COST ANALYSIS

What is cost?

• In producing a commodity a firm has to employ an aggregate of various factors of production such as land, labour, capital and entrepreneurship.

• These factors are to be compensated by the firm for their contribution in producing the commodity.

• This compensation (factor price) is the cost.

Various concepts of Cost

• 1. Real Cost

• 2. Opportunity or Alternative Cost

• 3. Money Cost – Explicit & Implicit Costs

• 4. Accounting & Economic Costs

• 5. Fixed and Variable Costs

Cost concepts

• 6. Production Costs –• Total Cost (TC)

• Total Fixed Cost (TFC)

• Total Variable Cost (TVC)

• Average Fixed Cost (AFC)

• Average Variable Cost (AVC)

• Average Total Cost (ATC) and

• Marginal Cost (MC)

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 of real productive resources absorbed in the production of a commodity (or a service).

Opportunity Cost

• The concept of opportunity cost is based on the scarcity and 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.

Economists’ Money Costs

• Economists wish to include imputed value of all the inputs provided by the producer himself in addition to outright money transactions between the firm and other parties from whom inputs are purchased for carrying out production.

• Thus money costs in economic terms or• Economic cost = explicit or Accounting costs +

implicit costs.

• Sunk cost is a cost once incurred cannot be retrieved. It is associated with commitment of funds to specialized equipment or facilities which cannot be used for anything else in the present or future. E.g.brewery plant during prohibition.

Sunk Costs

Shutdown Costs

• Shut down costs are costs which would be incurred when plan operation is suspended, but would have been saved if the operation was continuing.

• E.g. costs of sheltering plant and equipment.• Construction or hiring of sheds for storing

exposed property.• Expenses on recruitment and training incurred on

re-employment of workers.

Abandonment Costs

• Abandonment arises when there is complete cessation of activities and there is a problem of disposal of assets.

• E.g.discontinuance of using typewriters and shifting over usage to computers.

• Shifting to paperless operations.

Replacement and Historical Costs

• Historical cost means the cost of a plant at a price originally paid for it. Replacement cost means the price that would have to be paid currently for acquiring the same plant.

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 of raw materials, wages and salaries, power and fuel, rent, interest payments of capital invested, Insurance, Taxes and duties, Misc. expenses such as selling, transport, advertising & sales promotional expenses.

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 of labour rendered by the entrepreneur himself.

• Interest on capital supplied by him.

• Rent of land and premises owned by the entrepreneur and used for production.

• Normal returns or profits of entrepreneur as compensation for his management and organizational services.

Fixed Costs

• Fixed costs are those costs that are incurred as a result of the use of fixed factor inputs. They remain fixed at any level of output.

• While engaging in productive activity the producer always has to incur some expenditure which remains fixed whatever the level of production.

Fixed Costs

• In the short run, fixed costs remain fixed because the firm does not change its size and the amount of fixed factors employed which include:

• Payments of rent for building.

• Interest on capital.

• Insurance premium

• Depreciation and Maintenance allowances

• Adm. Expenses (Managerial & Staff salaries)

• Property and business taxes, licence fees etc.

Variable Costs

• Variable costs are those costs that are incurred by the firm as a result of the use of variable factor inputs. They are dependant on the level of output.

• The cost which keeps on changing with the changes in the quantity of output produced is known as variable cost.

Variable costs

• The short-run variable costs include• Prices of raw materials,

• Wages paid for labour

• Fuel and power

• Excise duties, sales tax, octroi, VAT.

• Freight (or transportation) charges..

Production Costs

• Total Cost (TC)

• Total Fixed Cost (TFC)

• Total Variable Cost (TVC)

• Average Fixed Cost (AFC)

• Average Variable Cost (AVC)

• Average Total Cost (ATC) and

• Marginal Cost (MC)

Theory of Cost in the Short run

• Total Cost TC = TFC + TVC• Average Fixed Cost AFC = TFC Q• Average Variable Cost AVC = TVC Q• Average Total Cost ATC = TC Q

= TFC/Q + TVC/Q Marginal Cost

MC = CRVCQQ

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

Cost curves

OUTPUT

CO

ST

MCATC

AVC

AFC

Average Fixed Cost, Average Variable Cost and Average Total cost of the Firm

Output

(Units)

Average

Fixed Cost

TFC Q

Average

Variable Cost

TVC Q

Average

Total Cost

TC Q

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

Output

(units)

Total Cost

(Rupees)

Total Variable Cost(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

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)

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)

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 your knowledge of the various measures of short run cost, complete the following table.

