Law of Variable Proportion

By Harpreet CSE

Introduction

 The law of variable proportions states that as the quantity of one factor is increased, keeping the other factors fixed, the marginal product of that factor will eventually decline. This means that upto the use of a certain amount of variable factor, marginal product of the factor may increase and after a certain stage it starts diminishing. When the variable factor becomes relatively abundant, the marginal product may become negative.

Assumptions: The law of variable proportions holds good under the following conditions:

1.      Constant State of Technology: First, the state of technology is assumed to be given and unchanged. If there is improvement in the technology, then the marginal product may rise instead of diminishing.

2.      Fixed Amount of Other Factors: Secondly, there must be some inputs whose quantity is kept fixed. It is only in this way that we can alter the factor proportions and know its effects on output. The law does not apply if all factors are proportionately varied.

3.      Possibility of Varying the Factor proportions: Thirdly, the law is based upon the possibility of varying the proportions in which the various factors can be combined to produce a product. The law does not apply if the factors must be used in fixed proportions to yield a product.

Illustration of the Law: The law of variable proportion is illustrated in the following table and figure. Suppose there is a given amount of land in which more and more labour (variable factor) is used to produce wheat.

It can be seen from the table that upto the use of 3 units of labour, total product increases at an increasing rate and beyond the third unit total product increases at a diminishing rate. This fact is shown by the marginal product which  is the addition made to Total Product as a result of increasing the variable factor i.e. labour.

Units of Labour	Total Product	Marginal Product	Average Product
1	2	2	2
2	6	4	3
3	12	6	4
4	16	4	4
5	18	2	3.6
6	18	0	3
7	14	-4	2
8	8	-6	1

It can be seen from the table that the marginal product of labour initially rises and beyond the use of  three units of labour, it starts diminishing. The use of six units of labour does not add anything to the total production of wheat. Hence, the marginal product of labour has fallen to zero. Beyond the use of six units of labour, total product diminishes and therefore marginal product of labour becomes negative. Regarding the average product of labour, it rises up to the use of third unit of labour and beyond that it is falling throughout. 

Three Stages of the Law of Variable Proportions: -

1.      Stage of increasing returns.

2.      Stage of diminishing returns.

3.      Stage of negative returns.

These stages are illustrated in the following figure where labour is measured on the X-axis and output on the Y-axis.

Stage 1. Stage of Increasing Returns: In this stage, total product increases at an increasing rate up to a point. This is because the efficiency of the fixed factors increases as additional units of the variable factors are added to it. In the figure, from the origin to the point F, slope of the total product curve TP is increasing i.e. the curve TP is concave upwards upto the point F, which means that the marginal product MP of labour rises. The point F where the total product stops increasing at an increasing rate and starts increasing at a diminishing rate is called the point of inflection. Corresponding vertically to this point of inflection marginal product of labour is maximum, after which it diminishes. This stage is called the stage of increasing returns because the average product of the variable factor increases throughout this stage. This stage ends at the point where the average product curve reaches its highest point.

Stage 2. Stage of Diminishing Returns: In this stage, total product continues to increase but at a diminishing rate until it reaches its maximum point H where the second stage ends. In this stage both the marginal product and average product of labour are diminishing but are positive. This is because the fixed factor becomes inadequate relative to the quantity of the variable factor. At the end of the second stage, i.e., at point M marginal product of labour is zero which corresponds to the maximum point H of the total product curve TP. This stage is important because the firm will seek to produce in this range.

Stage 3. Stage of Negative Returns: In stage 3, total product declines and therefore the TP curve slopes downward. As a result, marginal product of labour is negative and the MP curve falls below the X-axis. In this stage the variable factor (labour) is too much relative to the fixed factor.

Importance and Applicability of the Law of Variable Proportion:

The Law of Variable Proportion has universal applicability in any branch of production. It forms the basis of a number of doctrines in economics. The Malthusian theory of population stems from the fact that food supply does not increase faster than the growth in population because of the operation of the law of diminishing returns in agriculture.

Ricardo also based his theory of rent on this principle. According to him rent arises because the operation of the law of diminishing return forces the application of additional doses of labour and capital on a piece of land. Similarly the law of diminishing marginal utility and that of diminishing marginal physical productivity in the theory of distribution are also based on this theory.

