Production Function. Micro-economics

Transcription

1 Introduction to Theory of Production Hello everybody, Production Function Micro-economics The topic for today s discussion is Production Function. Before we move into this chapter I just want to make one thing clear that you should not get confused with your consumer behaviour and Production Theory, the reason is both the chapters look alike, but they are different (Production Function is different from consumer behaviour and Production Theory) in some perspective. The consumer behaviour analysis we have tried to capture the behaviour of the consumer, whose objective was maximization of utility. When you come to the Theory of Production here their objective is basically understanding the behaviour of producer. (Theory of Production, the objective is basically understanding the behaviour of producer) What is that behaviour of producer? Is most important for us. In the production process when there is a change in the prices of inputs, how the producer would react to this changes in the prices of inputs and also the change in the government regulations will definitely effect the output generated by these firms. Therefore, in this chapter we would understand what is the basic objective of a producer? As you all are aware that here also we are dealing with our rational producer whose objective is maximization of output with minimum cost of production. Before we go into the details of the Production Theory, let s first understand what does this Production in general mean? Production is nothing but the transformation of raw material into finished product. Now that transformation can be in the form of Change in form, change in space or change in time. For example: you take water in a tray and put it in the freezer, water which is in the liquid from gets converted into ice-cubs this is what I mean by Change n form of production. 1

2 Technically when you have to look into the Theory of Production, we need to understand that production function basically enable us to understand the relationship between output and the combination of the inputs. In other words, production function basically explains us the mathematical relationship between output and input. Now let s look into the Factors of Production which participate in this activity, as you all are aware that the four factors of production namely land, labour, capital and entrepreneurship. These are the factors of production which participate in the economic activity. Now when they are participating in the economic activity they (the factors of production) receive rewards in the form of rent, wage, Interest and profit. Let s look at the graphical representation of this production function Production Function Q Q 3 = f(l, K 30 ) Q Q 3 = f(k, L 30 ) Q 2 = f(l, K 20 ) Q 2 = f(k, L 20 ) Q 1 = f(l, K 10 ) Q 1 = f(k, L 10 ) 0 Production Function with Constant K: K 10 < K 20 < K 3 0 L 0 Production Function with Constant L: L 10 < L 20 < L 3 0 K Figure (a) Figure (b) 3 2

3 You have two graphs one on the right side i.e. b and one on your left side i.e. a, the graph (a), is indicating the change in the capital input resulting increase in the production while in the other figure we find labour input is being changed while that of capital is held constant. In a nutshell we understand there is a possibility to increase the output by changing the input. So let s now understand what is the technical relationship that exists between the output and the factor inputs? As you all aware producers might procure different inputs and combine production technologies to generate some level of output, but here in this chapter we are just confining only to two factor inputs namely Labour and Capital. So in a nutshell we understand that technological change either you might adopt a level in terms of technology i.e. using of more labour force so as to produce output, or capital intensive technology will definitely shift the production function. For example: take case of sweater manufacturing, you know basically the demand for sweaters is a seasonal demand. In the good olden days the sweaters have been done with needles or knitting, now as and when the demand for sweaters is increasing, there is a need to supply more of sweaters. In this instance producers might adopt capital intensive technologies and they might go back and buy a machine, so earlier they were coming out with the sweaters with hand-made or using needles. Now when they go the adoption of capital intensive technology, they are able to generate more and more of output. So that s why today we are wearing matching sari with matching sweaters i.e. thanks to the technological progress which is enabling us to increase the output with capital intensive technology. 3

4 Look at the graph which is explaining us how technological change would result in shift in your production function. Look at the function which is saying Q which is the function of x1, x2, x3, x4, xn, Q in this function is the quantity of the output, the variables x1, x2, x3, xn are all the independent variables, this is basically the mathematical form of representing production function. In the process of production though the time is very important but it is the factor inputs that determine the nature of production function. MEANING Q = f(x1,x2,x3,...,xn) where: Q = quantity of output X1,X2,X3,..., Xn = factor inputs (such as capital, labor, land or raw materials). Accordingly the Theory of Production will enable us to understand the behaviour of producer to the help of production function. Module 2 Short run Production function By Short run we mean that it is not too little time taken for the production activity. Here the short run means the inclusion of both the fixed factors and variable factors. It is not related to the short period of time you might take ten years of time for ship building, that does not mean that it is a long run production function, it is the number of fixed inputs and variable inputs that 4

