Page 1 Chapter 3 P P P P Production and Costs roduction and Costs roduction and Costs roduction and Costs roduction and Costs A Firm Effort In the previous chapter, we have discussed the behaviour of the consumers. In this chapter as well as in the next, we shall examine the behaviour of a producer. A producer or a firm acquires different inputs like labour, machines, land, raw materials, etc. Combining these inputs, it produces output. This is called the process of production. In order to acquire inputs, it has to pay for them. That is the cost of production. Once the output has been produced, the firm sells it in the market and earns revenue. The revenue that it earns net of cost is the profit of the firm. We assume here that the objective of a firm is to maximise its profit. A firm looking at its cost structure and the market price of output decides to produce an amount of output such that its profit reaches the maximum. In this chapter, we study different aspects of the production function of a firm. We discuss here â€“ the relationship between inputs and output, the contribution of a variable input in the production process and different properties of production function. Then we look at the cost structure of the firm. We discuss the cost function and its various aspects. We learn about the properties of the short run and the long run cost curves. 3.1 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. Consider a manufacturer who produces shoes. She employs two workers â€“ worker 1 and worker 2, two machines â€“ machine 1 and machine 2, and 10 kilograms of raw materials. Worker 1 is good in operating machine 1 and worker 2 is good in operating machine 2. If worker 1 uses machine 1 and worker 2 uses machine 2, then with 10 kilograms of raw materials, they can produce 10 pairs of shoes. However, if worker 1 uses machine 2 and worker 2 uses machine 1, which they are not good at operating, with the same 10 kilograms of raw materials, they will end up producing only 8 pairs of shoes. So with efficient use of inputs, 10 pairs of shoes can be produced whereas an inefficient use results in production © NCERT not to be republished Page 2 Chapter 3 P P P P Production and Costs roduction and Costs roduction and Costs roduction and Costs roduction and Costs A Firm Effort In the previous chapter, we have discussed the behaviour of the consumers. In this chapter as well as in the next, we shall examine the behaviour of a producer. A producer or a firm acquires different inputs like labour, machines, land, raw materials, etc. Combining these inputs, it produces output. This is called the process of production. In order to acquire inputs, it has to pay for them. That is the cost of production. Once the output has been produced, the firm sells it in the market and earns revenue. The revenue that it earns net of cost is the profit of the firm. We assume here that the objective of a firm is to maximise its profit. A firm looking at its cost structure and the market price of output decides to produce an amount of output such that its profit reaches the maximum. In this chapter, we study different aspects of the production function of a firm. We discuss here â€“ the relationship between inputs and output, the contribution of a variable input in the production process and different properties of production function. Then we look at the cost structure of the firm. We discuss the cost function and its various aspects. We learn about the properties of the short run and the long run cost curves. 3.1 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. Consider a manufacturer who produces shoes. She employs two workers â€“ worker 1 and worker 2, two machines â€“ machine 1 and machine 2, and 10 kilograms of raw materials. Worker 1 is good in operating machine 1 and worker 2 is good in operating machine 2. If worker 1 uses machine 1 and worker 2 uses machine 2, then with 10 kilograms of raw materials, they can produce 10 pairs of shoes. However, if worker 1 uses machine 2 and worker 2 uses machine 1, which they are not good at operating, with the same 10 kilograms of raw materials, they will end up producing only 8 pairs of shoes. So with efficient use of inputs, 10 pairs of shoes can be produced whereas an inefficient use results in production © NCERT not to be republished of 8 pairs of shoes. Production function considers only the efficient use of inputs. It says that worker 1, worker 2, machine 1, machine 2 and 10 kilograms of raw materials together can produce 10 pairs of shoes which is the maximum possible output for this input combination. 