Why Fuel Poverty? Dynamics
of Income and Expenditure of
Households in Yorkshire
KESHAB BHATTARAI
Business School, University of Hull
Yorkshire, United Kingdom
22nd Annual Congress of European Economic Association and
62nd European Meeting of Econometric Society, Budapest
August 26-31, 2007
1
Illnesses and Diseases Due to Coldness
•
•
•
•
•
•
Asthma
Chronic obstructive pulmonary disease, blood pressure
Heart attack
Arthritis
Loss of strengths of fingers and mental retardation
Isolation of elderly and created obstacles in smooth
education process of younger pupils
• 163,000 households in the Yorkshire and Humber (7.7%
of the households)
• Excess death of more than 3200 individuals annually in
Yorkshire alone.
2
Health risks due to cold
3
pneumonia
Health risks due to cold
4
5
Health risks due to cold
Health risks due to cold
6
Literature Review
Rowntree B. S. (1902) Poverty of Town Life, MacMillan, London.
Rowntree (1902)
7
Table A1
Income and source of income 1970 to 2002-03 based on un-weighted data unless otherwise footnoted
Grossed
number
of households
Number
of households in
the
sample
Weekly household income1
Current prices
Source of income
Constant prices
Wages
and
salaries
Self
employment
Annuities
and
pensions2
Investments
Social
security
benefits3
Other
sources
Disposable
Gross
Disposable
Gross
Number
£
£
£
£
1970
6,393
28
34
269
324
77
7
3
4
9
1
1980
6,944
115
140
299
366
75
6
3
3
13
1
1990
7,046
258
317
363
447
67
10
5
6
11
1
1995-96
6,797
307
381
363
450
64
9
7
5
14
2
1996-97
6,415
325
397
375
458
65
9
7
4
14
1
1997-98
1998-994
1999-2000
2000-01
2001-025
2002-03
6,409
6,630
7,097
6,637
7,473
6,927
343
371
391
409
442
453
421
457
480
503
541
552
383
402
417
424
451
453
470
495
512
521
552
552
67
68
66
67
69
68
8
8
10
9
9
8
7
7
7
7
7
7
4
4
5
4
4
3
13
12
12
12
11
12
1
1
1
1
1
1
(000s)
24,660
25,340
25,030
24,450
24,350
Percentage of gross weekly household income
1. Does not include imputed income from owner-occupied and rent-free households.
2. Other than social security benefits.
3. Excluding housing benefit and council tax benefit (rates rebate in Northern Ireland) and their predecessors in earlier years - see appendix D.
4. Based on grossed data from 1998-99
5. From 2001-02 onwards, weighting is based on the population figures from the 2001 census
8
Table A2
Household expenditure as a percentage of total expenditure 1978 to 2002-03 (revised4)
Year
1978
1980
1982
1984
1986
1988
1990
1992
1994
19951
Grossed number of households (thousands)
Total number of households in sample
Total number of persons
Average number of persons
per household
1995
1996
1997
1998
1999
2000
2001
2002
2003
24,130
24,310
24,560
24,660
25,330
25,030
24,450
24,346
24,350
7,001
6,944
7,428
7,081
7,178
7,265
7,046
7,418
6,853
6,797
6,797
6,415
6,409
6,630
7,097
6,637
7,473
6,927
6,927
19,019
18,844
20,022
18,557
18,330
18,280
17,437
18,174
16,617
16,586
16,586
15,732
15,430
16,218
16,786
15,925
18,122
16,586
16,586
2.7
2.7
2.6
2.5
2.5
2.5
2.4
2.4
2.4
2.5
2.3
2.4
2.4
2.4
2.4
15
15
17
16
17
18
18
17
16
17
16
16
15
16
16
17
17
17
17
6
6
6
6
6
5
4
5
5
4
4
4
4
3
3
3
3
3
3
24
23
21
21
20
19
18
18
18
18
18
18
17
17
17
16
16
16
16
Commodity or service
2.7
2.6
Percentage of total
expenditure
2.4
2.4
Percentage of total
expenditure
1
Housing (Net)
2
3
Fuel and power
Food and non-alcoholic
drinks
4
Alcoholic drink
5
5
5
5
5
4
4
4
4
4
4
4
4
4
4
4
4
4
4
5
Tobacco
3
3
3
3
3
2
2
2
2
2
2
2
2
2
2
2
1
1
1
6
Clothing and footwear
8
8
7
7
8
7
6
6
6
6
6
6
6
6
6
6
6
5
5
7
8
8
7
8
8
7
8
8
8
8
8
9
8
8
9
8
8
8
8
8
Household goods
Household
services
3
4
4
4
5
5
5
5
5
5
5
5
5
5
5
6
6
6
6
9
Personal goods and services
3
4
3
3
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
11
12
12
13
12
12
14
13
13
13
13
13
14
15
15
14
15
15
15
10
Motoring