5 enable us to understand whether it is a short run or a long run. Similarly take the example of manufacturing of soap it might take one week of time but if it involves complete change of the inputs that are employed then it can be referred to as long run. So in a nut shell you should understand time is not the only factor that decides whether it is a short urn or a long run. Short run is characterized by having both fixed factors and variable factors, in the long run we do not have any fixed factors. The law that is associated to understand the behaviour of the production function in the short run is known is Law of variables returns to factor proportions. Let us understand the definition of this law, in the last stage as we go on employing more of one factor of production keeping the factors constant its marginal productivity will diminish after some point of time. Law of Diminishing Returns As we go on employing more of one factor of production, keeping the other factors constant, its marginal productivity will diminish after some point 7 In a nut shell we understand as we go on increase the variable factor input the output is likely to diminish returns to factor proportions. Let s look at a production schedule which will enable us to understand and capture the operation of this law of diminishing returns to variable of factor proportion. Look at the production schedule 5

6 Production Schedule No. of Labors Employed (L) Total Product (TP L ) Average Product (AP L ) Marginal Product (MP L ) In this schedule we have No. of Labour units employed, Total product, Average product and marginal product. In order to understand capture the impact of the variable input on output here we are assuming capital as constant while labour is zero, that s why in this schedule you find the number of labourer s employed. Average Product as you all know it is nothing but Total product/ No.of Labourer s Will enable us to know the average productivity of labourer s. We have another concept called Marginal product. Marginal product is nothing but an additional unit of the input that is added to the production process, so we will be able to capture what is this additional input that is contributing to the production process, we be able to get from this particular value. Look at the schedule you will understand how the different values of average productivity is calculated, it is nothing but 40 divided 1 we are getting 40, similarly 100 divided by 2 to the average product is becoming 50, so on and so forth. If you look at the marginal product is nothing but we are trying to capture when you are employing one more variable unit input that does it really contribute anything to the production process. You look at the schedule for one labourer is the process at one more labourer then it is becoming 2 labourers, if you look at the marginal product take the difference between the successive units of the total product divided by the no. of change in the no. of labour units. For instance you take the difference between divided by 1 the value we are getting is 60, that means initially when we had 1 labourer the contribution of this labourer was 40 units when you have employed one more labour input, 6

7 the total output has increased to 100 units while if you look at what is the additional contribution made by this additional labourer its understood that the contribution of this labourer is 60 units this fact will encourage the producers to keep on adding more and more variable inputs so as to increase the output, so the producer proceeds of increasing the no. of labour units, you will find that after reaching or after employing 8 units of labour it s clear that the lobour was not contributing anything because you see in that schedule marginal product is value is zero. Which means the labour input is not contributing anything to production to process. If the producer tends to add one more variable input so as to increase the output look at the column of total product, the total product is declining, it is declining from to when you look at the marginal product column it is clear that the value is -10 this what we call it as negative marginal productivity, instead of contributing to the production process the additional factor input is not contributing but the contribution is in negative form. Module 3 Three stages of returns to variable graph The schedule can be represented in the form of a graph, the three stages of graphs returns to variable can be captured. In the stage one i.e. from the origin to point b the variable input is being used with variable increasing efficiency. Reaching at maximum at point B since the average physical product is at its maximum at that point. The average physical product of fixed inputs will also be rising in this stage though not refelcted in the graph Because the efficiency of both fixed and variable inputs is improving throughout stage 1, a firm will always try to operate beyond this particular stage. In stage 1 fixed inputs are underutilized. So in the stage 1 when the total product is increasing from its minimum to the maximum point we understand that initially total product is increasing at an increasing rate. 7

8 The Stages of Production 1st Stage In Stage 1 (from the origin to point B) the variable input is being used with increasing efficiency, reaching a maximum at point B (since the average physical product is at its maximum at that point). The average physical product of fixed inputs will also be rising in this stage (not shown in the diagram). Because the efficiency of both fixed and variable inputs is improving throughout stage 1, a firm will always try to operate beyond this stage. In stage 1 fixed inputs are underutilized. Let s look at the 2nd stage In Stage 2, output increases at a decreasing rate, and the average and marginal physical product is declining. So this the point where if you look at the graph that the total product curve is changing its curvature, and this changing in curvature is known as point of inflection where total productivity is becoming maximum and when you look at the corresponding marginal product curve it is touching the axis which means that marginal productivity is zero. So we should need to understand this is the optimum input output combination will be possible in stage 2. And we can also achieve maximum production, efficiency in this stage. 8

