COST THEORY AND ANALYSIS

NATURE OF COSTS Actual cost: cost incurred in production Opportunity cost: return from the second best use of

firm’s resources which the firm foregoes in order to avail the return

Explicit / Accounting Costs : Actual money spent in purchasing or hiring services of factor

Implicit / Imputed cost: Cost of self-owned and self-employed resources

Fixed costs: Costs which do not change with change in Out Put.

Variable or Prime costs: Costs which change with change in level of Out Put

Accounting costs: Cost as stated in books of accounts (explicit cost only)

Economic Costs: includes both explicit & implicit cost

NATURE OF COSTS

Marginal cost: Change in total cost associated with a one-unit change in output

Incremental Costs: Total additional cost of implementing a managerial decision

Sunk Costs: costs which do not change by varying the nature or level of business activity

NATURE OF COSTS

NATURE OF COSTS

Private cost: Actually incurred or provided for by an individual for its business activity

Social cost: Cost to society on account of production of good

Original cost: cost incurred originally Replacement cost: cost incurred in replacing

EXERCISEA Carpenter makes 100 chairs per month & sells them at Rs 150 per piece. His expenses on rent of shop, cost of wood & other materials are worth Rs 5000. He employs 2 workers whose monthly wage bill stand at Rs 2400 & pays electricity bill of Rs 500 per month. He has invested Rs 50,000 in the form of machines, tools & inventories of which Rs 25,000 is from his own fund & remaining 25,000 is a loan from bank at interest rate of 18% p.a. Assuming imputed cost of his own time, own shop & own savings of Rs 25000 as Rs 3000, Rs 1000 & Rs 250 respectively, find:

Explicit cost Implicit cost Accounting profit Economic profit

ANSWERS Explicit cost : Rs 8275 Implicit cost: Rs 4250 Accounting profit: Rs 6725 Economic profit: Rs 2475

COST FUNCTION

C = f (S, O, P, T……)

Where: C: Cost of O/P S: Size of plant O: level of O/P P: price of I/Ps used in production T: nature of technology

SR RELATIONSHIP BETWEEN PRODUCTION AND COST

A firm’s cost structure is intimately related to its production process

Costs are determined by the production technology and input prices

SR RELATIONSHIP BETWEEN PRODUCTION AND COST

In order to illustrate the relationship, consider the production process described in table

Total Input (L) Q (TP) MP0 01 1,000 1,0002 3,000 2,0003 6,000 3,0004 8,000 2,0005 9,000 1,0006 9,500 5007 9,850 3508 10,000 1509 9,850 -150

SR RELATIONSHIP BETWEEN PRODUCTION & COST

Total variable cost (TVC) is the cost associated with the variable input, in this case labor

Assume that labor can be hired at a price (w) of Rs 500 per unit

TOTAL I/P (L) Q (TP) MP

TVC (wL)

MC (∆TVC/ ∆Q)

0 0 0

1 1000 1000 500 0.5

2 3000 2000 1000 0.25

3 6000 3000 1500 0.16

4 8000 2000 2000 0.25

5 9000 1000 2500 0.5

6 9500 500 3000 1

7 9850 350 3500 1.4

8 10000 150 4000 3.33

9 9850 -150 4500

SR RELATIONSHIP BETWEEN PRODUCTION & COST TP and TVC are mirror images of each other When TP increase at an increasing rate, TVC increase at a

decreasing rate

RELATION B/W MP & MC

When MP is increasing, MC is decreasing

When MP is decreasing, MC is increasing

Total Input (L) Q MP

TVC (wL) MC

0 0 01 1,000 1,000 500 0.502 3,000 2,000 1,000 0.253 6,000 3,000 1,500 0.174 8,000 2,000 2,000 0.255 9,000 1,000 2,500 0.506 9,500 500 3,000 1.007 9,850 350 3,500 1.438 10,000 150 4,000 3.339 9,850 -150 4,500

SHORT-RUN COST FUNCTIONS

Total Cost = TC = f(Q)

TC = TFC + TVC

Total Fixed Cost = TFC

Total Variable Cost = TVC

SHORT-RUN COST FUNCTIONS

Average Fixed Cost = AFC = TFC/Q

Average Variable Cost = AVC =TVC/Q

Average Total Cost = ATC = TC/Q

Average Total Cost = AFC + AVC

Marginal Cost = TC/Q =TVC/Q

SHORT-RUN COST FUNCTIONS

Q TFC TVC TC AFC AVC ATC MC

0 60 0 60 - - - -

1 60 20 80 60 20 80 20

2 60 30 90 30 15 45 10

3 60 45 105 20 15 35 15

4 60 80 140 15 20 35 35

5 60 135 195 12 27 39 55

0

50

100

150

200

250

0 1 2 3 4 5 6Output

Output

Cost

Cost

Total Cost Function

Per Unit Cost Function

0

10

20

30

40

50

60

70

80

90

0 1 2 3 4 5 6

T C

A V C

A C

M C

T F C

T V C

AFC

SHORT RUN COST FUNCTION: IMPORTANT OBSERVATIONS

AFC declines steadily over the range of production In general, AVC, AC, and MC are U shaped When MC<AVC, AVC is falling When MC>AVC, AVC is rising When MC=AVC, AVC is at its minimum The distance between AC and AVC represents AFC

