18004333 Cost Theory And Analysis

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

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

NATURE OF COSTS 

Fixed costs: Costs which do not change with change in O/P

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Variable or Prime costs: Costs which change with change in level of O/P



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

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Economic Costs: includes both explicit & implicit cost

NATURE OF COSTS

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

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Incremental Costs: Total additional cost of implementing a managerial decision

NATURE OF COSTS 

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

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

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Original cost: cost incurred originally

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Replacement cost: cost incurred in replacing

EXERCISE

   

A 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

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

0

60

0

60

AFC

AVC

ATC

MC

-

-

-

-

60

20

80

20

1

60

20

80

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

Cost

250

Total Cost Function

200

TC

150

TVC

100

TFC

50

0

Cost

0

1

2

3

4

5

90

6

Output

Per Unit Cost Function

80 70

MC

60 50 40

AC

30

AVC

20

AFC

10 0

0

1

2

3

4

5

6

Output

SHORT RUN COST FUNCTION: IMPORTANT OBSERVATIONS 

AFC declines steadily over the range of production



In general, AVC, AC, and MC are U shaped When MCAVC, AVC is rising When MC=AVC, AVC is at its minimum

  



The distance between AC and AVC represents AFC

SR RELATIONSHIP BETWEEN PRODUCTION AND COST 

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



Costs are determined by technology and input prices

the

production

SR RELATIONSHIP BETWEEN PRODUCTION AND COST In order to illustrate the relationship, consider the production process described in table

Total Input (L) Q (TP) 0 0 1 1,000 2 3,000 3 6,000 4 8,000 5 9,000 6 9,500 7 9,850 8 10,000 9 9,850

MP 1,000 2,000 3,000 2,000 1,000 500 350 150 -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 Q (TP) I/P (L)

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 Also when MP= AP at max AP, MC = AVC at min AVC

Total Input (L) 0 1 2 3 4 5 6 7 8 9

Q 0 1,000 3,000 6,000 8,000 9,000 9,500 9,850 10,000 9,850

MP 1,000 2,000 3,000 2,000 1,000 500 350 150 -150

TVC (wL) 0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500

MC 0.50 0.25 0.17 0.25 0.50 1.00 1.43 3.33

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

EXERCISE Given Total Cost function: TC = 1000 + 10 Q – 0.9 Q 2 + 0.04 Q 3 Find the rate of O/P that result in minimum Average Variable cost

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

LR RELATIONSHIP B/W PRODUCTION & COST

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 It 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 LAC declines: firm experiences economies of scale (per-unit costs are falling)



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

LONG-RUN COST FUNCTION: GENERAL SHAPE

ECONOMIES OF SCALE Internal

External Pecuniary economies

Real economies

Quantity discounts

Specialization Indivisibility Advertising

Team work

Lower cost of capital transportation Sales promotion

DISECONOMIES OF SCALE Congestion

Scarcity of resources

Difficulty in Coordination & control

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

(2) BREAKEVEN VOLUME (TR = TC) (zero economic profit) Π = TR - TC = 0 TR = TC (P)(Q) = TFC + (AVC)(Q) QBE =

TFC (P - AVC)

EXAMPLE Fixed cost = Rs 10,000 Price = Rs 20 AVC = Rs 15 How much O/P should the firm produce in order to break even? Answer: 2000 units Also : TR = 20Q TC = 10,000 + 15Q TR = 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 # 239: Breaking even on Microcomputer software

NONLINEAR BREAKEVEN ANALYSIS TR/TC

TC

350 300

TR

250 200 150 100 50 0

Profit

0

1

2

3

4

1

2

3

4

5

6

Q

40 30 20 10 0

0

5

-10 -20 -30 -40 -50

Π

6

Q

(3) OPERATING LEVERAGE Operating Leverage = TFC/TVC Degree of Operating Leverage (or profit elasticity) = DOL

DOL = %∆ Π %∆ Q

= ∆ Π/Π ∆ Q/Q

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

= ∆ Π *Q = EΠ ∆Q Π

∆ Π = ∆ Q(P - AVC)

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 scope



NOTE: Positive: economies of scope Negative: diseconomies of scope

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