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 â€“ factor 1 and factor 2. Our production function, therefore, tells us what maximum quantity of output can be produced by using different combinations of these two factors. We may write the production function as q = f(x 1 , x 2 ) (3.1) It says that by using x 1 amount of factor 1 and x 2 amount of factor 2, we can at most produce q amount of the commodity. Table 3.1: Production Function Factor x 2 01 2 3 4 5 6 00 0 0 00 00 10 1 3 710 12 13 2 0 3 10 1824 2933 x 1 3 0 7 18 3040 4650 4 0 10 24 40 50 56 57 5 0 12 29 46 56 58 59 6 0 13 33 50 57 59 60 A numerical example of production function is given in Table 3.1. The left column shows the amount of factor 1 and the top row shows the amount of factor 2. As we move to the right along any row, factor 2 increases and as we move down along any column, factor 1 increases. For different values of the two factors, the table shows the corresponding output levels. For example, with 1 unit of factor 1 and 1 unit of factor 2, the firm can produce at most 1 unit of output; with 2 units of factor 1 and 2 units of factor 2, it can produce at most 10 units of output; with 3 units of factor 1 and 2 units of factor 2, it can produce at most 18 units of output and so on. Isoquant In Chapter 2, we have learnt about indifference curves. Here, we introduce a similar concept known as isoquant. It is just an alternative way of representing the production function. Consider a production function with two inputs factor 1 and factor 2. 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. 37 Production and Costs © NCERT not to be republished Page 3 Chapter 3 P P P P Production and Costs roduction and Costs roduction and Costs roduction and Costs roduction and Costs A Firm Effort In the previous chapter, we have discussed the behaviour of the consumers. In this chapter as well as in the next, we shall examine the behaviour of a producer. A producer or a firm acquires different inputs like labour, machines, land, raw materials, etc. Combining these inputs, it produces output. This is called the process of production. In order to acquire inputs, it has to pay for them. That is the cost of production. Once the output has been produced, the firm sells it in the market and earns revenue. The revenue that it earns net of cost is the profit of the firm. We assume here that the objective of a firm is to maximise its profit. A firm looking at its cost structure and the market price of output decides to produce an amount of output such that its profit reaches the maximum. In this chapter, we study different aspects of the production function of a firm. We discuss here â€“ the relationship between inputs and output, the contribution of a variable input in the production process and different properties of production function. Then we look at the cost structure of the firm. We discuss the cost function and its various aspects. We learn about the properties of the short run and the long run cost curves. 3.1 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. Consider a manufacturer who produces shoes. She employs two workers â€“ worker 1 and worker 2, two machines â€“ machine 1 and machine 2, and 10 kilograms of raw materials. Worker 1 is good in operating machine 1 and worker 2 is good in operating machine 2. If worker 1 uses machine 1 and worker 2 uses machine 2, then with 10 kilograms of raw materials, they can produce 10 pairs of shoes. However, if worker 1 uses machine 2 and worker 2 uses machine 1, which they are not good at operating, with the same 10 kilograms of raw materials, they will end up producing only 8 pairs of shoes. So with efficient use of inputs, 10 pairs of shoes can be produced whereas an inefficient use results in production © NCERT not to be republished of 8 pairs of shoes. Production function considers only the efficient use of inputs. It says that worker 1, worker 2, machine 1, machine 2 and 10 kilograms of raw materials together can produce 10 pairs of shoes which is the maximum possible output for this input combination. 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 â€“ factor 1 and factor 2. Our production function, therefore, tells us what maximum quantity of output can be produced by using different combinations of these two factors. We may write the production function as q = f(x 1 , x 2 ) (3.1) It says that by using x 1 amount of factor 1 and x 2 amount of factor 2, we can at most produce q amount of the commodity. Table 3.1: Production Function Factor x 2 01 2 3 4 5 6 00 0 0 00 00 10 1 3 710 12 13 2 0 3 10 1824 2933 x 1 3 0 7 18 3040 4650 4 0 10 24 40 50 56 57 5 0 12 29 46 56 58 59 6 0 13 33 50 57 59 60 A numerical example of production function is given in Table 3.1. The left column shows the amount of factor 1 and the top row shows the amount of factor 2. As we move to the right along any row, factor 2 increases and as we move down along any column, factor 1 increases. For different values of the two factors, the table shows the corresponding output levels. For example, with 1 unit of factor 1 and 1 unit of factor 2, the firm can produce at most 1 unit of output; with 2 units of factor 1 and 2 units of factor 2, it can produce at most 10 units of output; with 3 units of factor 1 and 2 units of factor 2, it can produce at most 18 units of output and so on. Isoquant In Chapter 2, we have learnt about indifference curves. Here, we introduce a similar concept known as isoquant. It is just an alternative way of representing the production function. Consider a production function with two inputs factor 1 and factor 2. 