11
Fares and other travel costs
3
3
3
2
2
2
3
3
2
2
2
2
3
2
3
2
2
2
2
12
Leisure goods
4
4
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
13
Leisure services
6
7
7
7
7
9
9
10
11
11
11
11
12
12
12
13
13
13
13
14
Miscellaneous
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
Jan-14
All expenditure groups
ONS, Family Spending 2002-03, © Crown copyright 2003
9
Table A3
Household expenditure by gross income decile group (based on weighted data and including children's expenditure)
Lowest
Ten
Per
cent
Second
decile
Third
decile
Fourth
Decile
Fifth
Decile
Sixth
decile
Seventh
decile
Eighth
decile
Ninth
decile
2,440
701
901
774
group
123
2,430
724
1,278
967
group
188
2,440
732
1,412
1,155
group
259
2,430
715
1,590
1,189
Group
341
2,440
719
1,718
1,282
group
435
2,440
697
1,807
1,295
group
541
2,430
687
1,967
1,409
group
662
2,440
672
1,917
1,407
1.3
1.7
1.9
2.2
2.4
2.5
2.8
2.8
Average weekly household expenditure (£)
21.3
27.7
34.5
36.3
40.1
5.9
6.3
8.8
10.5
10.6
6.2
7.9
11.4
15.8
18
20.9
28.4
29.3
34.8
37.6
11
12.7
17.6
23.2
22
42.8
12
20.2
38.1
29.8
Lower boundary of group (£ per week)
Grossed number of households (thousands)
Total number of households in sample
Total number of persons in sample
Total number of adults in sample
Weighted average number of persons per
household
Commodity or service
1 Food & non-alcoholic drinks
2 Alcoholic drinks, tobacco & narcotics
3 Clothing & footwear
4 Housing1, fuel & power
5 Household goods & services
6
7
8
9
10
11
12
01-Dec
Health
Transport
Communication
Recreation & culture
Education
Restaurants & hotels
Miscellaneous goods & services
All expenditure groups
1.6
13.1
5.4
16.6
3.1
36.9
8.8
43.1
1.2
22.3
22.1
258.3
4.5
46.9
9.5
46.7
2
28.5
25.9
292.3
3.2
2.4
24,350
6,927
16,586
12,450
Average weekly household expenditure (£)
49
52
56.9
66.9
14.1
13.1
15.8
16.4
26.2
31
36.6
49.6
37.1
39.7
42.8
60
33
36.7
44.4
71.9
42.7
11.4
22.3
36.9
30.2
44.8
13.2
50
11.9
5.6
17.4
23.1
15.4
11
36.3
6.9
13.3
276.7
5.2
66.3
11.3
68.4
3.4
40.8
37.4
392.3
6.5
84.8
13.6
79
4.3
48.1
45.1
454.1
5.3
107.8
15
89.3
8.5
61.5
51.2
535.2
9.9
139.6
18.3
116.4
25.8
83.4
76.5
734.9
4.8
59.2
10.6
56.4
5.2
35.4
33.1
348.3
13 Other expenditure items
12.5
14.9
22.5
36.9
42.7
58.6
Total expenditure
135.6
169.4
219.4
295.2
335
400.4
Average weekly expenditure per person (£)
Total expenditure
106
98.4
114.4
134.8
140.8
157.4
Note: The commodity and service categories are not comparable to those in publications before 2001-02
1 Excludes mortgage interest payments, council tax and NI rates
Source: http://www.statistics.gov.uk/statbase/Expodata/Spreadsheets/D7561.xls (accessed Feb 3, 2005)
63.6
455.9
80
534.1
99
634.2
148.5
883.4
57.9
406.2
161.6
192.2
213.6
274.4
170.5
10.2
10.2
123.1
4.4
22.6
7.5
28.6
0.7
15.5
16
196.9
3
2003
holds
5.5
58.1
10.7
54.7
3.6
32.5
33.8
341.8
..
2.2
16.1
5.9
21.3
1.7
11.6
12.7
154.5
All
house-
group
821
2,430
655
1,974
1,477
Highest
ten
per
cent
1,085
2,430
625
2,022
1,495
10
Why Fuel Poverty?
• Higher energy prices
– Rising prices of
• Gas, electricity and oil
• Low income
– Pensioners
– Unemployed/low skilled
Housing structure
Old and large
isolated
• Household composition
– Single person
– Single parent
11
It has something to
do with income
distribution.
Yorkshire and Humber
Levels of Income
in Different
Regions
Of UK
Source: ONS
12
13
0
.001
Density
.002
.003
Income Distribution from the British Household Panel Survey
Wave 1-11, 1991-2002 (Teaching Sampler data set)
0
2000
4000
6000
usual net pay per month: current job
8000
14
0
20
Percent
40
60
Income Distribution from the British Household Panel Survey
Wave 1-11, 1991-2002 (Teaching Sampler data set)
0
100000
200000
300000
400000
annual hh income (1.9.2000-1.9.2001)
500000
15
It has something to do with
fuel prices?
