Iso-Product Curve/Iso-Quant Curve:
From the above schedule iso-product curve can be
drawn with the help of a diagram. An. equal product curve represents all those
combinations of two inputs which are capable of producing the same level of
output. The Fig. 1 shows the various combinations of labour and capital which
give the same amount of output. A, B, C, D and E.
Iso-Product Map or Equal Product Map:
An Iso-product map
shows a set of iso-product curves. They are just like contour lines which show
the different levels of output. A higher iso-product curve represents a higher
level of output. In Fig. 2 we have family iso-product curves, each representing
a particular level of output.
Properties of
Iso-Product Curves:
The properties of
Iso-product curves are summarized below:
1. Iso-Product Curves
Slope Downward from Left to Right:
They slope downward
because MTRS of labour for capital diminishes. When we increase labour, we have
to decrease capital to produce a given level of output.
The Fig. 3 shows that
when the amount of labour is increased from OL to OL1, the amount of capital
has to be decreased from OK to OK1, The iso-product curve (IQ) is falling as
shown in the figure.
The possibilities of
horizontal, vertical, upward sloping curves can be ruled out with the help of
the following figure.
(i) The figure (A)
shows that the amounts of both the factors of production are increased- labour
from L to Li and capital from K to K1. When the amounts of both factors
increase, the output must increase. Hence the IQ curve cannot slope upward from
left to right.
(ii) The figure (B)
shows that the amount of labour is kept constant while the amount of capital is
increased. The amount of capital is increased from K to K1. Then the output
must increase. So IQ curve cannot be a vertical straight line.
(iii) The figure (C)
shows a horizontal curve. If it is horizontal the quantity of labour increases,
although the quantity of capital remains constant. When the amount of capital
is increased, the level of output must increase. Thus, an IQ curve cannot be a
horizontal line.
2. Isoquants are Convex
to the Origin:
Like indifference
curves, isoquants are convex to the origin. In order to understand this fact,
we have to understand the concept of diminishing marginal rate of technical
substitution (MRTS), because convexity of an isoquant implies that the MRTS
diminishes along the isoquant. The marginal rate of technical substitution
between L and K is defined as the quantity of K which can be given up in
exchange for an additional unit of L. It can also be defined as the slope of an
isoquant.
It can be expressed as:
MRTSLK = – ∆K/∆L = dK/
dL
Where ∆K is the change
in capital and AL is the change in labour.
Equation (1) states
that for an increase in the use of labour, fewer units of capital will be used.
In other words, a declining MRTS refers to the falling marginal product of
labour in relation to capital. To put it differently, as more units of labour
are used, and as certain units of capital are given up, the marginal
productivity of labour in relation to capital will decline.
This fact can be
explained in Fig. 5. As we move from point A to B, from B to C and from C to D
along an isoquant, the marginal rate of technical substitution (MRTS) of
capital for labour diminishes. Every time labour units are increasing by an
equal amount (AL) but the corresponding decrease in the units of capital (AK)
decreases.
Thus it may be observed
that due to falling MRTS, the isoquant is always convex to the origin.
3. Two Iso-Product
Curves Never Cut Each Other:
As two indifference
curves cannot cut each other, two iso-product curves cannot cut each other. In
Fig. 6, two Iso-product curves intersect each other. Both curves IQ1 and IQ2
represent two levels of output. But they intersect each other at point A. Then
combination A = B and combination A= C. Therefore B must be equal to C. This is
absurd. B and C lie on two different iso-product curves. Therefore two curves
which represent two levels of output cannot intersect each other.
4. Higher Iso-Product Curves Represent
Higher Level of Output:
A higher iso-product
curve represents a higher level of output as shown in the figure 7 given below:
In the Fig. 7, units of
labour have been taken on OX axis while on OY, units of capital. IQ1 represents
an output level of 100 units whereas IQ2 represents 200 units of output.
5. Isoquants Need Not
be parallel to Each Other:
It so happens because
the rate of substitution in different isoquant schedules need not be
necessarily equal. Usually they are found different and, therefore, isoquants
may not be parallel as shown in Fig. 8. We may note that the isoquants Iq1 and
Iq2 are parallel but the isoquants Iq3 and Iq4 are not parallel to each other.
6. No Isoquant can Touch Either Axis:
If an isoquant touches
X-axis, it would mean that the product is being produced with the help of
labour alone without using capital at all. These logical absurdities for OL
units of labour alone are unable to produce anything. Similarly, OC units of
capital alone cannot produce anything without the use of labour. Therefore as
seen in figure 9, IQ and IQ1 cannot be isoquants.
7. Each Isoquant is Oval-Shaped.
It means that at some
point it begins to recede from each axis. This shape is a consequence of the
fact that if a producer uses more of capital or more of labour or more of both
than is necessary, the total product will eventually decline. The firm will
produce only in those segments of the isoquants which are convex to the origin
and lie between the ridge lines. This is the economic region of production. In
Figure 10, oval shaped isoquants are shown.
Curves OA and OB are
the ridge lines and in between them only feasible units of capital and labour
can be employed to produce 100, 200, 300 and 400 units of the product. For
example, OT units of labour and ST units of the capital can produce 100 units
of the product, but the same output can be obtained by using the same quantity
of labour T and less quantity of capital VT.
Thus only an unwise
entrepreneur will produce in the dotted region of the iso-quant 100. The dotted
segments of an isoquant are the waste- bearing segments. They form the
uneconomic regions of production. In the up dotted portion, more capital and in
the lower dotted portion more labour than necessary is employed. Hence GH, JK,
LM, and NP segments of the elliptical curves are the isoquants.