• The principle of least cost combination states that if two factor inputs are considered for a given output the least cost combination will be such where their inverse price ratio is equal to their marginal rate of substitution.
• There are 3 methods to find solution to cost minimization problem.

i) Simple arithmetical calculations

• One possible way to determine the least cost combination is to compute the cost of all possible combinations and then select the one with the minimum cost.

Table: Computation of Least cost combination of two input for producing an output of 85 units.

Out of five combinations calculated in above table, 3 units of X2 and 6 units of X1 is the least cost combination of inputs i.e., Rs. 30.

ii) Algebraic method

• Procedure for finding out least cost combination is as under

i) Compute marginal substitution ratio (= ΔX2/ΔX1)

ii) Compute price ratio = Px1/Px2

iii) Work out least cost combination by equating i.e., ΔX2/ΔX1= Px1/Px2

• The least cost combination criterion is that MRS of X2 for X1 should be equal to Px1/Px2. i.e., ΔX2/ΔX1 should be equal to Px1/Px2

iii) Graphic method

• Since slope of Isocost line indicates the ratio of factor prices and slope of the isoquant represents the marginal rate of substitution, minimum cost for a given output will be indicated by the tangency of these iso-lines.
• The least cost criterion on a graph will be:

Slope of isoquant = Slope of isocost line