What is Production Function?

What is a Firm? | What is Cost of Production? | What are factors of Production? | What is Revenue and Profit?

Introduction

In previous sessions, we discussed in detail about the consumer behavior theory which focused on studying how the consumer make choices in the face of scarce resources i.e., income in a manner such that they gain maximum utility from consumption of goods and services.

But as we know, in an economy there are other economic agents too which make economic decisions in the face of scarcity. Now we will discuss in detail the behavior of a firm.

But before moving onto discuss about the behavior of a firm, it is important to understand what a firm does and what role it plays in an economy.

What is a Firm?

A firm is an entity which undertakes the process of production.

What is Production?

Production, in simple terms, is the process under which the inputs are transformed into outputs.

What does a firm do?

A firm acquires a set of various inputs like land, labor, capital, raw material, machines, etc. and uses these inputs to produce output.

These output can be anything, from a tiny pin to huge trucks, from salt to packaged foods, etc.

Who consumes these output produced by firms?

These output is then consumed by either the consumers or other firms, depending on what the output is. If the output here is packaged food, it will be consumed by consumers directly. But there are outputs which are consumed by other firms as inputs to carry out further production process e.g., the tyres manufactured by tyre producing firms, are further used by the car manufacturing firms for wheels.

The other example of the same is steel. The steel is produced by a steel manufacturing firm, which is then further consumed or used by the car manufacturing firms to manufacture cars.

Assumption

For the purpose of studying the production and behavior of firm, we will assume that no time is taken into consideration between acquiring inputs and producing output i.e., production is instantaneous.

Cost of Production

The firm acquired inputs in order to produce outputs. Firms incur costs to acquire these inputs and to process the same into output, which we call it as cost of production.

Revenue

The firm after producing the output, further sells these output and earns income which is known as revenue.

Profit

As we know firms incur expenditure for acquiring inputs and processing the same into outputs. And on selling these output, they earn revenue. The excess of revenue over the cost is called as the firm’s profit.

Objective of the Firm

While studying the behavior of a firm and how the firm undertakes the process of production, we consider an important assumption i.e., the objective of firm is to earn the maximum profit that is possible.

Study Map

So moving onwards we will discuss the relationship between inputs a firm uses and output the firm produces.

Production Function

We earlier studied the demand function which established relationship between the quantity demanded for a product and the price of the product keeping other factors constant.

In the same manner, even the production function establishes relationship for a firm between its inputs and outputs.

So to say, the production function of a firm is relationship between inputs acquired & used and the output produced by the firm.

But what we try to find out of that relationship?

Firm uses several inputs in different quantities. For various quantities of inputs used, the production function of a firm gives the maximum quantity of output that can be produced with those inputs.

Let us take an example to understand the production function.

Now a farmer produces wheat in the farm. And to produce the wheat the farmer uses two inputs namely land and labor.

So here in the example, the production function would tell us the maximum amount of wheat that the farmer can produce for given amount of land and given number of hours of labor that he works.

If we quantify the above values, supposing the farmer uses 4 hectares of land and 2 hours of labor per day, producing a maximum of 4 tons of wheat. The function that represents the above quantifiable relationship between the inputs i.e., land & labor and the output is called a production function.

Thus in form of an equation, the production function for above can be represented as

q = K * L

Where, the q is the total quantity of wheat produced, K is the hectares of land used, and L is the number of hours of labor per day.

Thus in this manner, the production function helps us to understand the exact relationship between inputs used and output produced.

In the above equation, if either K or L or both increases, the q will increase too. For a particular value of K and L, there will be an only one unique value of q. If any one of K or L changes, there will be a new value of q.

Assumptions

Since in the definition of production function itself, we are considering the maximum output that can be produced by the firm using a certain level of inputs, the production function assumes that the inputs are used in most efficient manner. Efficiency implies that firm produces the maximum level of output possible using the inputs and no excess output out of that is possible further.

Another important assumption is linked to the above assumption of efficiency and maximum output. The level of maximum output that can be produced out of a given amount of inputs depends on the technological knowledge and with the upgrade in technology, the maximum level of output from same inputs can be increased, which give birth to new production function. So at a particular time, the production function is obtained for a given technology.

What are these inputs called collectively?

The inputs that the firm uses in order to undertake the process of production are called the factors of production.

Final Consideration

In real life scenario, several factors of productions are employed by the firm to undertake the process of production. But here for the sake of understanding, for now, we will simply take into consideration two factors of production namely labor and capital.

So finally, the production function which takes into consideration the above inputs of labor and capital can be defined as – the maximum amount of output (q) that can be produced using different combinations of these two factors of production namely Labor (L) and Capital (K).

The production function can be mentioned as under;

q = f (L, K)

where the q is the maximum output that can be produced, L is labor and K is capital. 

The above discussion can be summarized in the following table.

The column on the left hand side shows the labour as an input and the top row shows capital as an input. Both the inputs are mentioned in units. The units of labour increases as from 0 to 6 and the units of capital also increases from 0 to 6.

For different level or quantities of inputs or factors of production i.e., labour and capital, the table shows the corresponding output levels. For example, using 1 unit of capital and 1 unit of labour, the firm can produce at maximum 2 units of output. At the same time, using 2 unit of capital and 2 units of labour, the firm can produce at maximum 20 units of output and so on and so forth.

One important thing to note that is that the availability of both the factors of production is necessary for the production. If any of the two inputs is 0, then there can be no production. And with increase in any of the two inputs, with other remaining same or increasing too, the total output increases. As long as, both the inputs are positive, the output too will be positive.

Conclusion

In this session, we studied the production function in detail. We discussed several concepts including the factors of production, the cost of production and various assumptions that are taken into consideration whole studying the production function.