The producer must be rational. The producer only uses labor and capital as inputs. i.e. Q = f(L,K) There is operation of law of diminishing MRTS. Labor and capital are perfectly divisible and can be substituted in any small quantity. Producer has his own production preference schedule.Kamal Regmi (CAB) 24 Assumptions of Iso-quants:
THEORY OF PRODUCTION
CHAPTER FOUR - Kamal Regmi, College Of Applied Business (CAB), Tangal, KTM 1 Kamal Regmi (CAB)
In general sense, production refers to the creation of new things but in economic sense, it is the process of creation and addition of utility in existing goods and services. Production can be done by the following functions: By changing form By changing place By changing time By changing person There are mainly four factors of production i.e. land, labor, capital and organization which are used to produce goods and services.
Meaning of Production and Production Function: 2 Kamal Regmi (CAB)
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The functional or technical relationship between factors of production (inputs) as independent variable and output as dependent variable is called as production function . Production function shows the flow of inputs to produce the flow of output over some specific period of time. It expresses a physical relation because both inputs and output are expressed in physical terms. If land, labor, capital and organization are considered as the inputs used in production process, then the production function can be written as, Q = f(Ld, L, K, O)
Production function: 3 Kamal Regmi (CAB)
Short Run Production function (Single variable Production function): Short run is that time period where only variable factors of production can be changed keeping fixed factors constant. Therefore, short-run production function is the Functional relationship between the units of variable factors of production and the output produced. Generally in short-run, single factor (mainly labor) is regarded as the variable factor of production. Therefore, short run production function is also called as single variable production function. The law of variable proportions is the example of it. Algebrically, Q = f(L) or Q = f(K) etc.
Types of Production function: 4 Kamal Regmi (CAB)
Long Run Production function (Multi-variable Production Function): long run is that time period in which all the factors of production involved in the production process can be changed. Long run production function is the functional relationship between all the inputs used in production system and the output produced. We can measure the effect of various factors under this production function, therefore it is also called as Multi-variable production function. The law of returns to scale, Cobb-Douglas production function are the examples of it. Algebrically, Q = f(Ld, L, K, M, T, O….etc)
5 Kamal Regmi (CAB)
Cobb-Douglas Production Function: Two economists C.W.Cobb and P.H.Douglas developed a empirical production function on the basis of Long-run production function. This production function assumes labor and capital as factors of production used in the production process. This function not only shows the effect of units of labor and capital to total output but also reveals the productivity of labor and capital to total output. It also explains the relationship between Units of labor with Productivity of capital and v.v. Theoretically, it reflects constant returns to scale.
6 Kamal Regmi (CAB)
Mathematically, Q = A Lα Kβ Where, Q = Output Produced A = Proportionality Constant L = Units of Labor α = Productivity of labor K = Units of capital β = Productivity of capital Characteristics of Cobb-Douglas Production Function: It measures average Productivity of labor and capital. APL = Q /L = A Lα Kβ /L = A Lα-1 Kβ APK = Q /K = A Lα Kβ /K = A Lα Kβ-1
7 Kamal Regmi (CAB)
It also measures marginal Productivity of Inputs: MPL = ΔQ / ΔL = ∂(A Lα Kβ )/ ∂L = α A Lα-1 Kβ = α APL MPK = ΔQ / ΔK = ∂(A Lα Kβ )/ ∂K = β A Lα Kβ-1 = β APK It also measures marginal rate of technical substitution: MRTSLK = MPL / MPK = α/ β . K /L It measures the factor intensity using ratio between α and β. If α/β > 1 , There is operation of labor intensive production technique. If α/β < 1 , There is operation of capital intensive production technique. It measures the efficiency of Production. If the value of A is higher, There is higher degree of efficiency of production. If the value of A is lower, there is lower degree of efficiency of production.
8 Kamal Regmi (CAB)
It measures returns to scale: If α + β = 1, there is operation of constant returns to scale. If α + β > 1, there is operation of increasing returns to scale. If α + β < 1, there is operation of decreasing returns to scale. Concepts of Total Product (TP), Average Product (AP) and Marginal Product (MP): Total product (TP) : It is the sum total of production made by using all the factors of production available with the producer in given period of time. Mathematically, TP = AP X N or, TP = Σ MP = MP1 +MP2 +………+MP TP initially increases reaches to its maximum Point and finally decreases.
