Production function in Short run and Long run

In economics, production theory explains the principles in which the business has to take decisions on how much of each commodity it sells and how much it produces and also how much of raw material ie., fixed capital and labor it employs and how much it will use. It defines the relationships between the prices of the commodities and productive factors on one hand and the quantities of these commodities and productive factors that are produced on the other hand.

Production is a process of combining various inputs to produce an output for consumption. It is the act of creating output in the form of a commodity or a service which contributes to the utility of individuals.

In other words, it is a process in which the inputs are converted into outputs.


The Production function signifies a technical relationship between the physical inputs and physical outputs of the firm, for a given state of the technology.

Q = f (a, b, c, . . . . . . z)

Where a,b,c ….z are various inputs such as land, labor ,capital etc. Q is the level of the output for a firm.

If labor (L) and capital (K) are only the input factors, the production function reduces to 

Q = f(L, K)

Production Function describes the technological relationship between inputs and outputs. It is a tool that analysis the qualitative input – output relationship and also represents the technology of a firm or the economy as a whole.

Features of Production Function:

Following are the main features of production function:

  1. Substitutability:

The factors of production or inputs are substitutes of one another which make it possible to vary the total output by changing the quantity of one or a few inputs, while the quantities of all other inputs are held constant. It is the substitutability of the factors of production that gives rise to the laws of variable proportions.

  1. Complementarity:

The factors of production are also complementary to one another, that is, the two or more inputs are to be used together as nothing will be produced if the quantity of either of the inputs used in the production process is zero.

The principles of returns to scale is another manifestation of complementarity of inputs as it reveals that the quantity of all inputs are to be increased simultaneously in order to attain a higher scale of total output.

  1. Specificity:

It reveals that the inputs are specific to the production of a particular product. Machines and equipment’s, specialized workers and raw materials are a few examples of the specificity of factors of production. The specificity may not be complete as factors may be used for production of other commodities too. This reveals that in the production process none of the factors can be ignored and in some cases ignorance to even slightest extent is not possible if the factors are perfectly specific.

Production involves time; hence, the way the inputs are combined is determined to a large extent by the time period under consideration. The greater the time period, the greater the freedom the producer has to vary the quantities of various inputs used in the production process.

In the production function, variation in total output by varying the quantities of all inputs is possible only in the long run whereas the variation in total output by varying the quantity of single input may be possible even in the short run.

Production analysis basically is concerned with the analysis in which the resources such as land, labor, and capital are employed to produce a firm’s final product. To produce these goods the basic inputs are classified into two divisions:

Variable Inputs

Inputs those change or are variable in the short run or long run are variable inputs.

Fixed Inputs

Inputs that remain constant in the short term are fixed inputs.

Cost Function

Cost function is defined as the relationship between the cost of the product and the output. Following is the formula for the same:

C = F [Q]

Cost function is divided into namely two types:

Short Run Cost

Short run cost is an analysis in which few factors are constant which won’t change during the period of analysis. The output can be changed i.e, increased or decreased in the short run by changing the variable factors.

Following are the basic three types of short run cost:

Long Run Cost

Long-run cost is variable and a firm adjusts all its inputs to make sure that its cost of production is as low as possible.

Long run cost = Long run variable cost

In the long run, firms don’t have the liberty to reach equilibrium between supply and demand by altering the levels of production. They can only expand or reduce the production capacity as per the profits. In the long run, a firm can choose any amount of fixed costs it wants to make short run decisions.

Law of Variable Proportions

The law of variable proportions has following three different phases:

  • Returns to a Factor
  • Returns to a Scale
  • Isoquants

Returns to a Factor

Increasing Returns to a Factor

Increasing returns to a factor refers to the situation in which total output tends to increase at an increasing rate when more of variable factor is mixed with the fixed factor of production. In such a case, marginal product of the variable factor must be increasing. Inversely, marginal price of production must be diminishing.

Constant Returns to a Factor

Constant returns to a factor refers to the stage when increasing the application of the variable factor does not result in increasing the marginal product of the factor rather, marginal product of the factor tends to stabilize. Accordingly, total output increases only at a constant rate.

Diminishing Returns to a Factor

Diminishing returns to a factor refers to a situation in which the total output tends to increase at a diminishing rate when more of the variable factor is combined with the fixed factor of production. In such a situation, marginal product of the variable must be diminishing. Inversely the marginal cost of production must be increasing.

Returns to a Scale

If all inputs are changed simultaneously or proportionately, then the concept of returns to scale has to be used to understand the behavior of output. The behavior of output is studied when all the factors of production are changed in the same direction and proportion. Returns to scale are classified as follows:

  • Increasing returns to scale: If output increases more than proportionate to the increase in all inputs.
  • Constant returns to scale: If all inputs are increased by some proportion, output will also increase by the same proportion.
  • Decreasing returns to scale: If increase in output is less than proportionate to the increase in all inputs.

For example: If all factors of production are doubled and output increases by more than two times, then the situation is of increasing returns to scale. On the other hand, if output does not double even after a 100 per cent increase in input factors, we have diminishing returns to scale.

The general production function is Q = F (L, K)

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