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. 37 Production and Costs © NCERT not to be republished 38 Introductory Microeconomics In our example, both the inputs are necessary for the production. If any of the inputs becomes zero, there will be no production. With both inputs positive, output will be positive. As we increase the amount of any input, output increases. 3.2 THE SHORT RUN AND THE LONG RUN Before we begin with any further analysis, it is important to discuss two conceptsâ€“ the short run and the long run. In the short run, a firm cannot vary all the inputs. One of the factors â€“ factor 1 or factor 2 â€“ cannot be varied, and therefore, remain fixed in the short run. In order to vary the output level, the firm can vary only the other factor. The factor that remains fixed is called the fixed input whereas the other factor which the firm can vary is called the variable input. Consider the example represented through Table 3.1. Suppose, in the short run, factor 2 remains fixed at 5 units. Then the corresponding column shows the different levels of output that the firm may produce using different quantities of factor 1 in the short run. In the long run, all factors of production can be varied. A firm in order to produce different levels of output in the long run may vary both the inputs simultaneously. So, in the long run, there is no fixed input. For any particular production process, long run generally refers to a longer time period than the short run. 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 long run or short run simply by looking at whether all the inputs can be varied or not. 3.3 TOTAL PRODUCT, AVERAGE PRODUCT AND MARGINAL PRODUCT 3.3.1 Total Product Suppose we vary a single input and keep all other inputs constant. Then for different levels of employment of that input, we get different levels of output from the production function. This relationship between the variable input and output, keeping all other inputs constant, is often referred to as Total Product (TP) of the variable input. In the diagram, we have three isoquants for the three output levels, namely q = q 1 , q = q 2 and q = q 3 in the inputs plane. Two input combinations (x' 1 , x'' 2 ) and (x'' 1 , x' 2 ) give us the same level of output q 1 . If we fix factor 2 at x' 2 and increase factor 1 to x''' 1 , output increases and we reach a higher isoquant, q = q 2 . When marginal products are positive, with greater amount of one input, the same level of output can be produced by using lesser amount of the other. Therefore, isoquants are negatively sloped. Factor 2 Factor 1 qq = 1 qq = 2 qq = 3 x x x x x O © NCERT not to be republished Page 4 Chapter 3 P P P P Production and Costs roduction and Costs roduction and Costs roduction and Costs roduction and Costs A Firm Effort In the previous chapter, we have discussed the behaviour of the consumers. In this chapter as well as in the next, we shall examine the behaviour of a producer. A producer or a firm acquires different inputs like labour, machines, land, raw materials, etc. Combining these inputs, it produces output. This is called the process of production. In order to acquire inputs, it has to pay for them. That is the cost of production. Once the output has been produced, the firm sells it in the market and earns revenue. The revenue that it earns net of cost is the profit of the firm. We assume here that the objective of a firm is to maximise its profit. A firm looking at its cost structure and the market price of output decides to produce an amount of output such that its profit reaches the maximum. In this chapter, we study different aspects of the production function of a firm. We discuss here â€“ the relationship between inputs and output, the contribution of a variable input in the production process and different properties of production function. Then we look at the cost structure of the firm. We discuss the cost function and its various aspects. We learn about the properties of the short run and the long run cost curves. 