9 Kamal Regmi (CAB)
Average Product (AP): AP is the output per unit of the input. It is the outcome of Total Product divided by the total units of input. AP = TP/N AP initially increases slowly reaches to maxm and finally decreases. Marginal Product (MP): MP is the addition made to the total product with employment of one additional unit of the input. It is also the ratio between change in Total Product and change in units of inputs. MP = TPn – TP n-1 or, MP = ΔTP / ΔN MP also initially increases reaches to its maxm and finally decreases, MP can be zero and negative.
10 Kamal Regmi (CAB)
The Trends of TP, AP and MP can be explained by the help of Following Schedule and Diagram. 11 Kamal Regmi (CAB)
O Inputs TP, AP and MP TP AP MP 1 6 4 12 Kamal Regmi (CAB)
It is the law based on short-run production function. Also called as law of diminishing returns. Shows the effect on the output with the variation in factor proportions. Statement of law, “If we increase the units of variable factors keeping fixed factors constant, initially TP, AP and MP i.e. productivity will increase, it reaches to its maximum point and finally productivity will decline.” This law assumes labor as a variable factor keeping all other factors as constant.
The Law of Variable Proportions: 13 Kamal Regmi (CAB)
Labor is only the variable factor of production. All the units of labor are homogeneous. Technology of production remains constant. Factors can be changed in fixed proportions. Law of variable proportions can be explained with the help of following table and diagram by dividing it into the following three stages.
Assumptions of the law: 14 Kamal Regmi (CAB)
O Inputs TP, AP and MP TP AP MP 1 6 4 Stage I-stage of increasing returns Stage II-stage of decreasing returns Stage III-stage of negative returns 15 Kamal Regmi (CAB)
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Three stages of Production: Stage I – Stage of Increasing Returns: Starts from origin and ends with the maximum point of AP, where MP and AP are equal. TP increases throughout this stage, initially it increases at increasing rate and later it increases at slower rate. AP increases slowly and reaches to its maximum point at the end of this stage. MP initially increases sharply, reaches to its maximum point and finally decreases and becomes equal to AP at the end of this stage. It is called as stage of increasing returns because the AP of variable factor i.e. labor increases throughout this stage.
Kamal Regmi (CAB) 16
Causes of operation of this stage: Scarcity of variable factor i.e. labor. Indivisibility of fixed factors. Specialization in work through division of labor. Learning by doing. Under utilization of fixed factors. etc. Stage II- stage of decreasing returns: This stage starts with the end of stage-I and ends with the maximum constant point of TP where MP is zero. TP initially increases at decreasing rate, reaches to its maximum point and remains constant up to the end of this stage. Both AP and MP are diminishing but positive.
Kamal Regmi (CAB) 17
MP will be zero at the end of this stage where TP is maximum and constant. Also called as stage of decreasing returns because both MP and AP are decreasing. Causes of operation of this stage: Optimum utilization of resources. Indivisibility of fixed factors. Imperfect substitution of variable factors. Stage III – stage of negative returns: This stage starts with the end of second stage and this is the last stage of the production process. TP will be decreasing i.e. TP curve is sloping downwards.
Kamal Regmi (CAB) 18
AP curve slopes downwards but never be zero and negative. MP is negative i.e. MP curve is negatively sloped and falls below X-axis. Also called as stage of negative returns because MP of variable factor in this stage is negative. Causes of operation of this stage: Over utilization of fixed factors. Problem of management. Scarcity of fixed factors. Problem of responsibility etc.
Kamal Regmi (CAB) 19
Why a rational producer always wants to produce in stage- II? Optimum utilization of resources. Maximum total product i.e. highest TP. AP and MP both are positive. Maximum return from the use of inputs.etc. Limitations of the Law: State of technology keep on changing. All the factors can’t be changed in same proportion. It differs according to the efficiency of fixed factor. All the units of labor can’t be homogeneous.etc.
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