# Production Function: Meaning and Types (2023)

#### Meaning of Production Function:

Production is a process whereby some goods and services, called inputs are transformed into other goods and services called output. The production function refers to the relationship between the input of factor services and the output of the resultant product. The production function is based on the idea that the amount of output in a production process depends upon the amount of inputs used in the process.

Output depends upon an input or a set of inputs in such a way that there is one unique amount of output resulting from each set of inputs. This unique relationship between output and inputs is termed as production function.

Halcrow defines production function as follows:

“Production function is the technical relationship between inputs & output indicating the amount of output that can be produced with each and every set or combination of the specified inputs”.A production function always assumes as given, a state of knowledge and technology.

A production function may be expressed in three forms:

(a) It can be expressed in the form of an arithmetic table where first few columns show the input of the factors and the last column shows total output of the product as has been depicted below. Here, for the sake of simplicity, we take only one input.)

In the above table, fertilizer is the variable input (applied to a fixed price of land with other fixed inputs). Total corn yield is increasing (column 2) as more units of fertilizers are applied.

(Video) Production function and types: Economics | LearnWith Ashu

(b) The production function can also be illustrated geometrically by means of a simple graph as shown in Fig. 1. Input level is measured along the horizontal axis and the total output upon he vertical axis.

The points on the curve OT indicate different quantities of output associated with particular levels of the input used.

(c) The production function may be shown through an algebraic expression in which output is a dependent variable and input, the independent variable.

In algebraic form, it can be expressed as:

Y =f(x),

where Y represents the output, x, the input and ‘f’ means is a function of, or ‘depends upon, or is determined by’. Here, it is assumed that output depends upon a single factor. However, it must be understood that in actual life, agricultural output (and for that matter, any output) is never a function of a single factor. It rather depends upon a variety of factors, such as seeds, amount of fertilizers used, irrigation, nature of soil and so on. This can be written as:

Y = f (x1, x2, x3………………….. xn) + u

This function means that output depends upon all factors represented by x1, x2etc., and also the level of unknown or uncontrollable factors represented by u. It is not feasible to consider all controllable factors simultaneously in any one study.

Therefore, each factor may be studied in combination with some factors considered as fixed. For illustration, a farmers may be interested in knowing how the output of wheat will change as the two inputs namely, the seeds and fertilizers are changed while other factors are held constant at fixed levels.

#### Types of Production Function:

We should note that a production function expresses a unique relationship between total output and the various inputs. Generally, the total output increases with an increase in inputs. Like any other function, all such functions where total output increase as the inputs increase, are known as increasing production functions,

(Video) Production Function And Its Types - Theory of Production and Cost - Business Economics

There are also situations in the real world where an increase in inputs, instead of bringing about an increase in the total output, may decrease it. Such a production function will be known as decreasing production function.

It is necessary to explain these two types of functions in some detail:

(A) Increasing Production Function:

Though, in case of such functions, the mathematicians do not generally discuss the way the production increases when the inputs increase, an economist has to give considerable attention to this aspect.

From his point of view, it is important to know whether the rate of increase in production in response to successive equi-proportional changes in all inputs taken together (expressed in terms of returns to scale) or to successive changes in the amount of single input taken in isolation (expressed in terms of returns to a variable factor), is itself increasing, is constant or is decreasing. In other words, he is deeply interested in knowing whether the marginal returns to scale or the marginal returns to a variable factor are increasing, constant or decreasing.

We may note here that in case of productions planning, it is the marginal returns to a variable factor which are the main focus of attention. As such, in the paragraphs that follow, we shall be explaining the increasing production function by categorizing it into parts, on the basis of constant, increasing, and decreasing marginal returns to a variable input (For this purpose, we consider change in production in response to change in one input only. We assume other variable inputs to be constant. Such an approach simplifies the analysis. At a later stage, we shall see that analysis pertaining to one input can be easily extended to over other inputs also).

(i) Increasing production function with constant marginal returns to the variable input. In this function, the total production increases by the same magnitude for each additional unit of input used. For example, consider the following hypothetical relationship between fertilizers used and the total yield of wheat.

Graphic representation of this function will be a linear increasing function as shown in Fig. 2.

(Video) Production Function - Meaning & Definition

The diagram shows that each successive dose of 10 Kg. fertilizers makes a contribution of 60 kgs. Of wheat to the total output. We rarely come across this type of relationship in agriculture.

(ii) Increasing production function with increasing marginal returns on the variable input:

In this case, every successive dose of input brings about an increasing addition to the total output i.e., the output increasing rate when more and more units of an input are used. This type of relationship generally emerges when the fixed factors being used in production are having an excess capacity and use of additional units of the variable input results in a better utilisation of these fixed factors. The following table shows this type of production function.

