Principle of Factor-substitution (Least-cost Combination)

In agriculture, various inputs or practices can be substituted in varying degrees for producing a given output. A producer has to choose a particular combination of inputs, which would be most profitable.

At a given level of output, he has to decide upon the least cost-combination of practices or inputs. There are large number of alternatives for performing different farm operations and obtaining output through different combinations of inputs. A few of such alternatives can be 1. use of bullocks v.s. tractor for a given size of a farm, 2. harvesting of crops by machines v.s. by manual labour, 3. milking machines v.s.hand milking for a given herd of cows, 4. wheat bhusa, green fodder and grains-mix in dairy feeds, 5. combinations of potash, phosphate, and nitrogen in fertilizers for crops.

A number of combinations of concentrates and green fodder, for example, can be used in producing a given amount of milk. Forage usually substitute at diminishing rate for grain. Problem here is to find the least cost combination of fodders and grains, milk production remaining the same a combination of fodders and grains which, cost remaining the same, will yield maximum output of milk.

Cost minimization will not depend only upon the cost of inputs and prices of products but also on the rate of substitution. For example, if hand labour costs less relative to cost of performing the operations by machines, costs may be lowered by substituting labour for machinery. If machine costs are low relative to labour, labour should get substituted with machine operations.

Procedure for Working Out the Least-Cost Combination

Step 1. – Compute the substitution ratio (marginal rate of substitution) by dividing the number of units of the replaced resource by the number of units of the added resource:

No. of units of replaced resource D X1

MRS = ------------------------------------------ = ------

No. of units of added resource D X2

Step 2. – Compute the price ratio by dividing the price of the "added" resource by the price of the "replaced" resource:

Cost per unit of added resource Px2

PR = ------------------------------------------ = -----

Cost per unit of replaced resource Px1

Step 3. – Find the point where the substitution ratios and price ratios are equal:

 D X1 Px2

------- = ------- OR D X 1. Px1 = D X2. Px2

D X2 Px1

Profit Rules:

1. If the substitution ratio is greater than the price ratio, one can reduce the costs by using more of "added" resource.
2. If the substitution ratio is less than the price ratio, costs can be reduced by using more of "replaced" resource.
3. If the substitution ratio equals the price ratio, it is the point of least cost.

Application of the principle

The rate at which the inputs can be exchanged to maintain a given level of output may be either constant or varying. Given the technical or physical rate of substitution, the least cost combination of resources will differ with different prices. As an example we consider a simple case of substitution with two variable inputs substitution at either constant or diminishing rate.

Least-Cost Combination of Farm Labour-Use for Hoeing of One Acre of Wheat – Men and Women Labour substituting at a Constant Rate.
Combination of labour Days for hoeing one acre of wheat		Added doses of inputs		Marginal rate of substitution		Cost of hoeing one acre with different levels of wages for men (Px2) & women (Px1)
Women Labour (X1)	Men Labour (X2)	X 1	X 2	X1 ------ X2	Px2 @ Rs.6 Px1 @ Rs.2/- (PR=3.00)	Px2 @ Rs.4/- Px1 @ Rs.3/- (PR = 1.33)	-Px2 @ Rs.6/- Px1 @ Rs.3/- (PR=2.00)
1	2	3	4	5	6	7	8
12 10 8 6 4 2 0	0 1 2 3 4 5 6	2 2 2 2 2 2	1 1 1 1 1 1	2 2 2 2 2 2	24 26 28 30 32 34 36	36 34 32 30 28 26 24	36 36 36 36 36 36 36

PR = Price Ratio

Special Cases of Substitution

There are certain practices, which substitute for other and also add to the output at the same time. An example is of hybrid maize seed replacing ‘desi’ maize seed. Hybrid maize uses about the same quantity of seed but produces more yield per acre. Here it may increase the cost but it adds more to the value of the production than it adds to the cost. The superiority of the substitute practice is established not only by the cost of the new practice but also by the value of the added yield. In estimating the profitability of such practices, budgeting technique becomes more useful. It is a case of shift in the production function.