9 2nd Stage In Stage 2, output increases at a decreasing rate, and the average and marginal physical product is declining. However the average product of fixed inputs (not shown) is still rising. In this stage, the employment of additional variable inputs increase the efficiency of fixed inputs but decrease the efficiency of variable inputs. The optimum input/output combination will be in stage 2. Maximum production efficiency must fall somewhere in this stage. Let s look into the 3rd stage of production In the 3rd stage too much variable input is being used relative to the available fixed inputs: variable inputs seems to be over utilized, Both the efficiency of variable inputs and the efficiency of fixed inputs decline through out in this stage. 9

10 3rd Stage In Stage 3, too much variable input is being used relative to the available fixed inputs: variable inputs are over utilized. Both the efficiency of variable inputs and the efficiency of fixed inputs decline through out in this stage. At the boundary between stage 2 and stage 3, fixed input is being utilized most efficiently and short-run output is maximum. At the boundary between stage 2 and stage 3, fixed input is being utilized most efficiently and short-run output is maximum at this point of time. Short run production function is not only enabling us to understand what exactly the maximum output that can be achieved but it is also establishing the relationship between total product, marginal product and average product from this law we understand that total productivity of any input is going to be maximum when it is when marginal productivity is zero. Similarly when you look at the marginal productivity and average productivity you should understand average productivity will be maximum when it is equal to marginal productivity. We can also summarise the three stages of returns, initially the first stage we understand it is the stage of increasing marginal returns. From the starting point of MP till MP reaches the maximum point, the second stage Is known as diminishing marginal returns, from the maximum point of MP till the marginal productivity becomes zero, then we have other stage where is is known as negative marginal returns this from the point where the marginal productivity is zero then entering into the negative. 10

11 Points to Remember When MP = AP, AP will be maximum When MP = 0, TP will be maximum Stages of Marginal Returns: Increasing marginal returns: From the starting point of AP until AP reaches its maximum point. Diminishing marginal returns: From the maximum point of AP until AP = 0. Negative marginal returns: From the point where AP = 0 15 The best possible or best advisable stage for a producer is the theory says that we should operate in the second stage of production. It means though the marginal product is falling it is positive though the total marginal product is falling it is positive. It tries to give the maximum output to the producer we cannot effort to confine to the first stage because the former industry must not have reached the maximum possible level of output because total product is still increasing once it reaches the constant position only we understand whether the total product tends to fall and corresponding total marginal product will be reaching its minimum value or zero. Now beyond the time if at all we employ more and more variable inputs the marginal productivity will be negative. So if a producer is a rational producer he would confine to the second stage of production. Module 4 Long run production functions Let s now move on to the long run production functions, In the long run as we all understood that there are no fixed factors, all factor inputs are variables and the law is popularly known as returns to scale. Returns to scale captures, the degree of responsiveness of the output to change in the inputs which means if there is change in the input combinations it might be reflected in the output generated in the production process. Accordingly there are three types of returns to scale. The name itself indicates that it is returns to scale means it is the change in the scale of operation which is possible in the long run only. 11

12 We have constant returns to scale (CRS), increasing returns to scale or decreasing returns to scale, when we say it is constant returns to scale it implies suppose if you increase the input by 1% the output is likely to increase by 1% then we can say constant returns to scale, suppose we increase the input by 1% but the generated output is less than 1% then we call is as decreasing or diminishing returns to scale. If you increase the of inputs by 1% and the output generated is greater than 1% we call it is as increasing returns to scale. We have a graph which is showing us Types of Returns to Scale Q IRS CRS DRS Returns to Scale 21 All these three types of returns to scale. Look at the graph the in between graph is showing us the constant returns to scale, so we have one side the increasing returns to scale and on the other side we have decreasing returns to scale which means the returns to scale is arising only with the change in the input combination leading to different returns to scale. In a nut shell returns to scale is capturing or the degree of responsiveness of output to the changes in the input combinations. There is a famous production function which will enable us to understand the production function that s known as Cobb-Douglas Production Function, the Cobb-Douglas functional form of production function is widely used to represent the relationship of an output to inputs. It was proposed by KNUT WICKSELL( ), and tested against statistical evidence by PAUL DOUGLAS and CHARLES in

13 Cobb-Douglas Production Function In economics, the Cobb-Douglas functional form of Production function is widely used to represent the relationship of an output to inputs. It was proposed by KNUT WICKSELL( ), and tested against statistical evidence by PAUL DOUGLAS and CHARLES in Here we have the specification of the model Y = AL α K β, where: Y = output L = labour input K = capital input A = technical efficiency α and β are constants determined by technology. 13