3.1 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. Consider a manufacturer who produces shoes. She employs two workers â€“ worker 1 and worker 2, two machines â€“ machine 1 and machine 2, and 10 kilograms of raw materials. Worker 1 is good in operating machine 1 and worker 2 is good in operating machine 2. If worker 1 uses machine 1 and worker 2 uses machine 2, then with 10 kilograms of raw materials, they can produce 10 pairs of shoes. However, if worker 1 uses machine 2 and worker 2 uses machine 1, which they are not good at operating, with the same 10 kilograms of raw materials, they will end up producing only 8 pairs of shoes. So with efficient use of inputs, 10 pairs of shoes can be produced whereas an inefficient use results in production © NCERT not to be republished of 8 pairs of shoes. Production function considers only the efficient use of inputs. It says that worker 1, worker 2, machine 1, machine 2 and 10 kilograms of raw materials together can produce 10 pairs of shoes which is the maximum possible output for this input combination. 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 â€“ factor 1 and factor 2. Our production function, therefore, tells us what maximum quantity of output can be produced by using different combinations of these two factors. We may write the production function as q = f(x 1 , x 2 ) (3.1) It says that by using x 1 amount of factor 1 and x 2 amount of factor 2, we can at most produce q amount of the commodity. Table 3.1: Production Function Factor x 2 01 2 3 4 5 6 00 0 0 00 00 10 1 3 710 12 13 2 0 3 10 1824 2933 x 1 3 0 7 18 3040 4650 4 0 10 24 40 50 56 57 5 0 12 29 46 56 58 59 6 0 13 33 50 57 59 60 A numerical example of production function is given in Table 3.1. The left column shows the amount of factor 1 and the top row shows the amount of factor 2. As we move to the right along any row, factor 2 increases and as we move down along any column, factor 1 increases. For different values of the two factors, the table shows the corresponding output levels. For example, with 1 unit of factor 1 and 1 unit of factor 2, the firm can produce at most 1 unit of output; with 2 units of factor 1 and 2 units of factor 2, it can produce at most 10 units of output; with 3 units of factor 1 and 2 units of factor 2, it can produce at most 18 units of output and so on. Isoquant In Chapter 2, we have learnt about indifference curves. Here, we introduce a similar concept known as isoquant. It is just an alternative way of representing the production function. Consider a production function with two inputs factor 1 and factor 2. 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. 37 Production and Costs © NCERT not to be republished 38 Introductory Microeconomics In our example, both the inputs are necessary for the production. If any of the inputs becomes zero, there will be no production. With both inputs positive, output will be positive. As we increase the amount of any input, output increases. 3.2 THE SHORT RUN AND THE LONG RUN Before we begin with any further analysis, it is important to discuss two conceptsâ€“ the short run and the long run. In the short run, a firm cannot vary all the inputs. One of the factors â€“ factor 1 or factor 2 â€“ cannot be varied, and therefore, remain fixed in the short run. In order to vary the output level, the firm can vary only the other factor. The factor that remains fixed is called the fixed input whereas the other factor which the firm can vary is called the variable input. Consider the example represented through Table 3.1. Suppose, in the short run, factor 2 remains fixed at 5 units. Then the corresponding column shows the different levels of output that the firm may produce using different quantities of factor 1 in the short run. In the long run, all factors of production can be varied. A firm in order to produce different levels of output in the long run may vary both the inputs simultaneously. So, in the long run, there is no fixed input. For any particular production process, long run generally refers to a longer time period than the short run. 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 long run or short run simply by looking at whether all the inputs can be varied or not. 3.3 TOTAL PRODUCT, AVERAGE PRODUCT AND MARGINAL PRODUCT 3.3.1 Total Product Suppose we vary a single input and keep all other inputs constant. Then for different levels of employment of that input, we get different levels of output from the production function. This relationship between the variable input and output, keeping all other inputs constant, is often referred to as Total Product (TP) of the variable input. In the diagram, we have three isoquants for the three output levels, namely q = q 1 , q = q 2 and q = q 3 in the inputs plane. Two input combinations (x' 1 , x'' 2 ) and (x'' 1 , x' 2 ) give us the same level of output q 1 . If we fix factor 2 at x' 2 and increase factor 1 to x''' 1 , output increases and we reach a higher isoquant, q = q 2 . When marginal products are