Long Run Cost Output Relations

8/8/2019 Long Run Cost Output Relations

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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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Long Run Cost Output Relations

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