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In this article we will discuss about:- 1. Concept of Isoquant 2. Characteristics of an Isoquant 3. Isoquant Map 4. Types of Isoquants 5. Iso-Cost Line 6. Shift in the Iso-Cost Line.
Concept of Isoquant:
An isoquant shows various combinations of two factors that will enable a producer to produce a same level of output. In other words, each point of an isoquant will represent a technology and as we move from one point to another on an isoquant we switch across technologies.
An isoquant, therefore, depicts all the technological possibilities graphically and show a substitution between two factors while keeping the output same.
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As such, an isoquant represents one specific level of output or for each level of output there will be an isoquant. Following text provides a few definitions of an isoquant.
An isoquant shows alternative combinations of the two factors, each of which enables to produce a same quantity of output. Defining differently, an isoquant is the contour of all the combination of two factors that give rise to a same level of output.
In the words of Cohen and Cyert, an iso-product curve is a curve along which the maximum achievable production is constant.
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According to Salvatore, isoquant shows the different combinations of two inputs that a firm can use to produce a specific quantity of output.
Table-8.1, in this regard, presents an isoquant schedule which shows different possible combinations of labour and capital to product 50 kilograms of tea.
One can observe from the table that 50 kilograms of tea can be produced by any combination ranging from A to E. The combination A uses more of capital (45 units) and less of labour (1 unit) while combination E other way round.
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The table further shows that as the producer uses more of one factor input, labour in the table, it reduces the use of other factor. For example, moving from combination A to B, labour increases by one unit while capital decline by 15 units or substituting 15 units of capital by one additional unit of labour. This will be further explained under the concept of marginal rate of technical substitution (MRTS).
All these combinations are plotted in Figure-8.1 by taking labour on X-axis and capital on Y-axis. It provides a curve, the isoquant, which is downward sloping and convex to the origin. It shows all the technically efficient alternative methods of production facilitating production of the same 50 kilograms of tea. The level of output being same, the producer will be indifferent across all the combinations on the isoquant. Hence, it is also named as producer’s indifference curve.
Characteristics of an Isoquant:
Basic characteristics of an isoquant are same as that of an indifference, hence, they are discussed briefly with regard to an isoquant below.
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Slopes Downwards from Left to the Right:
An isoquant slopes downward from left to right or is negatively sloped, as can be seen from Figure-8.1. Such a shape implies that if a firm employs more of labour, it will employ less of capital or vice versa, in order to maintain the level of output.
Such a shape of isoquant also means that the marginal factor productivities are positive, that is more of a factor will make a positive contribution in production and less of other factor will make a negative contribution. To remain on the same isoquant or to maintain the same level of output, the positive and negative factor contributions should be equal.
When we move from point A to B in Figure-8.1, labour contribution increases while that of capital will fall. Hence —
Only a downward sloping isoquant will satisfy such behaviour since it only shows substitution of one factor with other. No other shape of an isoquant, whether positively slopped or parallel to X-axis or parallel to Y-axis, will show such a feature. Thus, an isoquant, in general, should slope downward from left to right.
Convex to the Point of Origin:
This characteristic of isoquant means that the producer is willing to sacrifice fewer and fewer units of capital for every additional unit of labour and vice versa. It is depicted in Figure-8.2.
As we move down on the curve from point A to point F his willingness to sacrifice capital for every additional unit of labour comes down from 5 to 1. As such —
Such behaviour of an isoquant is based on the principle of diminishing MRTS. No other shape of isoquant, whether concave or a straight line, will show such a feature. In case of a concave isoquant the MRTS will be increasing while in case of a straight line isoquant, it will be constant.
Both of which are logically incorrect because no producer will be willing to sacrifice a larger or same quantities, respectively, of a factor for successively more of other if the marginal factor productivities are diminishing. Thus, an isoquant will be, in general, convex to the point of origin.
A Higher Isoquant Denotes a Higher Level of Output:
Another basic characteristic of an isoquant is that greater its distance from the point of origin, higher output level it will represent. This is shown in Figure-8.3 where combination B on isoquant Q2 (OL2 + OK2) shows more of both factors as compared to point A on isoquant Q1 (OL1 + OK1).
Given that marginal factor productivities across the entire length of an isoquant is positive, the point B should indicate a higher level of output than that of point A. This shows that a higher isoquant will represent a higher level of output vis-a-vis a lower isoquant.
Two Isoquants Never Intersect Each Other:
Two isoquants representing different levels of output can never intersect. If they do so, it will produce an absurd result. To show this, we have drawn two isoquants Q1 (= 100 units) and Q2 (= 200 units) intersecting each other at point A in Figure-8.4.