Graphically this functional relation appears in the form of a curve. The curve becomes steeper as the input increases. Fig. 3 shows the increasing production with increasing marginal returns to the variable input. The curve that emerges in case of such a production function is concave downwards to X-axis as shown in the following diagram.

This type of relationship has been observed in agriculture but only over fairly short ranges of production.

(iii) Increasing production function with decreasing marginal returns to the variable factor:

(Video) Types of Production Function

In this case, we find that though the total production increases as the input increases, each successive increase in output brought about by an additional dose of input declines. In other words, marginal returns to the input, though positive are declining. The following schedule shows his type of increasing production function.

Diagrammatically, the curve representing this type of production function will be concave upwards with regard to X-axis. Fig. 4 shows this curve.

We find that as each successive increase in output due to the use of an additional dose of input is declining, the curve becomes flatter as it moves towards the right.

(B) Decreasing Production Function:

A decreasing production function is one in which the total output declines when the input increase. In terms of marginal returns to the variable factor, one could say that it is negative (less than zero).

The decreasing production function could also be divided into three categories on the basis of increasing, decreasing or constant rate of decrease in output. However, as we shall see later, no rational producer will ever operate in a situation (or stage) of decreasing production function i.e., where the total production declines as the input is increased.

As such, the exercise concerning categorization of the decreasing production function on the basis of the nature of its (negative) marginal returns to the variable input will have no practical utility.

The table 5 shows the decreasing production function: In this Table we have started with the 11th dose of fertilizers and not with the first dose. This is because it will be rather unrealistic to assume, that after the very first dose of fertilizers, the output starts decreasing.

The following diagram shows the decreasing production function:

(Video) Production function: Meaning and types of production function

The decreasing production function implies a line or a curve with negative slope. The curve can be concave or convex to the origin depending upon whether the output declines at an increasing rate or at a decreasing rate when more and more doses of an input are used.

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## FAQs

### What is production function and its types? ›

Production function is a concept that explains the relationship between quantities of input and the output. Its formula is Q=f(K,L). Production function is of two types: short-run and long-run, depending on the number of fixed factors.

What are the 4 types of production function? ›

The 4 Factors of Production

There are four factors of production—land, labor, capital, and entrepreneurship.

What is production function? ›

The production function is a mathematical function stating the relationship between the inputs and the outputs of the goods in production by a firm. Entrepreneurship, labor, land, and capital are major factors of input that can determine the maximum output for a certain price.

What is the meaning of production function with example? ›

One very simple example of a production function might be Q=K+L, where Q is the quantity of output, K is the amount of capital, and L is the amount of labor used in production. This production function says that a firm can produce one unit of output for every unit of capital or labor it employs.

What are the 3 types of production? ›

There are three types of production - primary production, secondary production, and tertiary production.

What are different types of production? ›

The five types of production are:
• Mass production,
• Batch production,
• Job production,
• Service production, and.
• Customised production.

What are the 4 means of production? ›

Economists define four factors of production: land, labor, capital and entrepreneurship.

What are the 4 factors of production and give an example of each? ›

Solution
FactorExample
Land#4
Labor#2, #6
Capital#3, #5
Entrepreneurship#1
Jun 15, 2021

What are the five different production process types? ›

The five types of manufacturing processes
• Repetitive manufacturing.
• Discrete manufacturing.
• Job shop manufacturing.
• Process manufacturing (continuous)
• Process manufacturing (batch)

Why is production function important? ›

The production function explains the maximum quantity of output, which can be produced, from any chosen quantities of various inputs or the minimum quantities of various inputs that are required to produce a given quantity of output.

### Who defined production function? ›

Prof. Koutsoyiannis: – Defined as, “The production function is purely a technical relation which connects factor inputs and output.” Prof. Watson: – Defined production function as “The relation between a firm's physical production (output) and the material factors of production (inputs).”

What is a production function quizlet? ›

production function. is the relationship between the quantity of inputs a firm uses and the quantity of output it produces.

What happens in production function? ›

Production functions describe how output is determined by various inputs. The short run is defined as the period of time in which at least one input is fixed. Anything longer than that is considered the long run.

What is production in simple words? ›

Production is the process of making or manufacturing goods and products from raw materials or components. In other words, production takes inputs and uses them to create an output which is fit for consumption – a good or product which has value to an end-user or customer.

How many types are there in production? ›

Types of Production Processes. The five main types of production are Mass production, Batch production, job production and just-In-Time production, and flexible manufacturing system.

