Cost

Objectives

to introduce and discuss nature of costs

to outline short-run costs and examine the

determinants

to understand the process of constructing LATC

to outline how and why costs change in the long-run

to examine the importance of cost to the

organization

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Cost Concepts

Opportunity cost (normal profit) - cost measured in term of the next best alternative foregone

Economic costs – payment made to all the resources employed in the production of a good

Explicit costs – the payments to outside suppliers of inputs

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Implicit costs – costs which do not involve a direct payment of money to a third party, but which nevertheless involve a sacrifice of some alternatives

Historical costs – the original amount the firm paid for factors it now owns

Replacement costs – what the firm would have to pay to replace factors, it currently owns

Factors hired Cost (Rs.)

seed 750.00

labor 1900.00

tractor 2000.00

fertilizer 1100.00

tube well 1250.00

Explicit cost 7000.00

Self-owned factor Opportunity Cost (Rs.)

family labor 3500.00

land 5000.00

Implicit cost 8500.00

Economic cost 15500.00VG/lv/P-II-6

Cost functionInfluenced by the character of the underlying production

function markets inputs supply functions

c = ƒ (Q, E, Pr, G ---- )

Where C = costQ = outputE = efficiencyPr = price of resourcesG = government policy

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Cost-output relationships in the short run

The family of total cost conceptsTotal fixed cost (TFC) – the sum total of the

explicit costs of all the fixed inputs plus the implicit costs associated with the firm’s operations.

examples – salaries of top management officials, property taxes, interest, depreciation charges, rents on office space, insurance premiums.

TFC =

n

i

ipi1

x

where pi = prices of specified fixed inputs

xi = quantity of fixed inputs

n = number of various kinds of fixed inputs

Total variable cost (TVC)- sum of the amounts a firm spends for variable inputs employed in the production process

examples – raw material outlays, power and fuel charges, transportation cost

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m

TVC = Pj Xj j =1

Where Pj = prices of specified variable inputs Xj = quantity of variable inputs m = number of variable inputs

Total cost = TFC + TVC Q = 0, TVC = 0 , TC = TFC

The family of unit costsAverage fixed cost (AFC)AFC = TFC/Q = Pfi(FI/Q)The reduction of AFC by producing more

is called “spreading the overhead”APfi = Q/FI

Unit costs

Average variable cost (AVC)AVC = TVC/Q = Pvi(VI/Q)Since APvi = Q/VI thereforeAVC = Pvi(1/APvi)Average total cost (ATC)ATC = TC/QATC = TC/Q = TFC/Q +TVC/Q ATC = AFC + AVC

Marginal cost

MC = ΔTC/ΔQ = ΔTVC/ΔQΔTVC = Pvi(ΔVI)

MC = Pvi(ΔVI/ΔQ) = Pvi(1/MP)

Cost behavior with increasing and diminishing returns to variable inputs

TP = Q = a + bx +cx2 – dx3

APvi = b + cx – dx2

MPvi = b + 2cx – 3dx2

TFC = a

TVC = bQ – CQ2 + dQ3

TC = TFC + TVC = a + bQ – cQ2 + dQ3

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Cost conceptsQ TC

TFC+TVCTFC TVC ATC

AFC+AVCAFC

TFC/QAVC

TVC/QMC = ΔTC/

△ ΔQ

1. 1 107.00 85 22 107.00 85.00 22.00 22.00

2. 126.00 85 41 63.00 42.50 20.04 19.00

3. 143.00 85 58 47.66 28.33 19.33 17.00

4. 159.00 85 74 39.75 21.25 18.50 16.00

5. 174.00 85 89 34.80 17.00 17.80 15.00

6. 189.00 85 104 31.50 14.17 17.33 15.00

7. 205.00 85 120 29.28 12.14 17.14 16.00

8. 223.00 85 138 27.88 10.63 17.25 18.00

9. 243.00 85 158 27.00 9.44 17.56 20.00

10. 266.00 85 181 26.60 8.50 18.10 23.00

11. 293.00 85 208 26.64 7.73 18.91 27.00

12. 325.00 85 240 27.08 7.08 20.00 32.00

13. 363.00 85 278 27.92 6.54 21.38 38.00

14. 408.00 85 323 29.14 6.07 23.07 45.00

15. 461.00 85 376 30.74 5.67 25.07 53.00

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Results of empirical studies of short-run cost functions

Name Type of Industry Finding

Lester (1946) Manufacturing AVC decreases up to capacity level of output

Hall and Hitch (1939) Manufacturing Majority have decreasing MC.

Johnston (1960) Electricity multiple-product food processing

“Direct” cost is a linear function of output, and MC is constant.

Dean (1936) Furniture Constant MC which failed to rise

Dean (1941) Leather belts No significant increases in MC

Dean (1941) Hosiery Constant MC which failed to rise.

Dean (1942) Department store Declining or constant MC, depending on the department within the store.

Ezekiel and Wylie (1941) Steel Declining MC but large variation.

Yntema (1940) Steel Constant MC

Johnston Electricity ATC falls, then flattens, tending toward constant Mc up to capacity.

