Least cost Combination (LCC)

•There are innumerable possible combination of factors which can be used to produce a particular level of output.

•The problem is to find out the combination of inputs which should cost least, a cost minimization problem.

• There are three methods to find out the least cost combination of inputs.

They are:

•Arithmetical Method:

•Algebraic Method:

•Graphic Method:

1. Arithmetical Method:

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

•This method is suitable where only a few combination produce a particular level of output. 

•The product produced is 100 kg,

•Price of x1 input is Rs 3 per unit and price of x2 is Rs 2 per unit

2.Algebraic  method:

a. Compute marginal rate of technical substitution.

•MRS = Number of units of replaced resources/Number of units of added resources.

•MRS X1 X2 = Δ X2/Δ X1

•MRS X2 X1 = Δ X1/Δ X2

b. Compute price ratio (PR)

•PR = Price per unit of added resource/Price per unit of replaced resource

•PR = PX1/PX2 if MRS X1 X2 or PR = PX2/PX1 if MRS X2 X1

c. Work out least cost combination by equating MRS and PR.

 i.e. Δ X2/ Δ X1 = PX1/PX2 or Δ X1/ Δ X2 = PX2/PX1.

•The same can be expressed as Δ X2 PX2 = PX1 Δ X1 or Δ X1 PX1 = Δ X2 PX2

•The least cost combination is obtained when MRS = PR.

3. Graphical method:

•Since the slope of isoquant indicates MRTS and the slope of isocost line indicates factor price ratio, minimum cost for given output will be indicated by the tangency of these isolines.

• For this purpose isocost line and isoquant are drawn on the same graph for different levels of production.

•The least cost combination will be at the point where isocost line is tangent to the isoquant.

•i.e. slope of isoquant = slope of isocost line.

• i.e. MRS = PR