Post on 10-Apr-2018
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LONG-RUN COST-OUTPUT RELATIONS
-A SERIES OF SHORT-RUN PRODUCTION DECISION
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CONTENTS
Concepts Of Cost
Analytical Cost Concepts
Cost CurvesShort- Run Cost Output Relationship
Optimum point at Short-Run.
Long-Run Cost- Output Relationship
Optimum point at Long-Run.
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Theory Of Cost:
Behavior ofcost in relation to change in output.Basic Principle Of Cost:
Total Cost increaseswith increase in output.
Cost Functions:y Short-Run Cost Function
y Long-Run Cost Function
Cost output relations are determined by
Cost Functions and Cost Curves
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ANALYTICAL COST CONCEPTS
Total
Cost (T
C)
Total FixedCost (TFC)
TotalVariable
Cost (TVC)
Average
CostAverage
Fixed Cost(AFC)
AverageVariable
Cost (AVC)
Marginal
Cost
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Total Cost - Actual cost incurred in productionof goods and services.
TC=TFC+TVC .(1)
Total Fixed Cost The cost of plant, building etcwhich remains fixed in a period of time.
Total Variable Cost - Varies with the variation inoutput like raw material, labour etc.
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Average Cost- Dividing the total cost(TC) by the totaloutput (Q).
AC=TC/Q .(2)
Average Fixed Cost- Total Fixed Cost (TFC) to the totalquantity produced (Q).
Average Variable Cost- Total Variable Cost (TVC) tothe Total Quantity Produced (Q).
From (2) substitute (1)
AC = TFC/Q + TVC/QAC = AFC + AVC
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Marginal Cost- change in Total Cost (TC)divided by change in total Output(Q).
MC = TC/Q
As we know that from (1)
TC= TFC + TVC
TFC=0
MC = TVC
(under marginality concept)
When Q=1
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COST CURVESLinear Cost
Function:
In form: TC= a + b Q
AC = TC/Q= a/Q + b
MC =
TC/Q = b
Example:TC = 60 +
10Q
QuadraticCost
Function:
In form:
AC = TC/Q =a/Q + b + Q
MC =TC/Q = b +
2Q
Example: TC =50+ 5Q +
Cubic Cost
Function:
In form:
AC = TC/Q =a/Q + b - 2c
Q+ d
MC= TC/Q = b -
2c Q + 3d
Example: TC=10+ 6Q -0.9
+0.05
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SHORT RUN COST OUTPUT
RELATIONSHIP Consider equation of Quadratic cost function:
TC = 200 + 5Q +2
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Output Optimization in Short Run when
MC = ACAC = TC/Q = 200/Q + 5 + 2Q
MC = TC/Q = 5 +4 Q
200/Q+5+2Q = 5+4Q
Q = 10
Thus, cost function is optimum at Q=10
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Thus, cost function is optimum at Q=10
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LONG RUN COST OUTPUT RELATIONS
Defined as:
Relationship between the changing scale of firm to total
output.
Derive Long Run Cost Curve:
Composed ofaseries of Short Run Cost Curves.
Here Long Run variables are:
Long Run Total Cost (LTC) = min (STC1 + STC2 +STC3)
LongRunAverage Cost (LAC) = min (SAC 1 + SAC2 +SAC3)
LongRun Marginal Cost(LMC) = min (SMC1 + SMC2
+SMC3)
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EXAMPLE:
Consider WackyWilly Company. The
production of Wacky Willy Stuffed Amigos (thosecute and cuddly armadillos, tarantulas, and
scorpions).
Product Factory Size Average Total Cost
Productionlevel
Plant1 10,000 sq.ft 100
Plant2 20,000 sq.ft 200
Plant3 30,000 sq.ft 300
Plant4 40,000 sq.ft 400
Plant5 50,000 sq.ft 500
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PRODUCTION
PLANT
P1 P2 P3 P4 P5
RANGE 100-135 135-240 240-360 360-465 465+
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ADDING ANOTHERFOURPRODUCTSThe 4 additional factories reach their min values at 150, 250, 350,& 450Stuffed Amigos.
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OPTIMUM PLANT SIZE IN LONG-RUN Ensures most efficient utilization of resources.
The downtrend of LRAC curve indicates, it is
optimum utilization at the point of 300.
If it crosses the Minimum Optimum level, the cost
will be increasing.
Minimum average cost of factory is attained at
SAC=SMC=LAC=LMC
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