# MEANING AND USES OF PRODUCTION FUNCTION

In one of our previous posts, we discussed the nature of agricultural economics. We specifically discussed the meaning and scope of agricultural production economics, some concepts in agricultural production economics and the features of agricultural production. By going through the topics, we believe that you now have enough background information that you will come across in the later part of this curse. This topic is designed to give you further insight into the understanding of production economics. The topic will give the meaning and uses of production function.

At the end of this, you should be able to:

 explain the meaning of production function

 discuss four uses of production function

## Meaning of Production Function

The production function expresses a functional relationship between quantities of inputs and outputs. It shows how and to what extent, output changes with variations in inputs during a specified period of time.

Basically, production function is a schedule or table showing the amount of output obtained from various combinations of inputs given the state of technology.

Algebraically it can be expressed as

Y = Æ’(X1, X2, X3, X4)

Where:

Y = farm output per unit of time

X1, X2, X3, X4 = inputs such as land, labour, capital and entrepreneurial ability.

The production function is determined by technical conditions of production and may be rigid or flexible. In the short run, the technical conditions of production are rigid so that the various input resources used to produce a given output are fixed. This in the actual sense is a rare situation in the theory of production. Even in the short run, it is possible to increase the quantities of one input keeping the quantities of other inputs constant in order to have more output. It should be noted that production is a flow and therefore the transformation of factor inputs into output must be expressed in many units per period of time.

## Uses of Production Function

Production function was first developed by the physical and biological scientist in the experimental laboratory to find out the quantity of certain variable that will produce maximum output level. In doing this, they are transforming resources into output.

In the case of physical and biological scientists, simple linear relationship was enough to express the discrete relationship between input and output. For example, in artificial insemination, what they need to know is just the little quantity that will be enough to fertilize the ovum.

The physical and biological scientists still needed to know the basis for profitability of their products that is, the economic effects. For example, they needed to know the optimum level of the dosage that will achieve the expected desired goal. It was at this point that the economists found it as a useful tool of analysis to establish the production function as we have it today.

Olayide and Heady (1982) itemize some of the usefulness of production function as follows:

1. Production function enables us to derive how national product is produced from the various resources. Production function expresses the relationship between national product and the available resources used in producing it.

2. Production function is also used to assess inter-regional or international trade balances. Coefficient is used in the inter-regional and international trade to apportion goods to various countries. The coefficients derived from the production function serve as the base for determining optimum patterns of intra-state, inter-state, inter-regional and international trade.  This optimization of trade derived from production function is the natural consequence of optimum output at minimum cost that is based on comparative advantage for attainment of maximum net revenue. It is also the consequence of regional specialization.

3. Production function is equally useful in the allocation of total output or national income. In other words production function is a useful tool in the marginal production theory of distribution.

4. Production function served as a useful tool in the maximization of profit of a farm. In this aspect, production function provide the major data that is needed to determined or specify the use of resources and the pattern of outputs which maximize farm-firm profits.

5. Production function is useful in the algebraic function of the theory of supply. The algebraic nature of supply-functions rests in large part on the nature of the production function.

For the production function to actualize the usefulness above, production economist obtains the following data – experimental, cross-sectional, time series and engineering data to achieve the following goals:

1. the of point maximum output and input relationships

2. the point of economic optimum and

3. the quantity of resources to use in producing a given maximum either physical or economic maximum.

EXERCISE

i. Define a production function

ii. State the explicit form of a production function

iii. Itemize the usefulness of production function

## CONCLUSION

This topic explains the meaning of production function and highlighted some of the usefulness of production function. We can conclude from this post that production function is useful in all the sectors of the economy.

## SUMMARY

The main points in this unit are as follows:

a. Production function is defined as the physical relationship between the output and inputs used in the production of the product

b. Production function is useful in the estimation of balance of trade

c. Production function enable us to estimate the nature of production

d. Production function provides guide on the allocation of total output or national income.

e. Production function is also useful in the maximization of profit.

f. Production function is useful in the theory of supply

g. Data needed in production function are obtained from experiment, time serves, cross-sectional and engineering sector.

h. Production function data are needed to achieve the following goals.

i. point of maximum output and input relationship

i. point of economic optimum

ii. quantities of resources to use in producing a given maximum.

ASSIGNMENT

1. Define production function

2. Explain five usefulness of production function

3. List four data that can be generated for production function

4. List three goals of production function.

Abbot, J.C. and J.P. Makeham (1980). Agricultural Economics and Marketing in the Tropics. London, Longman Publishers.

Adegeye, A.J. and J.S. Dittoh (1985). Essentials of Agricultural Economics. Ibadan, Impact Publishers.

Nweze, N.J. (2002). Agricultural Production Economics: An Introductory Text. Nsukka. AP Express Publishers.

Olayide, S.O. and Heady E.O. (1982). Introduction to Agricultural Production Economics. Ibadan. University Press Ltd.

Olukosi, J.O. and A.O. Ogungbile (1989). Introduction to Agricultural Production Economics: Principles and Applications. Zaria. AGTAB Publishers Ltd.

Marshall A.C. (1998). Modern Farm Management Techniques. Owerri. Alphabet Nigeria Publishers.

Reddy, S.S., P.R. Ram, T.V. Sastry and I.B. Devi (2004). Agricultural Economics. New Delhi. Oxford and Ibh Publishers Ltd.