MCom I Semester Managerial Economics Production Function Iso Curves Iso Cost Lines Study Material

MCom I Semester Managerial Economics Production Function Iso Curves Iso Cost Lines Study Material: Meaning and Definition of Iso Product Curves Explanation Withe the Help of Table and Diagram Iso product Map Properties of Iso Product Curves Iso Cost Line Or Factor Price Line Producer Equilibrium With the Help or Iso Product Curves Estimation of Production Function  :

MCom I Semester International Trading Environment World Trade Problems developing Countries Notes

PRODUCTION FUNCTION ISO PRODUCT CURVES AND ISO COST LINES

MEANING AND DEFINITION OF ISO-PRODUCT CURVES

Every producer wants to achieve maximum production at minimum cost. For this purpose, he wants to establish optimum combination of the factors of production with which he can achieve his object. This problem is solved by ISO-product curves. ISO-product curves represent different combinations of two factors of production with which a firm can achieve equal amounts of product. It has been defined as under:

1 “An ISO-product curve is a curve along which the maximum achievable rate of production is constant.” -K. J. Cohen and R. M. Covert

2. “ISO-product curve represents all the possible combinations of two factors that will give the same total product.”

Thus, an ISO-product curve is a curve that represents all possible combinations of two factors of production which produce equal amounts of production. A producer is indifferent to all these combinations. It is known as Production Indifference Curve or ISOQUANTS.

EXPLANATION WITH THE HELP OF TABLE AND DIAGRAM

A given output can be achieved by employing different combinations of factors of production. Let us assume that a firm can produce 10 units of a commodity by employing any of the following alternative combinations of two factors ‘r’ and ‘y’. This is illustrated as above.

In given diagram, units of factor ‘r’ have been presented on ‘ox’ axis and the units of factory has been presented on ‘ov’ axis. A, B, C, D, E are the combinations of factor ‘x’ and factory which produce equal amount of production i.e., 10 units. A curve ‘IP’ has been drawn incorporating all these combinations. This curve is the ISO-product curve.

ISO-PRODUCT MAP

A producer may have a number of ISO-product curves. When a producer increases the quantity of one factor of production, keeping and quantity of other factors of production constant, quantity of production increases. When production. combinations are presented on a single graph, it is called ISO-product map. It can be explained with the help of 3 following diagram :

In this diagram, units of Factor x factor ‘y’ have been presented on ov-axis. IP, IP, IP3, IP: are ISO-product curves. At IP, the producer has employed ON units of factor x and OP units of factory and getting the production of 10 units. He keeps the units of factor y constant and increases the quantity of factor x to ON, ON, and ON). As a result, production increases to 20 units, 30 units and 40 units respectively on 1P, IP, and IP.

PROPERTIES OF ISO-PRODUCT CURVES

(1) ISO-Product Curves Slope Downwards to the right. Right. ISO product curves always slope downwards to the right. It implies that a decrease in the quantity of one factor of production must be associated with an increase in the quantity of another factor of production so that the same level of production may be maintained. It is illustrated in the above diagram.

In this diagram illust- rates that the quantity of one factor should be increased and that of another factor should be decreased to get the same quantity of production. Thus, ISO-product curve can neither slope are convex to the origin upward to the right, nor can it be horizontal

(2) ISO-Product Curves are Convex to the Origin. ISO-product curve are convex to the origin because the marginal rate of substitution diminishes along an ISO-product curve. It can be illustrated with the help of following diagram:

In this diagram illustrates that to YA obtain every additional unit of x less and less amount of y is given up. Due cannot be in this form to this reason, ISO-product curve has to be convex to the origin.

(3) ISO-Product Curves cannot Intersect Each Other. ISO-product curves cannot intersect each other because all the ISO-product curves represent different levels of production. It can be illustrated with the help of following diagram :

This diagram illustrates that two ISO-product curves intersect each other at a certain point which is a logical absurdity. It contradicts the statement that an ISO-product curve lying to the right represents a larger output.

(4) An ISO-Product Curve Lying to the Right lying to the right represents Represents Larger Output. An ISO-product curve lying to the right implies greater amount of both the factors of production. Therefore, it yields greater amount of production. It has been illustrated with the help of following diagram:

This diagram illustrates two ISO-product curves. IP, uses greater amount of both the factors of production that IP. As a result, it yields greater output.

ISO-COST LINE OR FACTOR PRICE LINE

ISO-cost line indicates different combinations of two factors of production which a firm can purchase at given prices with a given cost. ISO-cost line is always a straight line. If total cost increases, ISO-cost line moves represents different to the right and if total cost combinations of two factors of production which a firm can decreases, it moves to the left. It can be illustrated with the help of following diagram:

In this diagram, units of factor x have been presented on ox axis and the units of factory y have been presented on oy axis. AB is ISO-cost line. It represents various combinations of factor x and y which a firm can purchase for Rs. 1,000. If it wants to spend Rs. 1,200, ISO-cost line moves to the right and A, B, becomes new ISO-cost line. If the firm wants to spend Rs. 800, ISO-cost line moves to the left and AB becomes the ISO-cost line.

