17-05-2013, 12:23 PM
PRODUCTION FUNCTION
PRODUCTION FUNCTION.pdf (Size: 162.36 KB / Downloads: 18)
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,
© what input combination to use, and (d) what type of technology to use.
This Unit deals with the analysis of managers’ decision rules concerning
© 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.
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.
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 efficient, when it produces
a given amount of output at the lowest possible cost for a combination of
inputs provided that the prices of inputs are given. Therefore, when only input
combinations are given, we deal with the problem of technical efficiency; that
is, how to produce maximum output. On the other hand, when input prices are
also given in addition to the combination of inputs, we deal with the problem of
economic efficiency; that is, how to produce a given amount of output at the
lowest possible cost.
Total, Average, and Marginal Products
The production function given above shows us the maximum total product
(TP) that can be obtained using different combinations of quantities of inputs.
Suppose the metal parts company decides to know the output level for different
input levels of labour using fixed five machine tools. Table 7.1 explains the
total output for different levels of variable input. In this example, the TP rises
with increase in labour up to a point (six workers), becomes constant between
sixth and seventh workers, and then declines
The Law of Diminishing Marginal Returns
The slope of the MP curve in Figure 7.1 illustrates an important principle, the
law of diminishing marginal returns. As the number of units of the variable
input increases, the other inputs held constant (fixed), there exists a point
beyond which the MP of the variable input declines. Table 7.1 illustrates this
law. Observe that MP was increasing up to the addition of 4th worker (input);
beyond this the MP decreases. What this law says is that MP may rise or
stay constant for some time, but as we keep increasing the units of variable
input, MP should start falling. It may keep falling and turn negative, or may
stay positive all the time. Consider another example for clarity. Single
application of fertilizers may increase the output by 50%, a second application
by another 30% and the third by 20% and so on. However, if you were to
apply fertilizer five to six times in a year, the output may drop to zero.