Download is the cost. - SNS Courseware

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 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.
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 =
TC OR
TVC
Q
Q
Short-run Production costs
Figures in rupees
Output
(Units)
0
1
2
3
4
6
Total
Total
Total Cost
Fixed Cost Variable Cost
240
0
240
240
120
360
240
160
400
240
180
420
240
212
452
240
280
520
Cost curves
ATC
MC
AVC
AFC
OUTPUT
Average Fixed Cost, Average Variable Cost and
Average Total cost of the Firm
Output
(Units)
1
Average
Fixed Cost
TFC  Q
240 1 = 240
Average
Average
Variable Cost Total Cost
TVC Q
TC Q
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
Calculation of Marginal Cost
Output
(units)
0
Total Cost
(Rupees)
240
Total Variable Marginal Cost
Cost(Rupees)
(Rupees)
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
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)
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
X
X
X
X
1
---
---
2
---
204
3
---
---
4
---
---
5
---
525
6
---
---
7
---
---
8
---
768
9
---
---
1265
494
86
286
97
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
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 AC
A
B
M
P
NN
C
O
L
Q
OUTPUT
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 function
1.Linear Cost function
1. Linear function:
TC
=
(TFC + TVC)
a + bQ
(TFC) (AVCxQ)
TVC
a/Q + b
ATC = TC/Q = TFC/Q + TVC/Q =
TC=a + bQ
MC = dTC = b
dQ
Illustration:
TFC
TC = 100 + 0.5Q
(Q=10)
TFC = 100 ; TVC = 0.5Q
output
At Q = 10, TVC = 0.5 x 10 = 5 and TC = 100 + 5 = 105
ATC = a/Q + b = 100/10 + 0.5 = 10.5
MC = b = 0.5
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
TC = a + bQ + cQ2
ATC = a/Q + b + cQ
MC = b + 2cQ
TFC
output
Here, 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 250Q
Additional 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
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 units
per 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
TC=a + bQ = cQ2 +dQ3
returns.
Increasing Decreasing
Productivity Productivity
TFC
output
(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