costanalysis-100202064231-phpapp02

8/7/2019 costanalysis-100202064231-phpapp02

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COST ANALYSIS


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What is cost? In producing a commodity a firm has to

employ an aggregate of various factors of

production such as land, labour, capital andentrepreneurship.

These factors are to be compensated by the

firm for their contribution in producing the

commodity.

This compensation (factor price) is the cost.


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Various concepts of Cost

1. Real Cost 2. Opportunity orAlternative Cost

3. Money Cost Explicit & Implicit Costs

4. Accounting & Economic Costs 5. Fixed and Variable Costs


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Cost concepts 6. Production Costs

Total Cost (TC)

Total Fixed Cost (TFC)

TotalVariable Cost (TVC)

Average Fixed Cost (AFC)

Average Variable Cost (AVC)

Average Total Cost (ATC) and

Marginal Cost (MC)


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Real Cost The real cost of production refers to the

physical quantities of various factors used

in producing a commodity.

Real cost signifies the aggregate ofreal

productive resources absorbed in the

production ofa commodity (ora service).


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Opportunity Cost The concept of opportunity cost is based on the

scarcityand alternative applicability

characteristics of productive resources. The real cost of production of something using

a given resource if the benefit forgone (or

opportunity lost) of some other thing by not

using that resource in its best alternative use.

An opportunity cost or alternative cost is the

value of a resource in a foregone employment.


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Economists Money Costs Economists wishto include imputed value ofall

the inputs provided bythe producerhimself in

addition to outright moneytransactions betweenthe firm and otherparties from whom inputs are

purchased forcarrying out production.

Thus money costs in economic terms or

Economic cost = explicit or Accounting costs +

implicit costs.


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Sunk cost is a cost once incurred cannotbe

retrieved. It is associated with commitment

of funds to specialized equipment or

facilities which cannotbe used foranything

else in the present orfuture. E.g.brewery

plant during prohibition.

Sunk Costs


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Shutdown Costs Shut down costs are costs which would be

incurred when plan operation is suspended, but

would have been saved ifthe operation wascontinuing.

E.g. costs of sheltering plantand equipment.

Construction orhiring of sheds forstoring

exposed property. Expenses on recruitmentand training incurred on

re-employment of workers.


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Abandonment Costs Abandonmentarises when there is complete

cessation ofactivities and there is a problem

of disposal ofassets.

E.g.discontinuance of using typewriters and

shifting overusage to computers.

Shifting to paperless operations.


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Replacementand Historical Costs Historical cost means the cost ofa plantata

price originally paid forit. Replacement

cost means the price that would have to be

paid currently foracquiring the same plant.


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Economic Cost Explicit costs are direct contractual monetary

payments incurred through market

transactions. Explicit costs are usually costs shown in the

accounting statements and include costs ofrawmaterials, wages and salaries, powerand fuel,rent, interest payments of capital invested,Insurance, Taxes and duties, Misc. expenses suchas selling, transport, advertising & salespromotional expenses.


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Economic Cost (contd.) Implicit costs are the opportunity costs of the

use of factors which a firm does not buy or hire

but already owns. Implicit costs include

Wages oflabourrendered bythe entrepreneurhimself.

Interest on capital supplied byhim.

Rent ofland and premises owned bythe entrepreneurand usedforproduction.

Normalreturns orprofits of entrepreneuras compensation for

his managementand organizational services.


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Fixed Costs

Fixed costs are those costs that areincurred as a result of the use of

fixed factor inputs. They remainfixed at any level of output.

While engaging in productiveactivity the producer always has to

incur some expenditure whichremains fixed whatever the level ofproduction.


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Variable Costs

Variable costs are those costs that areincurred by the firm as a result of the

use of variable factor inputs. They aredependant on the level of output.

The cost which keeps on changing withthe changes in the quantity of output

produced is known as variable cost.