The law is of fundamental importance for understanding the problems of underdeveloped countries. In such agricultural economies the pressure of population on land increases with the increase in population. This leads to declining or even zero or negative marginal productivity of workers. This explains the operation of the law of diminishing returns in LDCs in its intensive form. Ragnar Nurkse have suggested ways to make use of these disguisedly unemployed labour by withdrawing them and putting them in those occupations where the marginal productivity is positive.

Cost Curves

By Rohit Chauhan ECE

 COST CURVES

  Cost function : The general name for the relation between output and cost is cost function.       Cost functions are derived functions. These are derived from the production function,which describes the available efficient methods of production at any one time.

 Concepts of cost: The concept of cost is used in a variety of ways .Important concepts of cost  are as follows-

1)      Money cost: The amount spent in terms of money for the production of a commodity is called money cost.

2)      Real cost: The mental and physical efforts and sacrifices undergone with a view to producing a commodity are its real cost

3)      Accounting cost: accounting cost refer to cash payments which firms make for factor and non-factor inputs, depreciation and other book keeping entries.

4)      Opportunity cost: Opportunity cost of a particular product is the value of the foregone alternative product that resources used in its production.

5)      Economic cost: In the economic analysis , economic cost includes both accounting costs and opportunity costs of self owned and  self – employed resources.

6)      Social cost: the social cost is the total to society of an economic activity. the economic organisation of every society is characterised by certain social cost such as pollution and noise which are not taken by firms in determining their price levels. Social cost is the opportunity cost rather than just one firm or individual.

7)      Private cost: private cost is the cost incurred by an individual firm for producing commodity. It includes both the explicit cost as well as implicit cost.

8)      Explicit cost: explicit costs are those cash payments which firms make to outsiders who supply labour services, material, fuel, transportation services, power and so forth are called explicit  costs.

9)      Implicit cost: Implicit costs are costs of self-owned or self-employed.

10)  Past and future costs: Past costs are actual costs incurred in the past. These costs are mentioned in the accounts. Future costs are those costs which are to be incurred in the near future. This is only a forecast. Future costs matter for managerial decision because, the management can evaluate the desirability of that expenditure. Since the past costs  are costs that have already been incurred, there is no scope for managerial decision.

Cost curve

In economics, a cost curve is a graph of the costs of production as a function of total quantity produced. In a free market economy, productively efficient firms use these curves to find the optimal point of production (minimising cost), and profit maximizing firms can use them to decide output quantities to achieve those aims. There are various types of cost curves, all related to each other, including total and average cost curves, and marginal ("for each additional unit") cost curves, which are the equal to the differential of the total cost curves. Some are applicable to the short run, others to the long run.

There are two types of cost curve which are given below-

A (I) Short-run average variable cost curve (SRAVC)

Average variable cost (which is a short-run concept) is the variable cost (typically labour cost) per unit of output: SRAVC = wL / Q where w is the wage rate, L is the quantity of labour used, and Q is the quantity of output produced. The SRAVC curve plots the short-run average variable cost against the level of output, and is typically drawn as U-shaped.

 (II)  Short-run average total cost curve (SRATC or SRAC)

                                                                                                                    short run average cost curve

The average total cost curve is constructed to capture the relation between cost per unit of output and the level of output, ceteris paribus. A perfectly competitive and productively efficient firm organizes its factors of production in such a way that the average cost of production is at the lowest point. In the short run, when at least one factor of production is fixed, this occurs at the output level where it has enjoyed all possible average cost gains from increasing production. This is at the minimum point in the diagram on the right.

Short-run total cost is given by

STC = P_KK+P_LL,

where P_K is the unit price of using physical capital per unit time, P_L is the unit price of labor per  unit time (the wage rate), K is the quantity of physical capital used, and L is the quantity of labor used. From this we obtain short-run average cost, denoted either SATC or SAC, as STC / Q:

SRATC or SRAC = P_KK/Q + P_LL/Q = P_K / AP_K + P_L / AP_L,

where AP_K = Q/K is the average product of capital and AP_L = Q/L is the average product of labor.

