Production Function

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PRODUCTION FUNCTION
Objectives
After going through this unit, you should be able to: familiarise with the concepts and rules relevant for production decision analysis; understand the economics of production; understand the set of conditions required for efficient production.

Introduction to Microbes

Structure
7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 Introduction Production Function Production Function with one Variable Input Production Function with two Variable Inputs The Optimal Combination of Inputs Returns to Scale Summary Self-Assessment Questions Further Readings

7.1 INTRODUCTION
Production process involves the transformation of inputs into output. The inputs could be land, labour, capital, entrepreneurship etc. and the output could be goods or services. In a production process managers take four types of decisions: (a) whether to produce or not, (b) how much output to produce, (c) what input combination to use, and (d) what type of technology to use. This Unit deals with the analysis of managers’ decision rules concerning (c) and (d) above. The analysis of the other two decisions will be covered in Units 8 and Unit 9 of this block. In this unit, we shall begin with a general discussion of the concept of production function. The analysis of this unit mainly focuses on the firms that produce a single product. Analysis on decisions related to multiproduct firms is also given briefly. The nature of production when there is only one variable input is taken up first. We then move on to the problem of finding optimum combination of inputs for producing a particular level of output when there are two or more variable inputs. You will learn various functional forms of production frequently used by economists and their empirical estimation in Unit 10. The unit concludes with the production decisions in case of product mix of multiproduct firms.

7.2 PRODUCTION FUNCTION
Suppose we want to produce apples. We need land, seedlings, fertilizer, water, labour, and some machinery. These are called inputs or factors of production. The output is apples. In general a given output can be produced with different combinations of inputs. A production function is the functional relationship between inputs and output. It shows the maximum output which can be obtained for a given combination of inputs. It expresses the technological relationship between inputs and output of a product.

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Production and Cost Analysis

In general, we can represent the production function for a firm as: Q = f (x1, x2, ….,xn) Where Q is the maximum quantity of output, x1, x2, ….,xn are the quantities of various inputs, and f stands for functional relationship between inputs and output. For the sake of clarity, let us restrict our attention to only one product produced using either one input or two inputs. If there are only two inputs, capital (K) and labour (L), we write the production function as: Q = f (L, K) This function defines the maximum rate of output (Q) obtainable for a given rate of capital and labour input. It may be noted here that outputs may be tangible like computers, television sets, etc., or it may be intangible like education, medical care, etc. Similarly, the inputs may be other than capital and labour. Also, the principles discussed in this unit apply to situations with more than two inputs as well.

Economic Efficiency and Technical Efficiency
We say that a firm is technically efficient when it obtains maximum level of output from any given combination of inputs. The production function incorporates the technically efficient method of production. A producer cannot decrease one input and at the same time maintain the output at the same level without increasing one or more inputs. When economists use production functions, they assume that the maximum output is obtained from any given combination of inputs. That is, they assume that production is technically efficient. On the other hand, we say a firm is economically...
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