The meaning of the Production Function Total Production, Average Production, Marginal Production

The meaning of the Production Function

It reveals various types of natural resources, land, labor and capital, which will have to be employed in order to produce one unit or a given quantity of certain commodity or service, in a given period of time. In other words, it indicates varieties of resources and their unique combinations that can be transformed into desired quantities of goods and services. It reflects the state of arts technological possibilities of the production processes and the size of the producing units.

Thus, the production function is a symbolical expression of the fact that output of a firm depends on the inputs employed in the production process.

Traditionally, the production function has been called the Law of Diminishing Returns and has been explained by economics in different ways in the last 200 years or so.

We may study the production function as follow:

(a)  Will land as fixed factor and labor and capital as variable factors. This is marshal's version of the law of diminishing returns.

(b)  With on factor variable and other factors fixed, this is the modern cession of the law of diminishing returns.

(c)  With all factors variable, this is the law of returns to scale.

In traditional production theory resource used for the production of product are known as factors of production. Factors of production are now termed as inputs that may mean the use of the services of land, labor, capital and organization in the process of production. Then term output refers to the commodity produced by the various inputs. Production theory concerns itself with the problems of combining various inputs, given the state of technology, in order to produce a stipulated output. The technological relationships between inputs and outputs are known as production functions.

Relation between Total Production Average Product and Marginal Product

In figure the total product curve is given by the curve OC, the average product curve is given by and the marginal product is given by the curve. At the point O, as the input of the factor, labor is equal to zero; the value of total product will also be zero. Obviously, the values of the marginal and average products at this point will be equal to zero. So, we can say that all the three curves TP, MP and AP emanate from the origin. According to the law of diminishing returns, the marginal product is first increasing and then decreasing. Hence, the total product curve (TP) is first convex from below and then concave. So long as the TP curve convex, MP is increasing. When the TP curve is concave, MP is decreasing. The point A on the TP curve is called the point of inflexion. At this point the curve is changing its curvature. Marginal product is maximum corresponding to this point of the TP curve. This is shown as the point of the MP curve. Average product curve will be maximum at point B on the TP A' curve where a tangent to the total product curve passes through the origin. At point B, both AP and MP are equal to the slope of OB. So, corresponding to point B, we have AP = MP and MP is decreasing and AP is maximum. The point B’ on the average product curve has showed this where the MP and the AP curves intersect each other. Corresponding to the maximum point of the TP curve MP is equal to zero.

Total, Average and Marginal Productivity

This happens at the point C where the total product curve is maximizing. To the left of C, total product is increasing and the marginal product is positive. To the right of C, TP curve is decreasing and the marginal product is negative. The point on the marginal product curve which corresponds to C of the TP curve is C'.

Since the MP curve must be decreasing when the average product is maximizing, the MP curve reached maximum before the average product curve. At point D on the total product curve there is again a point of inflexion. Corresponding to this point the MP curve is minimum at the point D'. The average product curve has only one extreme point whereas the marginal product curve has two extreme points. The region at which MP is negative represents the uneconomic region of production, and not considered for production.

Total Product, Marginal Product and Average Product
Number of workers employed per week	Total product of labor	MPL	APL
0 1 2 3 4 5 6 7 8 9 10 11 12	0 7 18 33 46 55 60 63 65 66 66 64 50	- 7 11 15 13 9 6 3 2 1 0 -1 -4	- 7.00 9.00 11.00 11.50 10.00 11.00 9.00 8.13 7.33 6.60 5.82 4.16

Fig. (A) Plots the total product of the labor as the number of workers employed per week changes. Initially, production increases at an increasing rate when the variable input, labor is increased. Then the production increase at a decreasing rate. Finally, total product starts declining.         Fig. (B) Plots the marginal and average products of labor. Initially, the marginal product increases. This is when the total product increases at an increasing rate in fig. (A). The declining portion of the marginal product relates to the decreasing rate of increase in production in fig. (A). Marginal product will be negative when the total product is declining. The relation between the marginal and average products can also be seen in fig. (B). When the MP is greater that AP, the AP is increasing. When the MP is less than AP, the AP is decreasing. And the AP is maximum when the MP is equal to AP.