Production Function

What is Production Function?
Definition and Explanation:
, Production of goods requires resources or inputs. These inputs are called factors of production named as land, labor, capital and organization. A rational producer is always interested that he should get the maximum output from the set of resources or inputs available to him. He would like to combine these inputs in a technical efficient manner so that he obtains maximum desired output of goods. The relationship between the inputs and the resulting output is described as production function. A production function shows the relationship between the amounts of factors used and the amount of output generated per period of time. Formula: It can be expressed in algebraic form as under: X = f (a1, a2 ,........, an) This equation tells us the quantity of the product X which can be produced by the given quantities of inputs (lands labor, capital) that are used in the process of production. Here it may be noted that production function shows only the maximum amount of output which can be produced from given inputs. It is because production function includes only efficient production process. The analysis of production function is generally carried with reference to time period which is called short period and long period. In the short run, production function is explained with one variable factor and other factors of productions are held constant. We have called this production function as the Law of Variable Proportions or the Law of Diminishing returns. In the long run, production function is explained by assuming all the factors of production as variable. There are no fixed inputs in the long run. Here the production function is called the Law of Returns according to the scale of production. As it is difficult to handle more than two variables in graph, we therefore, explain the Law of Returns according to scale of production by assuming only two inputs i.e., capital and labor and study how output responds to their use.
Short Period Analysis of Production/Law of Variable
Proportion:

The short run is a period of time in which only one input (say labor) is allowed to vary while other inputs land and capital are held fixed. In the short run, therefore, production can be increased with one variable factor and other factors remaining constant. In the short run, the law of variable proportion governs the production behavior of a firm. The law of variable proportion shows the direction and rate of change in the output of firm when the amount of only one factor of production is varied while other factor of production are held constant. The law of variable proportion passes mainly through two phases: (i) Increasing returns. (ii) Diminishing returns. Technical Efficient Combination: Production function establishes a physical relationship between output and inputs. It describes what is technical feasible when the firm uses each combination of input. The firm can obtain a given level of output by using more labor and less capital or more capital and less labor. Production function describes the maximum output feasible for a given set of inputs in technical efficient manner. Production Function takes Quantities of Inputs: It is imperative to note that production function does not take unto account the prices of input or of the output. It simply takes into account the quantities of inputs which are employed to produce certain quantities of output.
Long Run Production With Variable Inputs: The long run is the lengthy period of time during with all inputs can be varied. There are no fixed output in the long run. All factors of production are variable inputs. We now analyze production function by allowing two factors say labor and capital to very while all others are held constant. With both factors are variable, a firm can produce a given level of output by using more labor and less capital or a greater amount of capital and less labor or moderate amounts of both. A firm continues to substitute one input for another while continuing to produce the same level of output. If two inputs say labor and capital are allowed to vary, the resulting production function can be illustrated in the figure 12(a). Diagram/Figure:

In this figure each curve (called an isoquant) represents a different level of output. The curves which lie higher and to the right represent greater output levels than curves which are lower and to the left. For example, point D represents a higher output level of 250 units than point A or B which shows output level of 150 units. The curve isoquant which represents 150 units of output illustrate that the same level of output (150 units) can be produced with different combinations of labor and capital. Combination of labor and capital represented by A, can employ OL1 quantity of labor and OC1 units of capital to produce 150 units of output. The combination of labor and capital represented by point B will use only OL2 units of labor and OC1 of capital to produce the same level of output. Thus, if a country has surplus labor and less capital, it may use the combination of labor and capital represented by point A. In case the country has abundant capital and less labor, it might produce at point B. The isoquants through points A and B shows all the different combinations of labor and capita that can be used to produce 150 units of output.