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Production Costs

Total Cost (TC)

Total Fixed Cost (TFC) TotalVariable Cost (TVC)

Average Fixed Cost (AFC)

Average Variable Cost (AVC)

Average Total Cost (ATC) and

Marginal Cost (MC)


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Theory of Cost in the Shortrun

Total Cost TC = TFC + TVC

Average Fixed Cost AFC = TFC z Q

Average Variable Cost AVC = TVC z Q

Average Total Cost ATC = TC z Q

= TFC/Q + TVC/Q

Marginal Cost

MC = (8C 3R (8VC

(Q (Q


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Short-run Production costsFigures in rupees

Output

(Units)

Total

Fixed Cost

Total

Variable Cost

Total Cost

0 240 0 240

1 240 120 360

2 240 160 400

3 240 180 420

4 240 212 452

6 240 280 520


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Cost curves

OUTPUT

MCATC

AVC

AFC


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Average Fixed Cost, AverageVariable Costand

Average Total cost ofthe Firm

Output

(Units)

Average

Fixed Cost

TFC z Q

Average

Variable Cost

TVCz Q

Average

Total Cost

TCzQ

1 240 1 = 240 120 1 = 120 360 1 = 360

2 240 2 = 120 160 2 = 80 400 2 = 200

3 240 3 = 80 180 3 = 60 420 3 = 140

4 240 4 = 60 212 4 = 53 452 4 = 113

5 240 5 = 48 280 5 = 56 520 5 = 104

6 240 6 = 40 420 6 = 70 660 6 = 110


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Output(units)

Total Cost(Rupees)

TotalV

ariableCost(Rupees) Marginal Cost(Rupees)

0 240 0 --

1 360 120 120

2 400 160 40

3 420 180 20

4 452 212 32

5 520 280 68

6 660 420 140

Calculation of Marginal Cost


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Output

(units)

TFC TVC TC AFC

(TFC/Q)

AVC

(TVC/Q)

ATC

(TC/Q)

MC

(1) (2) (3) (4) (5) (6) (7) (8)

0 100 0 100 -- -- -- --

1 100 25 125 100 25 125 25 (125-100)

2 100 40 140 50 20 70 15(140-125)

3 100 50 150 33.3 16.6 50 10 (150-140)

4 100 60 160 25 15 40 10(160-150)

5 100 80 180 20 16 36 22(180-160)

6 100 110 210 16.3 18.3 35 30(210-180)

7 100 150 250 14.2 21.4 35.7 40(250-210)

8 100 300 400 12.5 37.5 50 150(400-250)

9 100 500 600 11.1 55.6 66.7 200(600-400)


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Output(units)

TFC TVC TC AFC(TFC/Q)

AVC(TVC/Q)

ATC(TC/Q)

MC

(1) (2) (3) (4) (5) (6) (7) (8)

0 --- --- 1200 X X X X

1 --- --- 1265

2 --- 204

3 --- --- 494

4 --- --- 86

5 --- 525

6 --- --- 286

7 --- --- 97

8 --- 768

9 --- --- 97

Problem: Based on yourknowledge ofthe various measures of

shortrun cost, complete the following table.


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Output(units)

TFC TVC TC AFC(TFC/Q)

AVC(TVC/Q)

ATC(TC/Q)

MC

(1) (2) (3) (4) (5) (6) (7) (8)

0 1200 0 1200 X X X X

1 1200 265 1265 1200 265 1265 265

2 1200 204 1404 600 102 702 139

3 1200 283 1483 400 94 494 79

4 1200 369 1569 300 92 392 86

5 1200 525 1725 240 105 345 156

6 1200 580 1780 200 96 286 65

7 1200 679 1879 171 97 239 99

8 1200 768 1968 150 96 246 89

9 1200 873 2073 133 97 230 105

Problem: Based on yourknowledge ofthe various measures of

shortrun cost, complete the following table.


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Relationship between Marginal Costand Average Cost

1.When Average Cost is minimum, Marginalcost is equalto Average Cost.

MC curve intersects atthe minimum point ofATC curve.

2.When MC curve is below AC curve, marginalcost is less than average cost, and the latterfalls.

3.When the MC curve is above AC curve,marginal cost is more than average cost, the latterrises.


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MARGINAL COST AND AVERAGE COST LINES

MCAC

OUTPUT

PM

NN

L Q

A

B

C

O


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Esimation of Cost FunctionsRelationship between costand output is

expressed by cost function.

