Law of variable properties

1. Laws of VariableLaws of Variable
ProportionsProportions
&&
Returns to ScaleReturns to Scale

2. Production in the Short runProduction in the Short run
• Production functionsProduction functions
• Long-run and short-run production:Long-run and short-run production:
– fixed and variable factorsfixed and variable factors
• The law of diminishing returnsThe law of diminishing returns
(Laws of variable proportions)(Laws of variable proportions)
change in one factor - labourchange in one factor - labour
• The short-run production function:The short-run production function:
– total physical product (total physical product (TPPTPP))

3. Wheat production per year from a particular farmWheat production per year from a particular farm
0
10
20
30
40
0 1 2 3 4 5 6 7 8
Number of farm workers
Tonnesofwheatproducedperyear
Number of
workers
0
1
2
3
4
5
6
7
8
TPP
0
3
10
24
36
40
42
42
40

4. 0
10
20
30
40
0 1 2 3 4 5 6 7 8
Number of farm workers
Tonnesofwheatproducedperyear
TPP
Wheat production per year from a particular farmWheat production per year from a particular farm

5. 0
10
20
30
40
0 1 2 3 4 5 6 7 8
Number of farm workers
Tonnesofwheatproducedperyear
TPP
a
Wheat production per year from a particular farmWheat production per year from a particular farm

6. 0
10
20
30
40
0 1 2 3 4 5 6 7 8
Number of farm workers
Tonnesofwheatproducedperyear
TPP
a
b
d
Maximum output
Wheat production per year from a particular farmWheat production per year from a particular farm

7. Production in the Short runProduction in the Short run
• Production functionsProduction functions
• Long-run and short-run production:Long-run and short-run production:
– fixed and variable factorsfixed and variable factors
• The law of diminishing returnsThe law of diminishing returns
• The short-run production function:The short-run production function:
– total physical product (total physical product (TPPTPP))
– average physical product (average physical product (APPAPP))

8. Production in the Short runProduction in the Short run
• Production functionsProduction functions
• Long-run and short-run production:Long-run and short-run production:
– fixed and variable factorsfixed and variable factors
• The law of diminishing returnsThe law of diminishing returns
• The short-run production function:The short-run production function:
– total physical product (total physical product (TPPTPP))
– average physical product (average physical product (APPAPP))
– marginal physical product (marginal physical product (MPPMPP))

9. Production in the Short runProduction in the Short run
• Production functionsProduction functions
• Long-run and short-run production:Long-run and short-run production:
– fixed and variable factorsfixed and variable factors
• The law of diminishing returnsThe law of diminishing returns
• The short-run production function:The short-run production function:
– total physical product (total physical product (TPPTPP))
– average physical product (average physical product (APPAPP))
– marginal physical product (marginal physical product (MPPMPP))
– the graphical relationship betweenthe graphical relationship between TPPTPP,, APPAPP
andand MPPMPP

10. 0
10
20
30
40
0 1 2 3 4 5 6 7 8
Wheat production per year from a particular farmWheat production per year from a particular farm
Number of
farm workers (L)
Tonnesofwheatperyear
TPP
-2
0
2
4
6
8
10
12
14
0 1 2 3 4 5 6 7 8
Tonnesofwheatperyear
Number of
farm workers (L)
∆TPP = 7
∆L = 1
MPP = ∆TPP / ∆L = 7

11. 0
10
20
30
40
0 1 2 3 4 5 6 7 8
Tonnesofwheatperyear
TPP
-2
0
2
4
6
8
10
12
14
0 1 2 3 4 5 6 7 8
Tonnesofwheatperyear
MPP
Number of
farm workers (L)
Number of
farm workers (L)
Wheat production per year from a particular farmWheat production per year from a particular farm

12. 0
10
20
30
40
0 1 2 3 4 5 6 7 8
Tonnesofwheatperyear
TPP
-2
0
2
4
6
8
10
12
14
0 1 2 3 4 5 6 7 8
Tonnesofwheatperyear
APP
MPP
APP = TPP / L
Number of
farm workers (L)
Number of
farm workers (L)
Laws of Variable ProportionsLaws of Variable Proportions

13. 0
10
20
30
40
0 1 2 3 4 5 6 7 8
Tonnesofwheatperyear
TPP
-2
0
2
4
6
8
10
12
14
0 1 2 3 4 5 6 7 8
Tonnesofwheatperyear
APP
MPP
b
Diminishing returns
set in here
Number of
farm workers (L)
Number of
farm workers (L)
b
Wheat production per year from a particular farmWheat production per year from a particular farm

