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# Optimum Factor Combination:

## Definition:

In the long run, all factors of production can be varied. The profit maximization firm will choose the least cost combination of factors to produce at any given level of output. The least cost combination or the optimum factor combination refers to the combination of factors with which a firm can produce a specific quantity of output at the lowest possible cost.

## Explanation:

There are two methods of explaining the optimum combination of factor:

(i) The marginal product approach.

(ii) The isoquant / isocost approach.

These two approaches are now explained in brief:

## (i) The Marginal Product Approach:

In the long run, a firm can vary the amounts of factors which it uses for the production of goods. It can choose what technique of production to use, what design of factory to build, what type of machinery to buy. The profit maximization will obviously want to use that mix of factors of combination which is least costly to it. In search of higher profits, a firm substitutes the factor whose gain is higher than the other. When the last rupee spent on each factor brings equal revenue, the profit of the firm is maximized. When a firm uses different factors of production or least cost combination or the optimum combination of factors is achieved when:

## Formula:

Mppa = Mppb = Mppc = Mppn

Pa         Pb        Pc        Pn

In the above equation a, b, c, n are different factors of production. Mpp is the marginal physical product. A firm compares the Mpp / P ratios with that of another. A firm will reduce its cost by using more of those factors with a high Mpp / P ratios and less of those with a low Mpp / P ratio until they all become equal.

## (ii) The Isoquant / Isocost Approach:

The least cost combination of-factors or producer's equilibrium is now explained with the help of iso-product curves and isocosts. The optimum factors combination or the least cost combination refers to the combination of factors with which a firm can produce a specific quantity of output at the lowest possible cost.

As we know, there are a number of combinations of factors which can yield a given level of output. The producer has to choose, one combination out of these which yields a given level of output with least possible outlay. The least cost combination of factors for any level of output is that where the iso-product curve is tangent to an isocost curve. The analysis of producers equilibrium is based on the following assumptions.

## Assumptions of Optimum Factor Combination:

The main assumptions on which this analysis is based areas under:

(a) There are two factors X and Y in the combinations.

(b) All the units of factor X are homogeneous and so is the case with units of factor Y.

(c) The prices of factors X and Y are given and constants.

(d) The total money outlay is also given.

(e) In the factor market, it is the perfect completion which prevails. Under the conditions assumed above, the producer is in equilibrium, when the following two conditions are fulfilled.

(1) The isoquant must be convert to the origin.

(2) The slope of the Isoquant must be equal to the slope of isocost line.

### Diagram/Figure:

The least cost combination of factors is now explained with the help of figure 12.9.

Here the isocost line CD is tangent to the iso-product curve 400 units at point Q. The firm employs OC units of factor Y and OD units of factor X to produce 400 units of output. This is the optimum output which the firm can get from the cost outlay of Q. In this figure any point below Q on the price line AB is desirable as it shows lower cost, but it is not attainable for producing 400 units of output. As regards points RS above Q on isocost lines GH, EF, they show higher cost.

These are beyond the reach of the producer with CD outlay. Hence point Q is the least cost point. It is the point which is the least cost factor combination for producing 400 units of output with OC units of factor Y and OD units of factor X. Point Q is the equilibrium of the producer.

At this point, the slope of the isoquants equal to the slope of the isocost line. The MRT of the two inputs equals their price ratio.

Thus we find that at point Q, the two conditions of producer's, equilibrium in the choice of factor combinations, are satisfied.

(1) The isoquant (IP) is convex the origin.

(2) At point Q, the slope of the isoquant ΔY / ΔX  (MTYSxy) is equal to the slope of the isocost in Px / Py. The producer gets the optimum output at least cost factor combination.

## Relevant Articles:

» What is Production Function
» Short Period Analysis of Production
»

## Long Run Production With Variable Inputs

» Isoquants
» Properties of Isoquants
» Isocost Lines
» Marginal Rate of Technical Substitution
» Optimum Factor Combination

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