Production Functions and Cost Analysis



Production Functions and Cost Analysis

Outline

Introduction: The intro discusses explains the principles by which a business firm decides how much of each commodity that it sells (its “outputs” or “products”) it will produce, and how much of each kind of labour, raw material, fixed capital good, etc.

Production Functions and Cost Analysis: This section discusses that the Production functions and cost functions are the cornerstones of the economic analysis of production.

Conclusion: The conclusion discusses that the level of technical efficiency of a particular firm is characterised by the relationship between observed production and some ideal or potential production.

Introduction

In economics, an effort to explain the principles by which a business firm decides how much of each commodity that it sells (its “outputs” or “products”) it will produce, and how much of each kind of labour, raw material, fixed capital good, etc., that it employs (its “inputs” or “factors of production”) it will use. The theory involves some of the most fundamental principles of economics.

Production Functions and Cost Analysis

Production functions and cost functions are the cornerstones of the economic analysis of production. A production function is a mathematical relationship that captures the essential features of the technology by means of which an organization transforms resources such as land, labour and capital into goods or services such as steel or education. It is the economist's distillation of the salient information contained in the engineer's blueprints. Mathematically, let y denote the quantity of a single output produced by the quantities of inputs denoted (x1,..., xn). Then the production function f(x1,...,xn) describes the maximum quantity of output that can be produced by the input combination (x1,.., xn), given the technology in use, and so y=f(x1,..,xn). Several important features of the structure of the technology are captured by the shape of the production function. Relationships among inputs include the degree of substitutability or complementarity among pairs of inputs, as well as the ability to aggregate groups of inputs into a shorter list of input aggregates. Relationships between output and the inputs include economies of scale and the technical efficiency with which inputs are utilized to produce output.

Each of these features has implications for the shape of the cost function, which is intimately related to the production function. A cost function is also a mathematical relationship, one that relates the expenses an organization incurs to the quantity of output it produces, and to the unit prices it pays for the inputs it employs in the production process. Mathematically, let E denote the expense an organization incurs in the production of output quantity y when it pays unit prices (p1,..., pn) for the inputs it employs. Then the cost function c(y, p1, ..., pn) describes the minimum expenditure required to produce output quantity y when input unit prices are (p1,..., pn), given the technology in use, and so E=c(y, p1,...,pn). A cost function is an increasing function of (y, p1,..., pn), but the degrees to which minimum cost increases with an increase in the quantity ...