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What is an Isoquant? | What is an Isoquant Curve? | Why the Isoquant Curve is negatively sloped?


Introduction

In economics, we study the behavior of individuals who make economic decisions to fulfill their needs and wants which are unlimited, in a manner to gain maximum utility given limited resources. Hence they face the problem of choice. Because they need to choose among the alternative possible to satisfy their needs and wants. Not all needs and wants could be fulfilled as resources to satisfy them are scarce. Now individual includes an individual consumer as a single economic agent, or a family which makes economic decisions, or even an Individual Firm. Till now we studied the theory of Consumer Behavior i.e., how consumer behaves i.e., makes economic decisions in face of scarce resources to satisfy their needs and wants in a manner in which they gain maximum utility or satisfaction. In the previous session, we started the discussion on Behavior of Firms.

Behavior of a Firm

A Firm is an economic entity which undertakes the process of production. Production is a process of transformation of inputs into outputs. Inputs are the resources used in production which are known as Factors of Production. Firms incurs costs to undertake the process of production, which is known as Costs of Production. And earns revenue on selling the output produced through process of production. The excess of revenue over the costs in the whole production process is known as Profit for the firm. Now what is the need and want of firm? The firm aims to earn maximum profit by undertaking the process of production.

So under behavior of firm in economics, we try to study how the firm behaves i.e., takes economic decisions in face of problem of choice. Because firm wants maximum profit but inputs with the firm is limited for production. So they need to utilize the limited inputs efficiently such that to achieve maximum production and therefore on selling the same to earn maximum profit.

Production Function

So in order to study the behavior of a firm, it becomes very important to study the production process i.e., conversion of input into output. Production Function does the same. Production function of a firm is a relationship between the inputs i.e., factors of production used and outputs produced. Production Function of a firm gives the maximum amount or quantity of output that can be produced for a given quantity of inputs used.

And here as we know in order to study the same, we will consider for simplicity for now, that there are two factors of production a firm use, which are Capital and Labor. The capital is denoted by K and the labor is denoted by L. In equation form, the production function of a firm can be described as

q = f (K, L)

where q is the maximum quantity that can be produced, K is the Capital used and L is hours of labor used per day.

Assumptions

While studying the production function, several assumptions are taken into consideration. Firstly, we know that the production function gives the maximum quantity of output that can be produced from a given quantity of input. Means it is implied that, out of given quantity of input, no more output can be produced over and above as given by the production function i.e., the inputs are used in the most efficient manner possible.

Another important thing to remember is that the production function is for a level of technological knowhow. The production function gives the maximum output that is possible for a given input and the increase in the maximum possible output depends on the technology, thus if technological knowhow increases, so increases the level of maximum output. Hence at any point in time, the production function is for a given technology.

Isoquant

While studying the consume behavior, we had come across the indifference curve concept which denoted all the points on the graph showing the consumption bundles among which the consumer would be indifferent to choose from, because those bundles were having combinations which gave equal utility. So consumer was fine to receive any of the bundles falling on the indifference curve.

Here in case of firms too, the concept of isoquant is similar to that of indifference. As we know we, the production function gives maximum output for a given level of input i.e., for given combinations of Labor (L) and Capital (K).

The set of all possible combinations of inputs i.e., Labor (L) and Capital (K) giving the same maximum possible level of output is known as Isoquant. So the isoquant curve on graph shows all the set of combinations of inputs which would lead to the same maximum possible output thus making the firm indifferent among those combinations of input as those combinations yield same or equal maximum output. 

Let us take an example for the same.


Let us consider a given level of maximum output or production that the firm aims to produce is 20 units. Now there are three possible combinations of inputs i.e., Labor (L) and Capital (K) giving the same maximum possible level of output of 20 units. They are (4L, 1K), (2L, 2K), and (1L, 4K). As these possible combinations of inputs i.e., Labor (L) and Capital (K) given the same maximum possible output, these sets or combinations of L and K would lie on the same Isoquant curve and would all represent the maximum possible output of 20 units assuming the maximum efficiency level.


The above graph summarizes the whole concept of the Isoquant. The X axis shows the Labor uses and Y axis shows the amount of Capital used. Now for different combination of inputs i.e., Labor (L) and Capital (K), there are different level of outputs. The level of outputs is represented by different Isoquant Curves namely q1, q2 and q3. If we see the first Isoquant, the two combinations of inputs i.e., (L1, K2) and (L2, K1), give the same level of maximum possible output, hence represented on the same Isoquant curve.

Now, as we know the production function is represented as q = f (L, K) i.e., the production is a function of Labor and Capital and if one of them at least increases, the other remaining the same or increases too, the maximum level of possible output increases too.

Similar thing can be seen in the above graph too. From the combination of input (L2, K1), if we increase the labor from L2 to L3, keeping the amount of Capital fixed at K1, we get new input combination i.e., (L3, K1) and the output increases to q=2 i.e., on a higher isoquant curve.

Why the Isoquant Curve is negatively sloped?

When the output can be increased by increasing a single input only keeping other input quantities constant, i.e., the marginal product is positive, to keep the output level same even after increasing one input, the second input needs to be curtailed. Hence the slope of the Isoquant curve is negative.

For example, in the input set (L1, K2), if labor is increased to L2, but if we want to continue with same output level, the other input K2 needs to be decreased to K1 i.e., new input set after increase in labor to keep the output level same needs to be (L2, K1).

Conclusion 

In this session, we discussed in detail the concept of behavior of a Firm. We discussed all the concepts related to firm, including the production function. And finally, we dwelled into the concept of Isoquants and Isoquant curves in detail.