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COST THEORY AND ANALYSIS
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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
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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
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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
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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
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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
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ANSWERS Explicit cost : Rs 8275 Implicit cost: Rs 4250 Accounting profit: Rs 6725 Economic profit: Rs 2475
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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
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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
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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
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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
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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
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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
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SHORT-RUN COST FUNCTIONS
Total Cost = TC = f(Q)
TC = TFC + TVC
Total Fixed Cost = TFC
Total Variable Cost = TVC
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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
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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
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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
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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
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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
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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
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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
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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
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DERIVATION OF LONG-RUN COST CURVES
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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
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RELATIONSHIP B/W LONG-RUN & SHORT-RUN AVERAGE COST CURVES
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RELATIONSHIP B/W LONG-RUN & SHORT-RUN AVERAGE COST CURVES
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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)
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LONG-RUN COST FUNCTION: GENERAL SHAPE
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ECONOMIES OF SCALE
Inventory
Specialization
Team work
Real economies Pecuniary economies
transportation
Lower cost of finance
Quantity discounts
Selling
Internal External
Sales promotion
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DISECONOMIES OF SCALE
Congestion Difficulty in Coordination &
control
Scarcity of resources
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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
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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
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SPECIAL TOPICS IN COST THEORY
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(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
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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
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= TR - TC = 0
TR = TC
(P)(Q) = TFC + (AVC)(Q)
(2) BREAKEVEN VOLUME (TR = TC) (zero economic profit)
QBE = TFC
(P - AVC)
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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
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LINEAR BREAKEVEN ANALYSIS
P = 10
TFC = 200
AVC = 5
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LINEAR BREAKEVEN ANALYSIS: SHORTCOMINGS
Assumes constant prices Assumes constant average variable costs
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EXCERCISE
Petersen & Lewis Page # 248: Breaking even on Microcomputer software
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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
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(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
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(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
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UTILITY OF LEARNING CURVES
To forecast needs of
personnel
machinery
raw materials
Scheduling production
Determining Selling price of product
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(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)
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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