What do we mean by production? ›

Production refers to all the activities which are undertaken to produce goods and services for generation of income and satisfaction of wants.

What are the 4 stages of the production process? ›

Product Manufacture – The 4 Steps
• Step 1 of Product Manufacture: Tool Making.
• Step 2 of Product Manufacture: Mass Production.
• Step 3 of Product Manufacture: Assembly.
• Step 4 of Product Manufacture: Packaging.
Mar 15, 2021

What is the theory of production? ›

theory of production, in economics, an effort to explain the principles by which a business firm decides how much of each commodity that it sells (its “outputs” or “products”) it will produce, and how much of each kind of labour, raw material, fixed capital good, etc., that it employs (its “inputs” or “factors of ...

Why are the 4 factors of production important? ›

All of the factors of production contribute to economic growth. No product can be made without raw materials (land). Those materials can't be extracted, refined, and transformed without people working (labor). Those people can't accomplish their work without tools and equipment (capital).

What are the 4 major economic systems? ›

Each economy functions based on a unique set of conditions and assumptions. Economic systems can be categorized into four main types: traditional economies, command economies, mixed economies, and market economies.

### What are the 6 types of production? ›

Service Production
• Production »
• Job Production »
• Batch Production »
• Batch »
• Mass Production »
• Continuous Production »
Sep 28, 2017

What are the 7 steps of production? ›

Mastering the 7 Stages of Film Production
• Development. ...
• Financing. ...
• Pre-production. ...
• Production. ...
• Post-production. ...
• Marketing. ...
• Distribution.
Jun 21, 2019

What are the 8 steps in production process? ›

To create and sell a new product, businesses typically follow these eight stages:
• Generate an idea. ...
• Plan out the product. ...
• Create a prototype. ...
• Establish a production process. ...
• Determine a distribution plan. ...
• Launch the product.
Dec 19, 2022

What does production function depend on? ›

Production functions are dependent upon technology. As new technology is used, the production of units usually goes up. This means that introduction of technology works as an enhancer of the production function. So, when technology is upgraded, we will have a new production function for the given example above.

What affects the production function? ›

The four factors of production are land, labor, capital and entrepreneurship.

How do you solve production functions? ›

The production function is a mathematical equation that calculates the maximum output a firm can achieve with a selected number of inputs (capital, labour, and land). The production function can be calculated using the formula: Q = f(Capital, Land, Labour), where the inputs are a function of the output.

What are the three stages of production function? ›

However, there are three key stages that take place in the production of any film: pre-production (planning), production (filming), and post-production (editing, color-grading, and visual effects).

What is production function related to *? ›

Production function relates to the use of inputs to produce an output. Hence, it can be concluded that production function relates input to output.

What is the conclusion of production function? ›

Conclusion. Production function is the relationship between the output and input of a firm. Factor of production involves variable factors and fixed factors. Fixed factors of production are those the application of which does not change with the change in output.

What are the 3 concepts of production functions? ›

In the production process, the output or product may be described in three (3) ways in economics: Total Product (TP), Average Product (AP), and Marginal Product (MP).

### What are the three functions of production? ›

Production management has three main functions: planning, control, and coordination.

What are the three main activities of production function? ›

The production function of a firm depends on the state of technology. With every development in technology the production function of the firm undergoes a change.
...
Following are the main features of production function:
• Complementarity: ...
• Specificity:

What is the concept of production? ›

Production is the process of making or manufacturing goods and products from raw materials or components. In other words, production takes inputs and uses them to create an output which is fit for consumption – a good or product which has value to an end-user or customer.

What is the most important factor in the production? ›

Land is generally considered one of the most important factors of production. Certain industries rely on land more than others.

What are the characteristics of production? ›

The four factors of production are inputs used in various combinations for the production of goods and services to make an economic profit. The factors of production are land, labor, capital, and entrepreneurship. They are the inputs needed for supply.

What are the three 3 factors of production? ›

The factors of production in an economy are its labor, capital, and natural resources.

What are 3 stages of production? ›

However, there are three key stages that take place in the production of any film: pre-production (planning), production (filming), and post-production (editing, color-grading, and visual effects).

What is stage 3 of production function? ›

Economic theory refers to stage III as the portion of the production function where additional variable input results in decreased output. Managers do not produce in Stage III. In this situation, the boundary between Stage II (not yet defined) and Stage III is at 15 units of variable input.

Which one is the most basic production function? ›

The first, and most simple, is the linear production function, which applies the same amount of output to each input.

## Videos

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