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
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