## Production and Costs Class 11 Chapter 3

**Production and Costs Class 11 Introduction **

Production and Costs Class 11 In the previous chapter, we discussed the behaviour of the consumers. In this chapter as well as in the next, we shall examine the behaviour of a producer. Production is the process by which inputs are transformed into ‘output’. Production is carried out by producers or firms.

A firm acquires different inputs like labour, machines, land, raw materials etc. It uses these inputs to produce output. This output can be consumed by consumers, or used by other firms for further production. For example, a tailor uses a sewing machine, cloth, thread and his labour to ‘produce’ shirts. A farmer uses his land, labour, a tractor, seed, fertilizer, water etc to produce wheat. A car manufacturer

uses land for a factory, machinery, labour, and various other inputs (steel, aluminium, rubber etc) to produce cars. A rickshaw puller uses a rickshaw and his own labour to ‘produce’ rickshaw rides. A domestic helper uses her labour to produce ‘cleaning services’. We make certain simplifying assumptions to start with.

**Production Function **

The production function of a firm is a relationship between inputs used and output produced by the firm. For various quantities of inputs used, it gives the maximum quantity of output that can be produced. Reprint 2024-25 Consider the farmer we mentioned above. For simplicity, we assume that the farmer uses only two inputs to produce wheat: land and labour.

A production function tells us the maximum amount of wheat he can produce for a given amount of land that he uses and a given number of hours of labour that he performs. Suppose that he uses 2 hours of labour/day and 1 hectare of land to produce a maximum of 2 tonnes of wheat. Then, a function that describes this relation is called a production function. One possible example of the form this could take is: q = K × L,

Where q is the amount of wheat produced, K is the area of land in hectares, and L is the number of hours of work done in a day. Describing a production function in this manner tells us the exact relation between inputs and output. If either K or L increases, q will also increase.

For any L and any K, there will be only one q. Since by definition we are taking the maximum output for any level of inputs, a production function deals only with the efficient use of inputs. Efficiency implies that it is not possible to get any more output from the same level of inputs.

A production function is defined for a given technology. It is the technological knowledge that determines the maximum levels of output that can be produced using different combinations of inputs. If the technology improves, the maximum levels of output obtainable for different input combinations increase. We then have a new production function.

The inputs that a firm uses in the production process are called factors of production. In order to produce output, a firm may require any number of different inputs. However, for the time being, here we consider a firm that produces output using only two factors of production – labour and capital.

Our production function, therefore, tells us the maximum quantity of output (q) that can be produced by using different combinations of these two factors of production: Labour (L) and Capital (K). We may write the production function as q = f(L, K) (3.1) where L is labour and K is capital and q is the maximum output that can be produced.

**The Short Run and The Long Run **

Before we begin with any further analysis, it is important to discuss two concepts—the short run and the long run. In the short run, at least one of the factors—labour or capital—cannot be varied and therefore remains fixed.

To vary the output level, the firm can vary only the other factor. The factor that remains fixed is called the fixed factor, whereas the other factor which the firm can vary is called the variable factor. Consider the example represented in Table 3.1. Production and Costs Class 11 Suppose, in the short run, capital remains fixed at 4 units. Then the corresponding column shows the different levels of output that the firm may produce using different quantities of labour in the short run.

In Chapter 2, we have learned about indifference curves. Here, we introduce a similar concept known as an isoquant. It is just an alternative way of representing the production function. Consider a production function with two inputs: labour and capital.

Production and Costs Class 11 An isoquant is the set of all possible combinations of the two inputs that yield the same maximum possible level of output. Each isoquant represents a particular level of output and is labelled with that amount of output.

Let us return to Table 3.1. Notice that the output of 10 units can be produced in 3 ways: (4L, 1K), (2L, 2K), (1L, 4K). All these combinations of L and K lie on the same isoquant, which represents the level of output 10. Can you identify the sets of inputs that will lie on the isoquant q = 50?

The diagram here generalizes this concept. We place L on the X-axis and K on the Y-axis. We have three isoquants for the three output levels, namely q = q1, q = q2, and q = q3. Two input combinations (L1, K2) and (L2, K1) give us the same level of output q1.

If we fix capital at K1 and increase labour to L3, output increases and we reach a higher isoquant, q = q2. When marginal products are positive, with a greater amount of one input, the same level of output can be produced only using a lesser amount of the other. Therefore, isoquants are negatively sloped.

In the long run, all factors of production can be varied. A firm, to produce different levels of output in the long run, may vary both inputs simultaneously. So, in the long run, there is no fixed factor. For any particular production process, the long run generally refers to a longer time period than the short run.

Production and Costs Class 11 For different production processes, the long-run periods may be different. It is not advisable to define short run and long run in terms of, say, days, months, or years. We define a period as a long run or short run simply by looking at whether all the inputs can be varied or not.

**Total Product Average Product and Material Product **

**Total Product**

Suppose we vary a single input and keep all other inputs constant. Then for different levels of that input, we get different levels of output. This relationship between the variable input and output, keeping all other inputs constant, is often referred to as the Total Product (TP) of the variable input. Let us again look at Table 3.1. Suppose capital is fixed at 4 units.

Now in Table 3.1, we look at the column where capital takes the value 4. As we move down along the column, we get the output values for different values of labour. This is the total product of the labour schedule with ( K = 4 ). This is also sometimes called total return to or total physical product of the variable input. This is shown again in the second column of Table 3.2.

Once we have defined the total product, it will be useful to define the concepts of average product (AP) and marginal product (MP). They are useful in order to describe the contribution of the variable input to the production process.

**Average Product**

Average product is defined as the output per unit of the variable input. We calculate it as:

[ AP_L = \frac{TP_L}{L} ]

The last column of Table 3.2 gives us a numerical example of the average product of labour (with capital fixed at 4) for the production function described in Table 3.1. Values in this column are obtained by dividing TP (column 2) by L (Column 1).

**Marginal Product**

The marginal product of an input is defined as the change in output per unit of change in the input when all other inputs are held constant. When capital is held constant, the marginal product of labour is:

**[ MP_L = \frac{\Delta TP_L}{\Delta L} ]**

where (\Delta) represents the change of the variable.

The third column of Table 3.2 gives us a numerical example of the marginal product of labour (with capital fixed at 4) for the production function described in Table 3.1. Values in this column are obtained by dividing the change in TP by the change in L. For example, when L changes from 1 to 2, TP changes from 10 to 24:

[ MP_L = (TP \text{ at } L \text{ units}) – (TP \text{ at } L – 1 \text{ unit}) ]

Here, Change in TP = 24 – 10 = 14

Change in L = 1

Marginal product of the 2nd unit of labour = (\frac{14}{1} = 14)

Since inputs cannot take negative values, the marginal product is undefined at zero level of input employment. For any level of an input, the sum of the marginal products of every preceding unit of that input gives the total product. So, the total product is the sum of marginal products.

### The Law of Diminishing Marginal Product and the Law of Variable Proportions

If we plot the data in Table 3.2 on graph paper, placing labour on the X-axis and output on the Y-axis, we get the curves shown in the diagram below.

Let us examine what is happening to TP. Notice that TP increases as labour input increases, but the rate at which it increases is not constant. An increase in labour from 1 to 2 increases TP by 10 units. An increase in labour from 2 to 3 increases TP by 12. The rate at which TP increases, as explained above, is shown by the MP. Notice that the MP first increases (up to 3 units of labour) and then begins to diminish.