Least cost combination principleLeast cost combination principle A rational firm/producer seeks maximisation of A rational firm/producer seeks maximisation of

profit.profit. For this, he tries to minimise its cost of For this, he tries to minimise its cost of

production.production. The cost is minimum, when input combination is The cost is minimum, when input combination is

optimal.optimal. Optimal input combination indicates the Optimal input combination indicates the

maximum returns to the factors employed.maximum returns to the factors employed. Thus, a rational firm would combine the various Thus, a rational firm would combine the various

factors of production its production function in factors of production its production function in such a way that with the minimum input and such a way that with the minimum input and maximum output is obtained at the minimum maximum output is obtained at the minimum cost.cost.

Such a combination is referred to as the least Such a combination is referred to as the least cost combination.cost combination.

Producer’s equilibrium occurs when he earns Producer’s equilibrium occurs when he earns maximum profit with optimal combination of maximum profit with optimal combination of factors.factors.

A profit maximisation producer faces two A profit maximisation producer faces two choices of optimal combination of factors choices of optimal combination of factors (inputs)(inputs)

1. To minimise its cost for a given output.1. To minimise its cost for a given output.2. to maximise its output for given cost.2. to maximise its output for given cost.

Thus the least cost combination of factors refers Thus the least cost combination of factors refers to a firm producing the largest volume of output to a firm producing the largest volume of output from a given cost & producing a given level of from a given cost & producing a given level of output with the minimum cost when the factors output with the minimum cost when the factors are combined in an optimum manner.are combined in an optimum manner.

Assumption of least cost combinationsAssumption of least cost combinations

1.1. There are two factors of production – labour There are two factors of production – labour & capital.& capital.

2.2. All units of labour & capital are All units of labour & capital are homogeneous.homogeneous.

3.3. The prices of units of labour (w) & capital (r) The prices of units of labour (w) & capital (r) are given & constant.are given & constant.

4.4. The cost outlay is given.The cost outlay is given.

5.5. The firm aims at profit maximisation.The firm aims at profit maximisation.

6.6. There is perfect competition in the factor There is perfect competition in the factor market.market.

The least cost combination may be stated The least cost combination may be stated thus –thus –

Marginal productivity of labour

Price of labour=

Marginal product of capital

Price of capital

MPL

PL

=MPC

PC

=

MPL = marginal productivity of labour

PL = Price of labour

MPC = marginal productivity of capital

Pc = price of capital

Appendix 7A Table 7A-2

CombinationCombination Labour Labour

(P(PLL = $2) = $2)

Capital (PCapital (PCC = =

$ 3)$ 3)Total costTotal cost

AA 11 66 2020

BB 22 33 1313

CC 33 22 1212

DD 44 11 1515

Least cost combination principle between two factors

The isoquant curve is tangent to an isocost line.The isoquant curve is tangent to an isocost line. The isocost line GH is tangent to the isoquant The isocost line GH is tangent to the isoquant

2000 at point M.2000 at point M. The firm employs the combination of OC of The firm employs the combination of OC of

capital & OL of labour to produce 2000 units of capital & OL of labour to produce 2000 units of output at point M with the given cost-outlay GH.output at point M with the given cost-outlay GH.

At this point, the firm is minimising its cost for At this point, the firm is minimising its cost for producing 2000 units.producing 2000 units.

Any other combination on the isoquant 2000, Any other combination on the isoquant 2000, such as R or T is on the higher isocost line KP such as R or T is on the higher isocost line KP which shows higher cost of production.which shows higher cost of production.

The isocost line EF shows lower cost but output The isocost line EF shows lower cost but output 2000 cannot be attained with it.2000 cannot be attained with it.

Therefore, the firm will choose the minimum Therefore, the firm will choose the minimum cost point is which is the least cost factor cost point is which is the least cost factor combination for producing 2000 unit of output.combination for producing 2000 unit of output.

M is the optimal combination for the firm.M is the optimal combination for the firm.

Limitation of least cost combinationsLimitation of least cost combinations

1.1. Factors may not be perfectly divisible – perfect Factors may not be perfectly divisible – perfect substitutions may not be possible.substitutions may not be possible.

2.2. It will be very difficult to calculate the marginal It will be very difficult to calculate the marginal product of each factor.product of each factor.

3.3. The producer has to decide not only the best The producer has to decide not only the best proportion of factors, but also the best scale of proportion of factors, but also the best scale of production.production.