SHORT-RUN COST FUNCTIONS

Average Variable Cost

AVC = TVC = w L

Q Q

= w = w

Q/L APL

Marginal Cost

TC/Q = TVC/Q = (w L)/Q

= w = w

Q/L MPL

LR RELATIONSHIP B/W PRODUCTION & COST

All I/Ps variable No fixed costs LR cost structure of firm is related to firm’s long run

production process which is described by RTS Economists hypothesize that a firm’s long-run

production function may exhibit at first IRS then CRS & finally DRS

LR RELATIONSHIP B/W PRODUCTION & COST IRS: A proportional increase in all I/Ps increases O/P by a greater

percentage than costs Costs increase at a decreasing rate CRS: A proportional increase in all I/Ps increases O/P by same

percentage as costs Costs increase at a constant rate DRS: A proportional increase in all I/Ps increases O/P by a

smaller percentage than costs Costs increase at an increasing rate

LONG-RUN COST CURVES

Long-Run Total Cost = LTC = f(Q)

Long-Run Average Cost = LAC = LTC/Q

Long-Run Marginal Cost = LMC = LTC/Q

DERIVATION OF LONG-RUN COST CURVES

LAC

shows the lowest average cost of producing each level of O/P when the firm can build the most appropriate plant to produce each level of O/P

RELATIONSHIP B/W LONG-RUN & SHORT-RUN AVERAGE COST CURVES

RELATIONSHIP B/W LONG-RUN & SHORT-RUN AVERAGE COST CURVES

LONG-RUN COST FUNCTION

When LRAC declines: firm experiences economies of scale (per-unit costs are falling)

When LRAC increases: firm experiences diseconomies of scale (per-unit costs are rising)

LONG-RUN COST FUNCTION: GENERAL SHAPE

ECONOMIES OF SCALE

Inventory

Specialization

Team work

Real economies Pecuniary economies

transportation

Lower cost of finance

Quantity discounts

Selling

Internal External

Sales promotion

DISECONOMIES OF SCALE

Congestion Difficulty in Coordination &

control

Scarcity of resources

MANAGERIAL USES OF COST FUNCTIONS: DETERMINING OPTIMUM OUTPUT LEVEL

O/P level at which AC is minimum Necessary condition: ∂(AC) / ∂Q = 0 Sufficient condition: ∂2(AC) / ∂Q2 > 0

MANAGERIAL USES OF COST FUNCTIONS: DETERMINING OPTIMUM SCALE

Value of plant size (K) at which total cost (C) is minimum

Necessary condition: ∂C / ∂K = 0 Sufficient condition: ∂2C / ∂K2 > 0

SPECIAL TOPICS IN COST THEORY

(1) PROFIT CONTRIBUTION ANALYSIS

Total Revenue = TR = (P)(Q)

Total Cost = TC = TFC + (AVC)(Q)

Profit = TR -TC

Profit = = PQ - [TFC + (AVC)(Q)]

Q = TFC +

P - (AVC)

Profit contribution = P - AVC

EXAMPLE

Fixed cost = Rs 10,000

Price = Rs 20

AVC = Rs 15

How much O/P should the firm produce to have a profit of Rs 20,000?

Answer: 6000 units

= TR - TC = 0

TR = TC

(P)(Q) = TFC + (AVC)(Q)

(2) BREAKEVEN VOLUME (TR = TC) (zero economic profit)

QBE = TFC

(P - AVC)

EXAMPLE

Fixed cost = Rs 10,000Price = Rs 20AVC = Rs 15How much O/P should the firm produce in

order to break even?

Answer: 2000 units

Also : TR = 20QTC = 10,000 + 15QTR = TC

LINEAR BREAKEVEN ANALYSIS

P = 10

TFC = 200

AVC = 5

LINEAR BREAKEVEN ANALYSIS: SHORTCOMINGS

Assumes constant prices Assumes constant average variable costs

EXCERCISE

Petersen & Lewis Page # 248: Breaking even on Microcomputer software

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6

TR/TC

Q

TC

TR

-50

-40

-30

-20

-10

0

10

20

30

40

0 1 2 3 4 5 6

Profit

Q

NONLINEAR BREAKEVEN ANALYSIS

(3) OPERATING LEVERAGE

Operating Leverage = TFC/TVC

Degree of Operating Leverage (or profit elasticity) = DOL

= PQ - TFC + (AVC)(Q) = Q(P - AVC) - TFC

= Q(P - AVC)

DOL = % = / = * Q = E %Q Q/Q Q

DOL = Q(P - AVC)Q = Q(P - AVC) Q[Q(P - AVC) - TFC] Q(P - AVC) - TFC

(4) LEARNING CURVE

Workers improve with practice so per unit cost of additional O/P declines

Measures % decrease in additional labor cost each time O/P doubles

An “80 percent” learning curve implies that each time O/P doubles, L costs associated with incremental output decrease to 80% of previous level

UTILITY OF LEARNING CURVES

To forecast needs of

personnel

machinery

raw materials

Scheduling production

Determining Selling price of product

(5) ECONOMIES OF SCOPE

The reduction of a firm’s unit cost by producing two or more goods or services jointly rather than separately

Degree of economies of scope =

TC(Q1) + TC(Q2) – TC(Q1 + Q2)TC(Q1 + Q2)

EXAMPLE Firm A produces 100 units of X & 500 units of Y per

month at the TC of Rs 1,00,000. If X & Y are produced separately by firms B & C then the TC to firm B of producing 100 X is Rs 25000 & firm C of producing 500 Y is Rs 90,000.Check whether firm A is experiencing economies or diseconomies of scope

Answer: 0.15 so economies of scopeNOTE:

Positive: economies of scope Negative: diseconomies of scope