14. 0
10
20
30
40
0 1 2 3 4 5 6 7 8
Tonnesofwheatperyear
TPP
-2
0
2
4
6
8
10
12
14
0 1 2 3 4 5 6 7 8
Tonnesofwheatperyear
APP
MPP
b
d
d
Number of
farm workers (L)
Number of
farm workers (L)
Maximum
outputb
Laws of Variable ProportionsLaws of Variable Proportions

15. 0
10
20
30
40
0 1 2 3 4 5 6 7 8
Tonnesofwheatperyear
TPP
-2
0
2
4
6
8
10
12
14
0 1 2 3 4 5 6 7 8
Tonnesofwheatperyear
APP
MPP
b
b
d
d
Number of
farm workers (L)
Number of
farm workers (L)
c
c
Three stages of diminishing returnsThree stages of diminishing returns
Stage I Stage II Stage III
TP, AP increase
at increasing rate
TP at
diminishing
MP +
MP
negative
Increasing
returns
Negative
Returns
Diminishing
Returns
Increasing
returns
Diminishing
Returns
Negative
Returns

16. • Increasing ReturnsIncreasing Returns
– TP is Rising (increasing rate)TP is Rising (increasing rate)
– AP is risingAP is rising
– MP risingMP rising
• Diminishing ReturnsDiminishing Returns
– TP increases (decreasing rate)TP increases (decreasing rate)
– AP fallingAP falling
– MP falling but positiveMP falling but positive
• Negative ReturnsNegative Returns
– TP fallingTP falling
– AP fallingAP falling
– MP negativeMP negative
Stage of Operation

17. TP, AP and MPTP, AP and MP
• From the table below find APFrom the table below find APLL and MPand MPLL
LandLand LabourLabour TPTP APAPLL
11 00 00
11 11 22
11 22 55
11 33 99
11 44 1212
11 55 1414
11 66 1515
11 77 1515
11 88 1414
11 99 1212

18. TP, AP and MPTP, AP and MP
• From the table below find APFrom the table below find APLL and MPand MPLL
LandLand LabourLabour TPTP APAPLL MPMPLL
11 00 00 00
11 11 22 22
11 22 55 2.52.5
11 33 99 33
11 44 1212 33
11 55 1414 2.82.8
11 66 1515 2.52.5
11 77 1515 2.12.1
11 88 1414 1.751.75
11 99 1212 1.331.33

19. TP, AP and MPTP, AP and MP
• From the table below find APFrom the table below find APLL and MPand MPLL
LandLand LabourLabour TPTP APAPLL MPMPLL
11 00 00 00 ----
11 11 22 22 22
11 22 55 2.52.5 33
11 33 99 33 44
11 44 1212 33 33
11 55 1414 2.82.8 22
11 66 1515 2.52.5 11
11 77 1515 2.12.1 00
11 88 1414 1.751.75 -1-1
11 99 1212 1.331.33 -2-2

20. -4
-2
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9
Labour
TP/AP/MP
TP 0
APL 0
MPL --

21. • All factors variable in long runAll factors variable in long run
• The scale of production:The scale of production:
– constant returns to scale (CRS)constant returns to scale (CRS)
– If outputs increase in the same proportion of inputs
– increasing returns to scaleincreasing returns to scale
– If output increases more than proportionately with an increase
in factor inputs
– decreasing returns to scaledecreasing returns to scale
– If output increases more than proportionately with an increase
in factor inputs
Production in the Long RunProduction in the Long Run

22. Technological changeTechnological change
• Shift in production functionShift in production function
Q
L
Q = f (L,K0
)
Q = f I
(L,K0
)
0

23. Isoquant - Isocost Analysis

24. 0
5
10
15
20
25
30
35
40
45
0 5 10 15 20 25 30 35 40 45 50
Units
of K
40
20
10
6
4
Units
of L
5
12
20
30
50
Point on
diagram
a
b
c
d
e
Units of labour (L)
Unitsofcapital(K)
An isoquantAn isoquant

25. 0
5
10
15
20
25
30
35
40
45
0 5 10 15 20 25 30 35 40 45 50
Units
of K
40
20
10
6
4
Units
of L
5
12
20
30
50
Point on
diagram
a
b
c
d
e
a
Units of labour (L)
Unitsofcapital(K) An isoquantAn isoquant

26. 0
5
10
15
20
25
30
35
40
45
0 5 10 15 20 25 30 35 40 45 50
Units
of K
40
20
10
6
4
Units
of L
5
12
20
30
50
Point on
diagram
a
b
c
d
e
a
b
Units of labour (L)
Unitsofcapital(K)
An isoquantAn isoquant