TC = f(Q)

TC = Total Cost Q = Quantity of output


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Three variants of Short-run Cost function

1.LinearCost function1. Linear function: TC = a + bQ

(TFC + TVC) (TFC) (AVCxQ)

TVC

ATC = TC/Q = TFC/Q + TVC/Q = a/Q + b

MC = H8C = bHQ

Illustration:

TC = 100 + 0.5Q (Q=10)

@8FC = 100 ; TVC = 0.5Q

At Q = 10, TVC = 0.5 x 10 = 5and TC = 100 + 5 = 105

ATC = a/Q + b = 100/10 + 0.5 = 10.5

@1C = b !

output

TFC

TC=a + bQ


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Explanation of LinearCost function

The firm has fixed costs which mustbe met irrespective ofthe quantity of

output produced. This is represented bya in the equation TC=a+bQ

The firm must pay proportionalamount forrawmaterials, labourand other

inputs, which is the TVC represented bybQ in the equation.

The equation forTotal Cost = Total Fixed Cost + TotalVariable Cost

Willthus be given as TC = a + bQ.

At Zero output TC = a + bxo = a =TFC

Average Total Cost = TC z Output Q = a/Q + b

Average Fixed Cost = a/Q and Average variable cost = bSince in the shortrun, TFC is the same irrespective of output, all increases

(differentials) in cost due to increase (differentials) in output willbe

the Marginal Cost MC = b


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Quadratic Cost FunctionTC = a + bQ + cQ2

ATC = a/Q + b + cQ

MC = b + 2cQ

TC=a + bQ + cQ2

TFC

outputHere, the firm has Fixed Costs Rs.5000 andV

ariable costs for(labour, raw materials etc.) to produce Q units are 250Q + 3Q

2

Firms initial cost of producing Q units is 250Q

Additional units can be produced at increased cost due to shortage ofraw materials

and otherinputs (theirprice being higher) ups theirprice by +3Q2which is the last

variable.


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Implications ofthe Quadratic equation:

a + bQ + cQ2

1. If Q = 0, TC = a = TFC

2. Numberofbends in the Graph is 1,

Numberofbends = 1less than highest

exponent.(Q2) .

ATC = TC/Q = a/Q + b + cQ

AFC = a/Q, therefore, AVC = b + cQ MC = b + 2cQ (by differentiation)

When Q = 0 MC = AVC = b


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There can be anothertype of Quadratic

Equation TC = a + bQ cQ2

Here cQ2represents reduction in costs on

account of increased productivity. The TC

curve willrise ata decreasing rate.

TC = a + bQ -- cQ2

TFC

output


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Problem:

ABC Ltd.estimates its total cost Rs.Y of manufacturing X units of

electronic gauges permonthas Y = 8000 + 300X + 0.1X2

(i) Calculate the average cost of producing 200 gauges permonth.

(ii) Ifthe company doubles this output, will ithalve its average cost?

(iii)If not, what willbe its average costbe?

(iv) How much is the average variable cost of producing 200 units

permonth?

(v)What willbe the average variable cost if no units are

Produced?

(vi) What willbe the marginal cost function ofthe company?


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(i)Total cost of producing 200 gauges

Y = 8000 + 300X + 0.1X2

= 8000 + 300(200) + 0.1(200)2

= 8000 + 60000 + 0.1(40000)= 8000 + 60000 + 4000

= 72000 Rs.72000

(ii) Doubling the output, X = 400

Y = 8000 + 300X + 0.1X2

= 8000 + 300(400) + 0.1(400)2

= 8000 + 120000 + 0.1(160000)

= 8000 + 120000 + 16000

= 144000 Rs.1,44,000.

(iii)Average cost of producing 200 units

Y = 8000 + 300 + 0.1(200)X 200

= 40 + 300 + 20

= 360. Rs.360

(iv) Average cost of producing 400 units

Y = 8000 + 300 + 0.1(400)

X 400

= 20 + 300 + 40

= 360 Rs.360

The average costhas notbeen halved.

The reduction in fixed costhas been

offsetby increase in AVC.

(v)Average variable cost of producing

200 units permointh is

AVC = b + cX

= 300 + 0.1(200)

= 300 + 20 = Rs.320If no units are produced, Xreally does

not exist. So no question of AC.

(vi)MC = 300 + 0.2X

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