Optimum Input combination or Least cost Combination
Optimum Input combination or Least cost Combination
A profit-maximizing firm seeks to minimize its cost for a
given output or to maximize its output for a given total cost. There are various
combinations of factors of production available to produce a given output
but a rational producer would seek to produce that output with the ‘optimum’ or
‘least cost’ combination of factors of production. Maximum output with minimum
cost is possible at the equilibrium point where the Isoquant curve
is tangent to the Iso-cost line.
Isoquant curve: An isoquant curve is locus of
points representing various combinations of two inputs-capital and labor-
yielding the same output. In other words, an isoquant curve shows all those
combinations of two variable inputs which yield a given quantity of product.
Isoquant Map
A number of isoquants representing different amount of output are known as isoquant map. Higher isoquant curve shows higher quantity of output.
Iso-Cost Line: Iso-cost line represents the different
combinations of the two inputs which the firm can purchase at the given prices
and the given amount of the total money which a firm wants to spend. It also
known as price-line, outlay-line or budget-line.
The slope of the iso-cost line represents the ratio of the
price of a unit of input X to the price of a unit of input Y. In case, the
price of any one of them changes, there would be a corresponding change in a
slope of the iso-cost curve and the equilibrium point would shift too.
Assumptions:
1. There are only two factors: Labour and capital.
2- All units of both inputs are homogeneous.
3- The price of both inputs are given and it should remain constant.
4- The producer aims at minimizing the cost and maximizing the profit.
Producer’s Equilibrium: Optimum Factor Combination
Marginal rate of technical substitution between both inputs must be
equal to the ratio of their marginal physical product.
Where ΔK | ΔL is the marginal rate of technical substitution between K and L and MPL/MPK is the ratio of marginal productivity of L and K.
The
marginal physical product ratio of Capital and Labor must be equal to their
price ratio. This condition can be written as:
The producer will be in equilibrium at the point E
where the Isoquant IQ and Iso-cost line K1L1 are
at the tangent to each other At the point of E1 and E2,
the producer will not reach, because they are on a higher iso-cost line.
In this diagram, the producer will be in
equilibrium at the point E where the Isoquant IQ and Iso-cost line KL are at
the tangent to each other. At the point of E1 and E2
on IQ1, the
producer will not be in equilibrium as it is not tangent to iso-cost line and showing
less output than IQ 2.
Thus, the point at which the
Isoquant is tangent to the Iso-cost line represents the minimum cost or least
cost combination. At this point, the
marginal rate of technical substitution (the ratio of the marginal physical
products of both the inputs) are equal to the price ratio of the two factors.
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