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Cost Analysis Dr. Kishor Bhanushali Faculty – Economics & Quantitative Methods
Relations Between Production and Cost
The cost function gives the functional relationship between total cost and total output The same level of output can be produced with different cost combinations Cost function gives the least cost combinations for the production of different level of output Cost functions are derived functions, they are derived from production functions The cost function derived from the expansion path of the firm represents the cost functions in its long run nature
Types of Costs
Explicit and Implicit costs Direct and Indirect costs Private cost versus Social cost Relevant cost and Irrelevant cost Economic cost and Accounting cost Separable and Common costs Fixed and Variable costs
Fixed Cost and Variable Cost of the Firm in the Short Run
Short run is a period during which the one of the factor of production is considered to be constant and the other variable TC = TVC + TFC
Units of Output
Total Fixed Costs
1
Total Variabl e Costs
2
Total Costs 2+3
3
Average Fixed Costs 2/1
4
Average Average Margin variable Costs al Costs Costs 5+6 3/1
5
6
7
8
0
30
0
30
-
-
-
-
1
30
10
40
30
10
40
10
2
30
18
48
15
9
24
8
3
30
24
54
10
8
18
6
4
30
32
62
7.5
8
15.5
8
5
30
50
80
6
10
16
18
6
30
72
102
5
12
17
22
Derivation of Cost Curves
TFC : Total Fixed Cost TVC: Total Variable Cost TC: Total Cost AFC: Average Fixed Cost AVC: Average Variable Cost AC: Average Cost MC: Marginal Cost
Relationship Between Average and Marginal Costs Y MC
MC AC
MC
AC
MC O
X
Long Run Average Cost Curve: The Envelope Curve
In the long run all factors of production are assumed to be variable The long run cost is also known as the planning curve, in the sense that it is a guide to the entrepreneur in his decision to plan for the future expansion of output The LAC curve is the locus of the tangency points of the SAC curves
y AC
AC M’
M
o
M
AC
A
M’
x
Derivation of Long Run Cost Average Cost Curve LAC & SAC
LAC
SAC SAC
SAC SAC
0
Q1
Q
Q2
Output
Why LAC Curves are Flatter
Over a long period of time size of the plant can be changed in order to deal with smaller or larger output Loner the period under consideration, the fewer costs are fixed and more costs are variable In the long run fixed costs can be reduced, average fixed costs will therefore be lower in the long run Variable costs will not rise as sharply in the long run as they do in the short run, as the size of the firm can be changed In the long run average cost will be lower and variable costs will not rise as sharply as in the short run period
Long Run Marginal Cost
The long run marginal cost curve is derived from the short run marginal cost curves but does not envelop them. LMC curve is formed from the points of intersection of the SMC curves with the vertical lines drawn from the point of tangency of the corresponding SAC curves and the LAC curve The LMC must be equal to the SMC for the output at which the corresponding SAC is tangent to the LAC curve. By joining this points of intersection points we get the LMC curve of the firm
Derivation of Long Run Marginal Cost Curve LAC & SAC & LMC & SMC
LMC
LAC
SMC SAC SMC
SAC
0 Q1
SMC
Q
Q2
Output
Economies of Scale A Production economies of scale 1. Labour Economies of Scale c) Specialization d) Time Saving e) Automation of production of process f) Cumulative volume economies 2. Technical Economies h) Specialization and indivisibility of capital i) Set-up cost j) Initial fixed cost k) Technical volume/output relations l) Reserve capacity requirement 3. Inventory Economies n) Inventory in spare parts o) Inventory in raw materials p) Inventory in ready products
Economies of Scale B. Selling or Marketing Economies 2. Advertising 3. Large scale promotion 4. Exclusive dealers with obligations for maintaining service departments 5. Model-change economies C. Managerial Economies 7. Specialization of management 8. Mechanization of managerial functions D. Transport and Storage Economies 10. Storage 11. Transport
Economies of Scale Pecuniary Economies of Scale 2. Lower prices of the materials, bought at special discounts from its suppliers 3. Lower costs of external finance 4. Lower advertising prices 5. Lower transport rates 6. Lower wags and salaries due to monopolistic power of large firms or to prestige associated with large firms
Traditional Envelope LAC Cost
There are diseconomies of scale at very large scale of output LAC
0
Q
Output
L- Shaped LAC Curve Cost
There is a minimum optimum scale of output at which all possible economies have been reaped so that cost remains costant beyond that level of output
LAC
0
Q
Output
Inverse – J shaped LAC Cost
There are economies of scale at all levels of output, although their magnitude becomes small beyond a certain scale
LAC 0
Output
Numerical STC = 1000 + 80Q − 6Q + 0.2Q 2
3
SMC
4
5.88
MPL
Q
L
TVC
SAC
0
0
0
-
40
2
100
4
150
6
190
8
224
10
254
12
274
14
284
16