positive, with greater amount of one input, the same level of output can be produced by using lesser amount of the other. Therefore, isoquants are negatively sloped. Factor 2 Factor 1 qq = 1 qq = 2 qq = 3 x x x x x O © NCERT not to be republished 39 Production and Costs In our production function, if we keep factor 2 constant, say, at the value 2 x and vary factor 1, then for each value of x 1 , we get a value of q for that particular 2 x . We write it in the following way q = f (x 1 ; 2 x ) (3.2) This is the total product function of factor 1. Let us again look at Table 3.1. Suppose factor 2 is fixed at 4 units. Now in the Table 3.1, we look at the column where factor 2 takes the value 4. As we move down along the column, we get the output values for different values of factor 1. This is the total product of factor 1 schedule with x 2 = 4. At x 1 = 0, the TP is 0, at x 1 = 1, TP is 10 units of output, at x 1 = 2, TP is 24 units of output and so on. This is also sometimes called total return to or total physical product of the variable input. Once we have defined 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. 3.3.2 Average Product Average product is defined as the output per unit of variable input. We calculate it as AP 1 = 1 TP x = 12 1 (: ) fxx x (3.3) Table 3.2 gives us a numerical example of average product of factor 1. In Table 3.1, we have already seen the total product of factor 1 for x 2 = 4. In Table 3.2 we reproduce the total product schedule and extend the table to show the corresponding values of average product and marginal product. The first column shows the amount of factor 1 and in the fourth column we get the corresponding average product value. It shows that at 1 unit of factor 1, AP 1 is 10 units of output, at 2 units of factor 1, AP 1 is 12 units of output and so on. 3.3.3 Marginal Product 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 factor 2 is held constant, the marginal product of factor 1 is MP 1 = change in output change in input = 1 q x ? ? (3.4) where ? represents the change of the variable. If the input changes by discrete units, the marginal product can be defined in the following way. Suppose, factor 2 is fixed at 2 x . With 2 x amount of factor 2, let, according to the total product curve, x 1 units of factor 1 produce 20 units of the output and x 1 â€“ 1 units of factor 1 produce 15 units of the output. We say that the marginal product of the x 1 th unit of factor 1 is MP 1 = f(x 1 ; 2 x ) â€“ f(x 1 â€“ 1; 2 x ) (3.5) = (TP at x 1 units) â€“ (TP at x 1 â€“ 1 unit) = (20 â€“ 15) units of output = 5 units of output © NCERT not to be republished Page 5 Chapter 3 P P P P Production and Costs roduction and Costs roduction and Costs roduction and Costs roduction and Costs A Firm Effort In the previous chapter, we have discussed the behaviour of the consumers. In this chapter as well as in the next, we shall examine the behaviour of a producer. A producer or a firm acquires different inputs like labour, machines, land, raw materials, etc. Combining these inputs, it produces output. This is called the process of production. In order to acquire inputs, it has to pay for them. That is the cost of production. Once the output has been produced, the firm sells it in the market and earns revenue. The revenue that it earns net of cost is the profit of the firm. We assume here that the objective of a firm is to maximise its profit. A firm looking at its cost structure and the market price of output decides to produce an amount of output such that its profit reaches the maximum. In this chapter, we study different aspects of the production function of a firm. We discuss here â€“ the relationship between inputs and output, the contribution of a variable input in the production process and different properties of production function. Then we look at the cost structure of the firm. We discuss the cost function and its various aspects. We learn about the properties of the short run and the long run cost curves. 3.1 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. Consider a manufacturer who produces shoes. She employs two workers â€“ worker 1 and worker 2, two machines â€“ machine 1 and machine 2, and 10 kilograms of raw materials. Worker 1 is good in operating machine 1 and worker 2 is good in operating machine 2. If worker 1 uses machine 1 and worker 2 uses machine 2, then with 10 kilograms of raw materials, they can produce 10 pairs of shoes. However, if worker 1 uses machine 2 and worker 2 uses machine 1, which they are not good at operating, with the same 10 kilograms of raw materials, they will end up producing only 8 pairs of shoes. So with efficient use of inputs, 10 pairs of shoes can be produced whereas an inefficient use results in production © NCERT not to be republished of 8 pairs of shoes. Production function considers only the efficient use of inputs. It says that worker 1, worker 2, machine 1, machine 2 and 10 kilograms of raw materials together can produce 10 pairs of shoes which is the maximum possible output for this input combination. 