 9. static parameters of production functions 10. Technical efficiency inbuilt into production function. Output: An Output/product is any good or service that comes out of production. This is measured ​ in physical quantities and is usually referred to as Total Physical Product (TPP). ​ ​ Input: An input or resource is any good or service that goes into production. ​ Factors of Production: The production resources required to produce a given product. ​ Traditionally, these are classified as land, labour, capital, and organization. Land: “The material and forces which nature gives freely for man’s aid, in land and water, in air ​ ​ and light and heat.” ​ Labour: “Any exertion of mind or body undergone partly or wholly with a view to earn some good ​ ​ other than the pleasure derived directly from the work.” ​ Capital: “Produced means of production” ​ ​ ​ Gourav Kumar Vani, Assistant Professor, Department of Agricultural Economics and Farm Management, JNKVV, Jabalpur First draft created at 12:43:16 AM on 09/18/18 3 Terminology of Agricultural Production Economics by Gourav Kumar Vani for course of ​ AgEcon 504 & Agecon 604 Last updated on 07-04-2020 at 16:34 PM Farm Entrepreneur: The person who organizes the agricultural production as a farm business and ​ bears the responsibility of the outcome of the business. Every farmer is a farm entrepreneur and farming is a business for him/her. Resource: Anything that aids in production is called a resource. ​ Long run: It is a planning period during which all resources can vary in quantity. The supply can ​ be fully adjusted according to demand. Short run: The planning period during which one or more resources are fixed. In the short run, ​ output can be varied by intensive use of fixed resources. Fixed Resources: Resources the level of which remains unchanged with changes in level of output. ​ The level of such resources is unaltered only in the short run but can be altered in the long run. Farmers have very little control over the use of these resources. The cost associated with a fixed resource is termed as fixed cost. ​ ​ Variable Resource: Resources the level of which changes according to the level of output. Farmers ​ have considerable control over the level of these resources. The costs associated with a variable resource is known as variable cost. ​ ​ Production function: A technical and mathematical relationship among outputs and inputs which ​ describes the manner and extent to which a particular product depends upon the quantities of inputs, at a given level of technology and time. A short run production function is denoted as following ​ Y = f (X1|X2, X3, ..., Xn) Where Y is the output from a particular enterprise, X is the variable resource and X , X , ..., X are 1 2 3 n ​ fixed resources. | (Vertical bar) which is read as ‘given’, separates variable resources from fixed resources. In some places instead of separating fixed inputs by vertical bar, either a vertical line is 0 drawn over fixed inputs X2 or superscript is used to mark the fixed inputs X 2 . Ceteris Paribus ('key-te,ris 'pa-ri,bûs): It is a Latin phrase which means other things ​ ​ ​ remaining/being the same or constant. This is a major assumption in economic analysis. Mutatis mutandis: This is a Latin phrase which approximately translates in English as "allowing other things to change accordingly" or "the necessary changes having been made." Average Physical Product of input Xi (APPXi): Total physical product (Y ) produced per unit of ​ ​ ​ the variable input X keeping other inputs constant at some specified levels. i ​ ​ ​ Y f(Xi|X1,X2,X3,..., Xi−1,Xi+1,..,Xn) AP P X = = . Geometrically, at a point on production function, it is the i Xi Xi slope of a line segment connecting that with origin. If 40 kg of nitrogen application along with other inputs results in production of 2400 kg of output then it can be interpreted that each kg of nitrogen applied on an average results in 60 kg of output, ceteris paribus. ​ ​ Yield: This is the average amount of output produced per unit of area under cultivation. This is ​ usually expressed in quintal per hectare. This is a special type of average physical product. Gourav Kumar Vani, Assistant Professor, Department of Agricultural Economics and Farm Management, JNKVV, Jabalpur First draft created at 12:43:16 AM on 09/18/18 4 Terminology of Agricultural Production Economics by Gourav Kumar Vani for course of ​ AgEcon 504 & Agecon 604 Last updated on 07-04-2020 at 16:34 PM Marginal Physical Product of input Xi (MPPXi): The change in total physical product (Y ) due to ​ ​ ​ ​ an infinitesimally small change in the input X , keeping other inputs constant at some specified i ​ level.
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