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 your knowledge of the various measures of short run cost, complete the following table.

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)

Relationship between Marginal Cost and Average Cost

• 1. When Average Cost is minimum, Marginal cost is equal to Average Cost.

• MC curve intersects at the minimum point of ATC curve.

• 2. When MC curve is below AC curve, marginal cost is less than average cost, and the latter falls.

• 3.When the MC curve is above AC curve, marginal cost is more than average cost, the latter rises.

MARGINAL COST AND AVERAGE COST LINES

MC ACC

OS

T

OUTPUT

PM

NN

L Q

AB

C

O

Esimation of Cost Functions

Relationship between cost and output is expressed by cost function.

TC = f(Q)

TC = Total Cost Q = Quantity of output

Three variants of Short-run Cost function1.Linear Cost function

1. Linear function: TC = a + bQ

(TFC + TVC) (TFC) (AVCxQ)

TVC

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

MC = C = b

Q

Illustration:

TC = 100 + 0.5Q (Q=10)

FC = 100 ; TVC = 0.5Q

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

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

C =bco

st

output

TFC

TC=a + bQ

Explanation of Linear Cost function

The firm has fixed costs which must be met irrespective of the quantity of output produced. This is represented by a in the equation TC=a+bQ

The firm must pay proportional amount for rawmaterials, labour and other inputs, which is the TVC represented by bQ in the equation.

The equation for Total Cost = Total Fixed Cost + Total Variable Cost

Will thus be given as TC = a + bQ.

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

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

Average Fixed Cost = a/Q and Average variable cost = b

Since in the shortrun, TFC is the same irrespective of output, all increases (differentials) in cost due to increase (differentials) in output will be the Marginal Cost MC = b

Quadratic Cost Function

TC = a + bQ + cQ2

ATC = a/Q + b + cQ

MC = b + 2cQ

TC=a + bQ + cQ2

TFCcost

outputHere, the firm has Fixed Costs Rs.5000 and Variable costs for (labour, raw materials etc.) to produce Q units are 250Q + 3Q2

Firm’s initial cost of producing Q units is 250QAdditional units can be produced at increased cost due to shortage of raw materials and other inputs (their price being higher) ups their price by +3Q2 which is the last variable.

Implications of the Quadratic equation:a + bQ + cQ2

• 1. If Q = 0, TC = a = TFC• 2. Number of bends in the Graph is 1,• Number of bends = 1 less 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

There can be another type of Quadratic Equation TC = a + bQ – cQ2

Here – cQ2 represents reduction in costs on account of increased productivity. The TC curve will rise at a decreasing rate.

TC = a + bQ -- cQ2

TFC

cost

output

Problem:ABC Ltd.estimates its total cost Rs.Y of manufacturing X units of electronic gauges per month as Y = 8000 + 300X + 0.1X2

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

(ii) If the company doubles this output, will it halve its average cost?(iii)If not, what will be its average cost be?

(iv) How much is the average variable cost of producing 200 unitsper month? (v)What will be the average variable cost if no units are Produced?

(vi) What will be the marginal cost function of the company?

Cubic Cost Functions• Cubic type of function will be

• TC = a + bQ + cQ2 + dQ3

• Here the highest exponent is 3. Hence one less than 3 bends will be thre in the cost curve.

• This function combines both increasing and decreasing productivity or returns.

IncreasingProductivity

DecreasingProductivity

TC=a + bQ = cQ2 +dQ3

TFC

output

cost

(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 cost has not been halved. The reduction in fixed cost has been offset by increase in AVC.

(v)Average variable cost of producing 200 units per mointh is

AVC = b + cX

= 300 + 0.1(200)

= 300 + 20 = Rs.320

If no units are produced, X really does not exist. So no question of AC.

(vi)MC = 300 + 0.2X