Least-Cost Combination
The
problem of least-cost combination of factors refers to a firm getting the
largest volume of output from a given cost outlay on factors when they are
combined in an optimum manner.
In
the theory of production, a producer will be in equilibrium when, given the
cost-price function, he maximizes his profits on the basis of the least-cost
combination of factor. For this he will choose that combination of factors
which maximizes his cost of production. This will be the optimum combination
for him.
Assumptions
The
assumptions on which this analysis is based are:
1. There are two factors. Capital and labor.
2. All units of capital and labor are homogeneous.
3. The prices of factors of production are given and constant.
4. Money outlay at any time is also given.
5. Perfect competition is prevailing in the factor market.
On the basis of given prices of
factors of production and given money outlay we draw a line A, B.
The firm cannot choose and neither
combination beyond line AB nor will it chooses any combination below this line.
AB is known as the factor price line or cost outlay line or iso-cost line. It
is an iso-cost line because it represents various combinations of inputs that
may be purchased for the given amount of money allotted. The slope of AB shows
the price ratio of capital and labour, i.e.,
By combining the isoquants and the factor-price line, we can find out the
optimum combination of factors. Fig. illustrates this point.
In the Fig. equal product curves IQ1,
IQ2 and IQ3 represent outputs of 1,000 units, 2,000 units
and 3,000 units respectively. AB is the factor-price line. At point E the
factor-price line is tangent to iso-quant IQ2 representing 2,000
units of output. Iso-qunat IQ3 falls outside the factor-price line
AB and, therefore, cannot be chosen by the firm. On the other hand, iso-quant
IQ, will not be preferred by the firm even though between R and S it falls with
in the factor-price line. Points R and S are not suitable because output can be
increased without increasing additional cost by the selection of a more
appropriate input combination. Point E, therefore, is the ideal combination
which maximizes output or minimizes cost per units: it is the point at which
the firm is in equilibrium.
What does the point of tangency tell
us? At that point the slope of the factor-price line AB and the slope of the
iso-quant IQ2 are equal. The slope of the factor-price line reflects
the ratio of prices of the two factors. Viz, capital and labour. The slope of
the iso-quant reflects the marginal rate of technical substitution. At point E
the ratio of prices of capital and labour is equal to the marginal rate of
technical substitution. The condition of optimal combination is, therefore,
given by the equality of the ratio of prices between any two factors and the
rate of technical substitution between them. This is the point at which and
firm is able to produce maximum quantity and at minimum cost.
Every firm, interested in maximising
output or minimising cost, must therefore, consider (a) factor-price ratio
which tells the firm the rate at which it can substitute one factor for another
in purchasing, and (d) the marginal rate of technical substitution which tells
the firm the rate at which it can substitute one factor for another in
production. So long as the two are not equal, a firm can achieve a greater output
or a lower cost by moving in the direction of equality.
No comments:
Post a Comment