PRODUCER’S EQUILIBRIUM WITH THE HELP OF ISO-PRODUCT CURVES

With the help of ISO-product curves, a producer can choose an optimum factor combination. Optimum factor combination refers to the combination of factors of production which produces output at minimum cost. A firm can achieve a given output with several factor combination, so a producer always seeks to achieve a combination that may yield a given output at minimum cost per unit.

Equilibrium of a producer can take place in two different forms:

(1) When ISO-Cost Line is Given. If ISO-cost line is given for a producer, he will be at equilibrium at the point at which an ISO-Product curve touches the ISO-Cost line. It implies that the producer is not in a position to change his cost of production. The only thing he can do is that he can change The quantity of production. Naturally, he would like to produce at the point h his cost is minimum. It can be illustrated with the help of following

In this diagram, units of producer is in the state of factory which Iso-cost line touches have been presented on AB is ISO-cost line. IP, IP2 and IP, are ISO-product curves. AB line touches IP, at the point E. Itwill be the point of equilibrium. At this point, the

Units of Factor X producer will use OM units of factor x and ON units of factory and will get a given output at Equilibrium minimum cost. He would not

when ISO-Cost Line is given. like to work at IP, because he will be working below his capacity at this curve. IP: is out of his cost line, so would not like to work at this curve also.

(2) When ISO-Product Curve is Given. If ISO-product curve is given for the producer, he will be at equilibrium at the point at which this curve touches an ISO-cost line. It implies that the producer is not A producer will be in the state in a position to change the equilibrium at the point quantity of production. The touches an Iso-cost line. only thing he can do is that he can change the combination which will minimise his cost. It can be illustrated with the help

Quantity of Factor X ox axis and the units of factory y on oy axis. IP is the Fig. 16.9. Producer’s Equilibrium when ISO-product curve. A,B,A,B A3B; and ABare the ISO-cost lines. IP curve touches AB, line. It is the point of equilibrium. At this point, the producer will use OM quantity of factor x and ON quantity of factor y. At this point, the producer will get maximum production at minimum cost. The producer cannot produce at A,B, and A2B2 cost lines because they are out of his reach. A.B. is the cost line which is below his production capacity. Therefore, he would always be working at the point of equilibrium.

ESTIMATION OF PRODUCTION FUNCTION

The production function is the central part of production theory is a theoretical interest in its estimates. A few important production functions are given below to estimate the problem: 1. Linear Homogeneous Production Function

When all the inputs are increased in the same proportion, the production function is said to be homogeneous. The degree of production function is equal to one. This is known as linear homogeneous production function. In order to estimate the production function, it is necessary to express the function as:

nQ = f(nL, nk) This production function implies constant returns to scale. That is if L and K are increased by n-fold, the output also increases by n-fold. This firm of Production function makes the task of the enterpreneur quite simple and convenient. 2. Cobb-Douglas Production Function

Charles W. Cobb and Paul H. Douglas studied the relationship of inputs and outputs and formed an empirical production function, popularly known as Cobb-Douglas production function. The Cobb-Douglas production function is expressed by

Q = AL“ K Where is output and L and K are inputs of labour and capital respectively. A, a and Bare positive parameters, where a > 0, B>0.

The equation tells that output depends directly on L and K and that part of output which cannot be explained by L and K is explained by A which is the ‘residual’, often called technical change.

The marginal products of labour and capital are the functions of the parameters A, a and B and the ratios of labour and capital inputs. That is,

og =a ACK SL

MP3

MPx =

=B AL“ KB-1

SK The two parameters a and B taken together measure the degree of the homogeneity of the function. In other words, this function characterises the returns to scale thus :

a+B>1 : Increasing returns to scale a + B = 1 : Constant returns to scale

a+B<1 : Decreasing returns to scale.

The Cobb-Douglas production function is a multiplicative type and is non-linear in its general form, it can be transferred into linear function by taking it in its logarithmic form. That is why, this function is also known as log linear function, which is

Log = log A + a log L+ Blog K

It is easier to compute this function when expressed in log linear form.

Properties of Cobb-Douglas Production Function

The Cobb-douglas production function has the following properties :

(i) There are constant returns to scale.

(ii) Elasticity of substitution is equal to one.

(iii) a and B represent the labour and capital shares of outpout! respectively.

(iv) a and B are also elasticities of output with respect to labour and capital respectively

(v) If one of the inputs is zero, output will also be zero.

(vi) The marginal product of labour is equal to the increase in output when the labour input is increased by one unit.

(vii) The average product of labour is equal to the ratio between output and labour input.

Importance Or Merit of Cobb-Duglas Production Function

This production function possesses the following merits :

(i) It suits to the nature of all industries.

(ii) It is convenient in international and inter-industry comparisons.

(iii) It is the most commonly used function in the field of econometrics.

(iv) It can be fitted to time series analysis and cross section analysis.

(v) The function can be generalised in the case of ‘n factors of production.

(vi) The unknown parameters a and B in the function can be easily computed.

(vii) It becomes linear function in logarithm.

(viii) It is more popular in empirical research.

Limitations of Cobb-Douglas Production Function

1 Cobb-Douglas Production Function is based upon the assumption that total production increases only according to the law of constant returns but his assumption is not real.

2.This Production Function is based upon the assumption that the labour and capital are the only inputs but this assumption is also not correct.

3. Cobb-Douglas Production Function is not suitable for agriculture production.

4 This function considers difference between industries only. It does not consider the difference between firms of industry.