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 â€“ factor 1 and factor 2. Our production function, therefore, tells us what maximum quantity of output can be produced by using different combinations of these two factors. We may write the production function as q = f(x 1 , x 2 ) (3.1) It says that by using x 1 amount of factor 1 and x 2 amount of factor 2, we can at most produce q amount of the commodity. Table 3.1: Production Function Factor x 2 01 2 3 4 5 6 00 0 0 00 00 10 1 3 710 12 13 2 0 3 10 1824 2933 x 1 3 0 7 18 3040 4650 4 0 10 24 40 50 56 57 5 0 12 29 46 56 58 59 6 0 13 33 50 57 59 60 A numerical example of production function is given in Table 3.1. The left column shows the amount of factor 1 and the top row shows the amount of factor 2. As we move to the right along any row, factor 2 increases and as we move down along any column, factor 1 increases. For different values of the two factors, the table shows the corresponding output levels. For example, with 1 unit of factor 1 and 1 unit of factor 2, the firm can produce at most 1 unit of output; with 2 units of factor 1 and 2 units of factor 2, it can produce at most 10 units of output; with 3 units of factor 1 and 2 units of factor 2, it can produce at most 18 units of output and so on. Isoquant In Chapter 2, we have learnt about indifference curves. Here, we introduce a similar concept known as isoquant. It is just an alternative way of representing the production function. Consider a production function with two inputs factor 1 and factor 2. 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. 37 Production and Costs © NCERT not to be republished 38 Introductory Microeconomics In our example, both the inputs are necessary for the production. If any of the inputs becomes zero, there will be no production. With both inputs positive, output will be positive. As we increase the amount of any input, output increases. 3.2 THE SHORT RUN AND THE LONG RUN Before we begin with any further analysis, it is important to discuss two conceptsâ€“ the short run and the long run. In the short run, a firm cannot vary all the inputs. One of the factors â€“ factor 1 or factor 2 â€“ cannot be varied, and therefore, remain fixed in the short run. In order to vary the output level, the firm can vary only the other factor. The factor that remains fixed is called the fixed input whereas the other factor which the firm can vary is called the variable input. Consider the example represented through Table 3.1. Suppose, in the short run, factor 2 remains fixed at 5 units. Then the corresponding column shows the different levels of output that the firm may produce using different quantities of factor 1 in the short run. In the long run, all factors of production can be varied. A firm in order to produce different levels of output in the long run may vary both the inputs simultaneously. So, in the long run, there is no fixed input. For any particular production process, long run generally refers to a longer time period than the short run. 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 long run or short run simply by looking at whether all the inputs can be varied or not. 3.3 TOTAL PRODUCT, AVERAGE PRODUCT AND MARGINAL PRODUCT 3.3.1 Total Product Suppose we vary a single input and keep all other inputs constant. Then for different levels of employment of that input, we get different levels of output from the production function. This relationship between the variable input and output, keeping all other inputs constant, is often referred to as Total Product (TP) of the variable input. In the diagram, we have three isoquants for the three output levels, namely q = q 1 , q = q 2 and q = q 3 in the inputs plane. Two input combinations (x' 1 , x'' 2 ) and (x'' 1 , x' 2 ) give us the same level of output q 1 . If we fix factor 2 at x' 2 and increase factor 1 to x''' 1 , output increases and we reach a higher isoquant, q = q 2 . When marginal products are positive, with greater amount of one input, the same level of output can be produced by using lesser amount of the other. Therefore, isoquants are negatively sloped. Factor 2 Factor 1 qq = 1 qq = 2 qq = 3 x x x x x O © NCERT not to be republished 39 Production and Costs In our production function, if we keep factor 2 constant, say, at the value 2 x and vary factor 1, then for each value of x 1 , we get a value of q for that particular 2 x . We write it in the following way q = f (x 1 ; 2 x ) (3.2) This is the total product function of factor 1. Let us again look at Table 3.1. Suppose factor 2 is fixed at 4 units. Now in the Table 3.1, we look at the column where factor 2 takes the value 4. As we move down along the column, we get the output values for different values of factor 1. This is the total product of factor 1 schedule with x 2 = 4. At x 1 = 0, the TP is 0, at x 1 = 1, TP is 10 units of output, at x 1 = 2, TP is 24 units of output and so on. This is also sometimes called total return to or total physical product of the variable input. Once we have defined 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. 