It means that at the point of intersection the factor combination, OK + OL can produce 100 units as well as 200 units of output. Such a situation makes no sense as one factor combination can produce only one level of output.
Even at other points, two intersecting isoquants will produce absurd results which will make it impossible to decide which one of them represents a higher level of output – a higher isoquant will show a higher level of output at one point and lower output at other point. Similar will be the case on a lower isoquant. Hence, it can be concluded that isoquants will never intersect with each other.
Isoquant Map:
An isoquant map, as shown in Figure-8.6, is a cluster of isoquants, each one of which represents production of a specific quantity of output. As we move on an isoquant map, away from the point of origin or on a higher isoquant, it will show a higher level of output. In other words, an isoquant closer to the point of origin will indicate a lower level of output. In the figure, isoquant Q1 represents a lower level of output as compared to isoquant Q2 and Q3.
Types of Isoquants:
The isoquant may assume various shapes depending upon the degree of substitutability of factors.
While a smooth and convex isoquant is its normal shape, there are a few exceptional shapes as well, two of which are discussed below:
Linear Isoquant:
This type of isoquant are depicted by a straight line sloping downward from left to right, as shown in Figure-8.6 (a). It indicated a perfect and unlimited substitutability between two factors implying that the product may be produced even by using only capital or labour or by infinite combinations of the two factors.
Input-Output Isoquant:
Input-output isoquants are L-shaped curve [Figure-8.6 (b)] and also known as Leontief isoquants. They assume a perfect complementary nature between factors implying zero substitutability. Factors are jointly used in a fixed proportion. It means that there is only one method of production to produce a commodity. Hence, to increase output, both factors are to be increased holding the proportion constant.
Iso-Cost Line:
The iso-cost line shows various possible combinations of the two factors which a producer can have given the factor prices and producer’s total outlay.
An iso-cost line is the locus of all the combinations of two factors that a producer can procure from the market at the given factor prices from a given amount of outlay.
An iso-cost line shows various possible combinations of the two factors which a producer can procure from the market at the given factor prices from a given amount of outlay.
The iso-cost function in a two factor modal can be written as —
Firm’s total outlay = Payment to labour + Payment to capital
Or, C = w.L + r.K
Where, C is the total outlay incurred by the firm on the two factors; the w and L are the price of labour (or wage rate) and number of labour units and, r and K are the price of capital (or interest rate) and number of capital units, respectively.
If the firm spends its entire outlay on labour, then —
C = w.L + r.0 = w.L or, L = C/w
Similarly, if L = 0, than, C = w.0 + r.K = r.k or, K = C/r
Based on it, an iso-cost line can be drawn, as shown in Figure-8.7.
In the figure, labour is taken on X-axis as OL (= C/w) and capital on Y-axis as OK (= C/r), the maximum quantity of labour and capital the firm can have. Joining points K and L by a straight line we get the iso-cost line which shows the combinations of labour and capital that the firm can purchase at given factor prices. The slope of this line can be estimated as —
OK/OL = (C/r)/(C/w) = w/r
In other words, slope of iso-cost line will be ratio of two factor prices (PL/PK).
Shift in the Iso-Cost Line:
An iso-cost line is drawn on two assumptions – First, at given total outlay of the firm and, second, at given factor prices. Thus, an iso-cost line will shift either because of a change in total outlay or a change in factor prices.
A change in total outlay will cause a parallel shift in the iso-cost line, as there will be no change in its slope, factor prices being constant. If the total outlay increases, the iso-cost line will shift upward, away from the point of origin, and if the total outlay decreases, the line will shift downward or towards the origin.
Both the types of shift have been shown in Figure-8.8 (a). The iso-cost line shifts in a parallel fashion from AB to CD when total outlay increases and from AB to EF if it declines.
A change in price of labour (wage rate) or capital (interest) or both will result into a change in the slope of the iso-cost line making it flatter or steeper depending upon the nature of change in factor prices.
If the wage rate declines, for example, without any change in the interest rate or in the total outlay, the firm can buy more of labour and, hence the iso-cost line will become flatter. Similarly, if labour becomes expensive the line will become steeper. In the Figure 8.8 (b), the iso-cost line (AB) becomes flatter (AB1) when wage rate falls and becomes steeper (AB2) when it rises.
In the same manner, slop of iso-cost line will change when interest rate changes and it may become steeper or flatter. In the Figure 8.8 (c), the iso-cost line (AB) becomes flatter (A2B) when interest rate increases and becomes steeper (A1B) when the interest rate falls.
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