Fixed Cost Rs. 300 Wages Rs 100
12.50
5.91
Relations Between Production and Cost
The cost function gives the functional relationship between total cost and total output The same level of output can be produced with different cost combinations Cost function gives the least cost combinations for the production of different level of output Cost functions are derived functions, they are derived from production functions The cost function derived from the expansion path of the firm represents the cost functions in its long run nature
Types of Costs
Explicit and Implicit costs Direct and Indirect costs Private cost versus Social cost Relevant cost and Irrelevant cost Economic cost and Accounting cost Separable and Common costs Fixed and Variable costs
Fixed Cost and Variable Cost of the Firm in the Short Run
Short run is a period during which the one of the factor of production is considered to be constant and the other variable TC = TVC + TFC
Units of Output
Total Fixed Costs
1
Total Variabl e Costs
2
Total Costs 2+3
3
Average Fixed Costs 2/1
4
Average Average Margin variable Costs al Costs Costs 5+6 3/1
5
6
7
8
0
30
0
30
-
-
-
-
1
30
10
40
30
10
40
10
2
30
18
48
15
9
24
8
3
30
24
54
10
8
18
6
4
30
32
62
7.5
8
15.5
8
5
30
50
80
6
10
16
18
6
30
72
102
5
12
17
22
Derivation of Cost Curves
TFC : Total Fixed Cost TVC: Total Variable Cost TC: Total Cost AFC: Average Fixed Cost AVC: Average Variable Cost AC: Average Cost MC: Marginal Cost
Relationship Between Average and Marginal Costs Y MC
MC AC
MC
AC
MC O
X
Long Run Average Cost Curve: The Envelope Curve
In the long run all factors of production are assumed to be variable The long run cost is also known as the planning curve, in the sense that it is a guide to the entrepreneur in his decision to plan for the future expansion of output The LAC curve is the locus of the tangency points of the SAC curves
y AC
AC M’
M
o
M
AC
A
M’
x
Derivation of Long Run Cost Average Cost Curve LAC & SAC
LAC
SAC SAC
SAC SAC
0
Q1
Q
Q2
Output
Why LAC Curves are Flatter
Over a long period of time size of the plant can be changed in order to deal with smaller or larger output Loner the period under consideration, the fewer costs are fixed and more costs are variable In the long run fixed costs can be reduced, average fixed costs will therefore be lower in the long run Variable costs will not rise as sharply in the long run as they do in the short run, as the size of the firm can be changed In the long run average cost will be lower and variable costs will not rise as sharply as in the short run period
Long Run Marginal Cost
The long run marginal cost curve is derived from the short run marginal cost curves but does not envelop them. LMC curve is formed from the points of intersection of the SMC curves with the vertical lines drawn from the point of tangency of the corresponding SAC curves and the LAC curve The LMC must be equal to the SMC for the output at which the corresponding SAC is tangent to the LAC curve. By joining this points of intersection points we get the LMC curve of the firm
Derivation of Long Run Marginal Cost Curve LAC & SAC & LMC & SMC
LMC
LAC
SMC SAC SMC
SAC
0 Q1
SMC
Q
Q2
Output
Economies of Scale A Production economies of scale 1. Labour Economies of Scale c) Specialization d) Time Saving e) Automation of production of process f) Cumulative volume economies 2. Technical Economies h) Specialization and indivisibility of capital i) Set-up cost j) Initial fixed cost k) Technical volume/output relations l) Reserve capacity requirement 3. Inventory Economies n) Inventory in spare parts o) Inventory in raw materials p) Inventory in ready products
Economies of Scale B. Selling or Marketing Economies 2. Advertising 3. Large scale promotion 4. Exclusive dealers with obligations for maintaining service departments 5. Model-change economies C. Managerial Economies 7. Specialization of management 8. Mechanization of managerial functions D. Transport and Storage Economies 10. Storage 11. Transport
Economies of Scale Pecuniary Economies of Scale 2. Lower prices of the materials, bought at special discounts from its suppliers 3. Lower costs of external finance 4. Lower advertising prices 5. Lower transport rates 6. Lower wags and salaries due to monopolistic power of large firms or to prestige associated with large firms
Traditional Envelope LAC Cost
There are diseconomies of scale at very large scale of output LAC
0
Q
Output
L- Shaped LAC Curve Cost
There is a minimum optimum scale of output at which all possible economies have been reaped so that cost remains costant beyond that level of output
LAC
0
Q
Output
Inverse – J shaped LAC Cost
There are economies of scale at all levels of output, although their magnitude becomes small beyond a certain scale
LAC 0
Output
Numerical STC = 1000 + 80Q − 6Q + 0.2Q 2
3
SMC
4
5.88
MPL
Q
L
TVC
SAC
0
0
0
-
40
2
100
4
150
6
190
8
224
10
254
12
274
14
284
16
Fixed Cost Rs. 300 Wages Rs 100
12.50
5.91
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