27. 0
5
10
15
20
25
30
35
40
45
0 5 10 15 20 25 30 35 40 45 50
Units
of K
40
20
10
6
4
Units
of L
5
12
20
30
50
Point on
diagram
a
b
c
d
e
a
b
c
d
e
Units of labour (L)
Unitsofcapital(K)
An isoquantAn isoquant

28. 0
2
4
6
8
10
12
14
0 2 4 6 8 10 12 14 16 18 20
Unitsofcapital(K)
Units of labour (L)
g
h
∆K = 2
∆L = 1
isoquant
MRS = 2 MRS = ∆K / ∆L
Diminishing marginal rate of factor substitution

29. 0
2
4
6
8
10
12
14
0 2 4 6 8 10 12 14 16 18 20
Unitsofcapital(K)
Units of labour (L)
g
h
j
k
∆K = 2
∆L = 1
∆K = 1
∆L = 1
isoquant
MRS = 2
MRS = 1
MRS = ∆K / ∆L
Diminishing marginal rate of factor substitutionDiminishing marginal rate of factor substitution

30. 0
10
20
30
0 10 20
IQ1
IQ2
IQ3
IQ4
IQ5
Unitsofcapital(K)
Units of labour (L)
An isoquant mapAn isoquant map
The further out the
isoquant, the
higher the level of
output.
All points on an
isoquant represent a
particular level of
output.

31. Returns to scaleReturns to scale

32. 0
1
2
3
4
0 1 2 3
Unitsofcapital(K)
Units of labour (L)
200
300
400
500
600
a
b
c
R
Constant returns to scale(Change in Output = Change in Inputs)

33. 0
1
2
3
4
0 1 2 3
Unitsofcapital(K)
Units of labour (L)
200
300
400
500
600
a
b
c
R
700
Increasing returns to scale (Increasing returns to scale (Change in Output > Change in Inputs))

34. 0
1
2
3
4
0 1 2 3
Unitsofcapital(K)
Units of labour (L)
200
300
400
500
a
b
c
R
Decreasing returns to scale (Change in Output < Change in Inputs)

35. Production in the Long runProduction in the Long run
• Changing both factorsChanging both factors
• Increasing Returns to ScaleIncreasing Returns to Scale
– Change in Output > Change in InputsChange in Output > Change in Inputs
• Constant Returns to ScaleConstant Returns to Scale
– Change in Output = Change in InputsChange in Output = Change in Inputs
• Decreasing Returns to ScaleDecreasing Returns to Scale
– Change in Output < Change in InputsChange in Output < Change in Inputs

36. 0
5
10
15
20
25
30
0 5 10 15 20 25 30 35 40
Units of labour (L)
Unitsofcapital(K)
Assumptions
PK = Rs.20 000
W = Rs.10 000
TC = Rs.300 000
An isocostAn isocost

37. 0
5
10
15
20
25
30
0 5 10 15 20 25 30 35 40
Units of labour (L)
Unitsofcapital(K)
TC = Rs.300 000
a
b
c
d
Assumptions
PK = Rs.20 000
W = Rs.10 000
TC = Rs.300 000
An isocostAn isocost
pKK +wL = C

38. The least-costThe least-cost
method of productionmethod of production

39. 0
5
10
15
20
25
30
35
0 10 20 30 40 50
Units of labour (L)
Unitsofcapital(K)
Assumptions
PK = Rs.20 000
W = Rs.10 000
TC = Rs.200 000
TC = Rs.300 000
TC = Rs.400 000
TC = Rs.500 000
The least-cost method of production

40. 0
5
10
15
20
25
30
35
0 10 20 30 40 50
Units of labour (L)
Unitsofcapital(K)
TPP1
TC = Rs.400 000
TC = Rs.500 000
r
s
t
The least-cost method of production

41. • Why Returns to Scale?Why Returns to Scale?
• Economies of scaleEconomies of scale
– specialisation & division of labourspecialisation & division of labour
– indivisibilitiesindivisibilities
– greater efficiency of large machinesgreater efficiency of large machines
– by-productsby-products
– multi-stage productionmulti-stage production
– organisational & administrative economiesorganisational & administrative economies
– financial economiesfinancial economies
• Diseconomies of scaleDiseconomies of scale
Production in the Long runProduction in the Long run

42. • External economies and diseconomies ofExternal economies and diseconomies of
scalescale
• LocationLocation
– balancing the distance from suppliers andbalancing the distance from suppliers and
consumersconsumers
– importance of transport costsimportance of transport costs
– Time period (Short run, Very Short run……)Time period (Short run, Very Short run……)
Production in the Long runProduction in the Long run

43. • Thank you………..Thank you………..