Short run average cost equals average fixed costs plus average variable costs. Average fixed cost continuously falls as production increases in the short run, because K is fixed in the short run. The shape of the average variable cost curve is directly determined by increasing and then diminishing marginal returns to the variable input (conventionally labour)

(III) Short-run marginal cost curve (SRMC)

                                                                                                                             Typical marginal cost curve

A short-run marginal cost curve graphically represents the relation between marginal (i.e., incremental) cost incurred by a firm in the short-run production of a good or service and the quantity of output produced. This curve is constructed to capture the relation between marginal cost and the level of output, holding other variables, like technology and resource prices, constant. The marginal cost curve is U-shaped. Marginal cost is relatively high at small quantities of output; then as production increases, marginal cost declines, reaches a minimum value, then rises. The marginal cost is shown in relation to marginal revenue, the incremental amount of sales revenue that an additional unit of the product or service will bring to the firm. This shape of the marginal cost curve is directly attributable to increasing, then decreasing marginal returns (and the law of diminishing marginal returns). Marginal cost equals w/MP_L. For most production processes the marginal product of labour initially rises, reaches a maximum value and then continuously falls as production increases. Thus marginal cost initially falls, reaches a minimum value and then increases. The marginal cost curve intersects both the average variable cost curve and (short-run) average total cost curve at their minimum points. When the marginal cost curve is above an average cost curve the average curve is rising. When the marginal costs curve is below an average curve the average curve is falling. This relation holds regardless of whether the marginal curve is rising or falling.

B (I) Long-run average cost curve (LRAC)

                                                                                                                        long run average cost curve

The long-run average cost curve depicts the cost per unit of output in the long run—that is, when all productive inputs' usage levels can be varied. All points on the line represent least-cost factor combinations; points above the line are attainable but unwise, while points below are unattainable given present factors of production. The behavioural assumption underlying the curve is that the producer will select the combination of inputs that will produce a given output at the lowest possible cost. Given that LRAC is an average quantity, one must not confuse it with the long-run marginal cost curve, which is the cost of one more unit. The LRAC curve is created as an envelope of an infinite number of short-run average total cost curves, each based on a particular fixed level of capital usage. The typical LRAC curve is U-shaped, reflecting increasing returns of scale where negatively-sloped, constant returns to scale where horizontal and decreasing returns (due to increases in factor prices) where positively sloped. Contrary to Viner’s, the envelope is not created by the minimum point of each short-run average cost curve This  mistake is recognized as Viner's Error.

In a long-run perfectly competitive environment, the equilibrium level of output corresponds to the minimum efficient scale, marked as Q2 in the diagram. This is due to the zero-profit requirement of a perfectly competitive equilibrium. This result, which implies production is at a level corresponding to the lowest possible average cost,  does not imply that production levels other than that at the minimum point are not efficient. All points along the LRAC are productively efficient, by definition, but not all are equilibrium points in a long-run perfectly competitive environment.

In some industries, the bottom of the LRAC curve is large in comparison to market size (that is to say, for all intents and purposes, it is always declining and economies of scale exist indefinitely). This means that the largest firm tends to have a cost advantage, and the industry tends naturally to become a monopoly, and hence is called a natural monopoly. Natural monopolies tend to exist in industries with high capital costs in relation to variable costs, such as water supply and electricity supply.

B(II) Long-run marginal cost curve (LRMC)

The long-run marginal cost curve shows for each unit of output the added total cost incurred in the long run, that is, the conceptual period when all factors of production are variable so as minimize long-run average total cost. Stated otherwise, LRMC is the minimum increase in total cost associated with an increase of one unit of output when all inputs are variable.

The long-run marginal cost curve is shaped by economies and diseconomies of scale, a long-run concept, rather than the law of diminishing marginal returns, which is a short-run concept. The long-run marginal cost curve tends to be flatter than its short-run counterpart due to increased input flexibility as to cost minimization. The long-run marginal cost curve intersects the long-run average cost curve at the minimum point of the latter. When long-run marginal costs are below long-run average costs, long-run average costs are falling (as to additional units of output). When long-run marginal costs are above long run average costs, average costs are rising. Long-run marginal cost equals short run marginal-cost at the least-long-run-average-cost level of production. LRMC is the slope of the LR total-cost function.