3.3.2 Average Product Average product is defined as the output per unit of variable input. We calculate it as AP 1 = 1 TP x = 12 1 (: ) fxx x (3.3) Table 3.2 gives us a numerical example of average product of factor 1. In Table 3.1, we have already seen the total product of factor 1 for x 2 = 4. In Table 3.2 we reproduce the total product schedule and extend the table to show the corresponding values of average product and marginal product. The first column shows the amount of factor 1 and in the fourth column we get the corresponding average product value. It shows that at 1 unit of factor 1, AP 1 is 10 units of output, at 2 units of factor 1, AP 1 is 12 units of output and so on. 3.3.3 Marginal Product 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 factor 2 is held constant, the marginal product of factor 1 is MP 1 = change in output change in input = 1 q x ? ? (3.4) where ? represents the change of the variable. If the input changes by discrete units, the marginal product can be defined in the following way. Suppose, factor 2 is fixed at 2 x . With 2 x amount of factor 2, let, according to the total product curve, x 1 units of factor 1 produce 20 units of the output and x 1 â€“ 1 units of factor 1 produce 15 units of the output. We say that the marginal product of the x 1 th unit of factor 1 is MP 1 = f(x 1 ; 2 x ) â€“ f(x 1 â€“ 1; 2 x ) (3.5) = (TP at x 1 units) â€“ (TP at x 1 â€“ 1 unit) = (20 â€“ 15) units of output = 5 units of output © NCERT not to be republished 40 Introductory Microeconomics 3.4 THE LAW OF DIMINISHING MARGINAL PRODUCT AND THE LAW OF VARIABLE PROPORTIONS The law of diminishing marginal product says that if we keep increasing the employment of an input, with other inputs fixed, eventually a point will be reached after which the resulting addition to output (i.e., marginal product of that input) will start falling. A somewhat related concept with the law of diminishing marginal product is the law of variable proportions. It says that the marginal product of a factor input initially rises with its employment level. But after reaching a certain level of employment, it starts falling. The reason behind the law of diminishing returns or the law of variable proportion is the following. As we hold one factor input fixed and keep increasing the other, the factor proportions change. Initially, as we increase the amount of the variable input, the factor proportions become more and more suitable for the production and marginal product increases. But after a certain level of employment, the production process becomes too crowded with the variable input and the factor proportions become less and less suitable for the production. It is from this point that the marginal product of the variable input starts falling. Let us look at Table 3.2 again. With factor 2 fixed at 4 units, the table shows us the TP, MP 1 and AP 1 for different values of factor 1. We see that up to the employment level of 3 units of factor 1, its marginal product increases. Then it starts falling. Table 3.2: Total Product, Marginal product and Average product Factor 1 TP MP 1 AP 1 00 - - 110 10 10 224 14 12 3 40 16 13.33 4 50 10 12.5 5 56 6 11.2 6 57 1 9.5 Since inputs cannot take negative values, marginal product is undefined at zero level of input employment. Marginal products are additions to total product. For any level of employment of an input, the sum of marginal products of every unit of that input up to that level gives the total product of that input at that employment level. So total product is the sum of marginal products. Average product of an input at any level of employment is the average of all marginal products up to that level. Average and marginal products are often referred to as average and marginal returns, respectively, to the variable input. In the example represented through Table 3.1, if we keep factor 2 constant say, at 4 units, we get a total product schedule. From the total product, we then derive the marginal product and average product of factor 1. The third column of Table 3.2 shows that at zero unit of factor 1, MP 1 is undefined. At x 1 = 1, Mp 1 is 10 units of output, at x 1 = 2, MP 1 is 14 units of output and so on. © NCERT not to be republishedRead More

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