Mansfield & Wein (1958) Railways Constant MC

Source: A.A. Walters, “production and cost functions”, Econometrica, Vol. 31, No.1 (January 1963), pp.1-66 VG/lv/P-II-6

Reasons for increasing MC & AC wage premium for overtime

intensive use of equipments induces more breakdowns

leaves less time for maintenance

hiring standards to be lowered

less efficient resources

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Case - McGraw Hill’s annual survey of manufacturing firms

What percentage of production capacity is currently being used?

At what percentage they would prefer to operate?

0 100% OF CAPACITY90%50%

cost

AFC

AVCMC

AC

100% OF CAPACITY90%0 50%

cost

McGraw Hill Study

TFC

TVCTC

Cost-output relationship in the long run

Objective Q at lowest cost, Find the ‘right size’ scale Increasing returns to scale – cost increases less

than proportionately – factor price increase Constant returns to scale – LTC increases in the

same proportion Decreasing returns to scale – LTC increases at

an increasing rate

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Large scale – aircraft, electricity, automobile, steel, oil refining, paper, glassware, aluminum. etc.

Small scale – garments, shoes, furniture printing, publishing, farming etc.

Cost behavior and plant size

Long run minimum average cost (LRAC) or least

unit cost attainable for a given output rate

when the firm has time to change the rate of

usage of any and all inputs and firm enjoys

economies of scales more than it suffers from

diseconomies of scale

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LRAC

Economies negligible Economies never exhausted – natural monopoly –

barriers – public utilities Minimum efficient scale – beyond which AC is

constant, least volume of output at which LAC is minimum.

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Minimum efficient scale C F Pratten’s Study (1988)

Many firms especially in manufacturing experience substantial economies of scale

AC falls as Q increases or may remain constant MES – is the size beyond which no significant

additional economies achieved Pratten – ½ MES is the scale above which any

possible doubling in scale would reduce AC by less than 5% leading to MES

Q

MES

1/3 1/2 1

AC

0

cost

Pratten’s Study

Industry Cost disadvantage

(%)

Industry Cost disadvantage

(%)

Flour mill 3.0 Synthetic rubber

15.0

Bread baking

7.5 Detergents 2.5

Paper printing

9.0 Bricks 25.0

Sulphuric acid

1.0 Machine tools

5.0

Cost disadvantage of plants that are 50% of MES

Reasons for economies of scale at the plant level

Economies of mass production – greater specialization,

learning by doing

Learning cure- separate out technical breakthroughs,

input-cost inflation, output scale effect

Learning rate = (1 – AC2/AC1) . 100

(1 – 90/100) . 100 = 10%

Continuous process utilizing by products

Marketing economies – quantity discounts

Transport economies

Reasons for diseconomies of scale at the plant level

Increasing transportation cost

Inefficient supervision and coordination

Labor unions

Cost behavior and firm size

Reasons for economies of scale at the firm level common management economies mass marketing economies – nationwide distribution

systems and sales promotion campaigns R&D, designing new products greater market visibility and recognition financial economies economies of scope diversification as an asset in surviving fundamental

market changes control over costs, selling price, production technology,

source of financial capital, relationship with govt. .

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Diseconomies of scale at the firm level Increasing difficulties and costs of managing ever-larger

enterprise

Results of empirical studies of long-run cost function

Name Type of Industry FindingBain (1956) Manufacturing Small economies of scale for Multiplant firms.

Holton (1956) Retailing LRAC is L-shaped.

Alpert (1959) Metal Economies of scale up to an output of 80,000 lbs per month; constant returns to scale and horizontal LRAC thereafter.

Moore (1959) Manufacturing Economies of scale prevail quite generally.

Lomax (1951) and Gribbin (1953)

Gas (Great Britain) LRAC of production declines as output rises.

Loxam (1952) and Johnston (1960)

Electricity (Great Britain) LRAC of production declines as output rises.

Johnston (1960) Life assurance LRAC declines.

Johnston (1960) Road passenger transport (Great Britain)

LRAC either falling or constant.

Nerlove (1961) Electricity (U.S.) LRAC (excluding transmission costs) declines and then shows signs of increasing.

Source – A.A. Walters, “ production and cost functions,” Econometrica, vol. 31, no.1 (January 1963), pp. 1-66

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Case - Economies of scale

Survey by NCAER

Pre investment survey group reported manufacturing cost of writing and printing paper declines from Rs. 1489 (in 100 tonne per day plant) to Rs. 1238 (200 t. per day) and further to Rs. 1104 (300 t. per day) per t.

size of plant (t. per day)

fixed investments

(per t.)

cost of raw material

(per t.)

operating cost

(per t.)100 4473 324 1307

200 4070 263 1116

300 3945 258 1056

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Sources – State Bank of India Monthly Review, November. 1975, pp. 416 -17

Case - Economies of scale

Economic and Scientific Research Foundation found that single cement plant producing 3,200 tpd required 46% less capital investment than 8 plants of 400 tpd. Cost of production was lower by Rs.100 per t. in 3,200 tpd plant.

during 1960s – 600 tpd 1200 tpd 32,00 tpd

Source -The Economic Times – March 14,1983

-The Cement Industry, K S Rajan, Economic Times, May 3, 1979,p 5.

Output elasticity of total cost-

Responsiveness of TC to the change in total production.

TC

Q

Q %

TC

Q IN %

TC IN % QeTC,

If eTC, Q <1 Economies of scale

etc, Q >1 Diseconomies of scale

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