14 Contd Y = AL α K β, where: Y = output L = labor input K = capital input A, α and β are constants determined by technology. The exponents α and β are output elasticities with respect to labour and capital, respectively. Output elasticity the exponents α and β are output elasticities with respect to labour and capital, respectively. Output elasticity basically measures the responsiveness of output to a change in the levels of either labour or capital used in production, ceteris paribus. For example if α = 1.7, a 1% increase in labour would lead to approximately a 1.7% increase in output. 14

15 Contd The exponents α and β are output elasticities with respect to labour and capital, respectively. Output elasticity measures the responsiveness of output to a change in levels of either labour or capital used in production, ceteris paribus. For example if α = 1.7, a 1% increase in labour would lead to approximately a 1.7% increase in output. We when we take up the sum of these elasiticities i.e. if you add-up the α + β = 1, It means CONSTANT RETURNS TO SCALE (if L and K are each increased by 20%, Y increases by 20%) so by taking up the some of the elasticity we can directly derive returns to scale if α + β > 1 we call it as increasing returns to scale, if α + β < 1 we call it as decreasing returns to scale. 15

16 RETURNS TO SCALE α + β = 1, The production function has CONSTANT RETURNS TO SCALE (if L and K are each increased by 20%, Y increases by 20%) Summary Let s now summarize what we have learnt from this chapter. We understood that production theory deals with the behaviour of the producer and his/her reactions to the changes in the government regulations and the changes in the inputs prices in order to understand the behaviour of the producer. Economic theory provides two laws of production function Short run production function and Long run production function. Short urn or the long run in this theory are not confined to the interial alarm. Short run and long run here imply that whether we have fixed and variable inputs or only variable inputs. If you have both fixed inputs and variable inputs we understand that it is a short run production function. If you have only variable inputs we should understand that it is long run production function. Short run production function enables us to understand and establish relationship between total product, marginal product and average product. Total product is said to be maximum when marginal product is equal to zero. 16

17 And one more important thing we understand from returns to scale is when there is a scope for change in the complete set up of production business, how the responsiveness of output to changes in the input levels. So accordingly we have three types of returns to scale, we have constant returns to scale, increasing returns to scale and decreasing returns to scale. Let us now check our progresss as what we have learnt in this chapter, FAQ s: 1. What is the difference between the Short run and long run production function? 2. Explain the relationship between the total product, marginal product and average product with the help of law of diminishing marginal returns? Books for reference: Micro economics by Pindyck Rubinfeld Modern micro economics by A koutsoyiannis Economics by Paul Samuelson Quiz 1. The law that explains the relationship between Total product and marginal product is referred to as : a. Law of variable proportions b. Law of returns to scale c. Law of diminishing returns to scale d. Law of constant returns to scale 2. Identify the stage of short run production function where too much variable input is being used relative to the available fixed inputs: variable inputs are over utilized: a. Ist stage of production b. IInd stage of production c. IIIrd stage of production d. Constant returns to scale 3. The Cobb-Douglas functional form of Production function is widely used to represent the relationship between: a. Output to Inputs b. Inputs to output c. Total Product to Average product d. Average product to Marginal Product 17

18 4. The ratio of change in total product by change in the number of labour inputs is indicated by : a. Total productivity of capital b. Marginal productivity of capital c. Marginal productivity of labour d. Total productivity of labour Glossary Average physical product: Average physical product (APP) of a variable factor (Capital,K) is the total physical output (Q) divided by the amount of capital employed. The average physical product of K is denoted by AP K. Mathematically it can be represented as : AP K = Q/K Capital : Capital means the stock of goods that are produced and are employed as factor inputs for further production. The important characteristic features of capital is : it increases the productivity of other factors of production namely labour and land and further creation of capital involves a sacrifice as resources are devoted to making non-consumable capital goods instead of goods for immediate consumption. Capital- Labour Substitution: The process of varying the factor proportions of capital and labour in a production technique,if employment of one input factor costs less than the other, there will be a inclination for the costly input factor to be substituted by the cheaper one in free market situation. Elasticity of Output: The degree of responsiveness of output to change in one factor input. In other words the elasticity of output with respect to factor capital (K) is the relative change in output over the relative change in the amount of the variable factor input (capital) used in the process of production Returns to scale: It refers to changes in output as factors change by the same proportion. Returns to variable factor: The expansion of output with one factor input constant while employing more of variable factor (s) is referred to as returns to variable factor. Objectives: This programme aims at explaining Introduction to Theory of Production Short run Production function Three stages of returns to variable graph Long run production functions 18

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