16
It has something to do with fuel efficiency of houses
17
Fuel poverty can be studies in the perspective on literature on Poverty
and household income and expenditure survey
Smith (1776) Rowntree B. S. (1902) Hansen A H (1926)
Keezer D M (1943) Davis J. S, (1945) Atkinson, A. B.:(1970)
Sen A. (1976) Beckerman W. (1979) Schultz TW (1979)
Townsend P. (1979) Kakwani N. (1980) Danziger and
Gottschalk,(1983) Cutler (1984) Basu,(1985) Piachaud(1987)
Pyatt G (1987) Swinton,(1987) Atkinson, A. B.:(1987) Kniesner T.
J., M B McElroy and S P Wilcox (1988) Lewis G. W. and D.T.
Ulph (1988) Hagenaars and Vos, Klaas de (1988)
Davidson(1988) Webb S (1889) Brown J C (1990) Jenkins(1991)
Sharif (1991) Gaude and Watzlawick(1992) Keen M (1992)
Blackburn(1994) Zheng (1994) Preston (1995) Bardhan P (1996)
Ravallion M. (1996) Whitehouse E. (1996) Barrington L (1997)
Betson D.M. and J L Warlick (1998) Triest R K (1998)
Besley T, R. Burgess (2003) Blaug M (1963) Casper L M (1994)
Shorrocks A. F. (1995) Slesnick D.T. (1996) Deaton A (1998)
Haveman R A Bershadker (1998) Foster J. E. (1998)
Foster J E and A F Shorrocks (1988) Garfinkel I. (1994)
Micklewright J and K Stewart (1999) Guo G, K.M. Harris (2000)
Sutherland H and D Piachaud (2001) Hillman A L (2002)
Stifel, D.C. Thorbecke, E.(2003)
18
Papers particularly reviewed for the current paper
•
Barker,Blundell and Micklewright (1989) Modelling household energy expenditure using micro data, Economic
Journal 99:397:720-738.
•
Bellman R. (1957) Dynamic Programming, Princeton University Press, New Jersey.
•
Bhattarai K. (2007) Input-Output and General Equilibrium Models for Hull and Humber Region in England, Atlantic
Economic Journal, forthcoming.
•
Boardman B.(1991) Fuel poverty: from cold homes to affordable warmth, Belhaven Press, London.
•
Department of Trade and Industry (DTI(2006)) Fuel Poverty Methodology Documentation,
http://www.dti.gov.uk/energy/index.html.
•
Geary R.C. (1949-50) A note on a constant utility index of the cost of living, Review of Economic Studies, 18: 6566.
•
Henderson J. M. and R. E. Quandt (1980) Microeconomic Theory: A Mathematical Approach, McGraw-Hill,
London.
•
Rowntree B. S. (1902) Poverty of Town Life, MacMillan, London.
•
Sargent T. J. (1987) Dynamic Macroeconomic Theory, Chapter 1, Harvard University Press.
•
Stone R (1954) Linear Expenditure System and Demand Analysis: An Application to the
Demand, Economic Journal 64:511-527.
•
Townsend P. (1979) Poverty in the United Kingdom: A survey of Household Resources and
of Living, Penguin Books
Standard
•
Yorkshire and Humber Public Health Observatory (YGPHO (2006)) Fuel Poverty in Yorkshire and the
Promoting Health Through Affordable Warmth, Number 5,
October. www.yhpho.org.uk.
Humber:
Pattern of British
Arayayam Kim Kimi (2007) Regression based
Fertig and Tamm (2007)- Duration model of Child poverty in Germany;
Camelia Minoiu (2007) Kernal Density approach to poverty
19
Basic Microecoomic Demand
Side Model with Minimum Need
Stone Geary Preference for
Analysing Fuel Poverty
20
Figure 1
Stone Geary Preferences for Fuel and Other Goods
g1
q
h
2
u
(
)
(
u h = α 1h ln q 1h − γ 1h + α 2h ln q 2h − γ 2h
)
u
g2
γ 2h
A
0
γ 1h
q1h
21
Stone-Geary preferences
(
)
(
u h = α 1h ln q1h − γ 1h + α 2h ln q2h − γ 2h
(
u = B ln q − γ
h'
h
1
h
1
h
1
) + B ln(q
h
2
(
)
h
2
−γ
h
2
(
)
)
α 1h
α 2h
h
with B = h
and B2 = h
h
α1 + α 2
α 1 + α 2h
Max u h ' = B1h ln q1h − γ 1h + B2h ln q2h − γ 2h
Subject to
y h = p1q1h + p2 q2h
h
1
)
(1)
(2)
The Lagrangian constrained optimisation function for this problem becomes:
(
)
(
)
(
)
(
L q1h , q1h , λh = B1h ln q1h − γ 1h + B2h ln q2h − γ 2h + λh y h − p1q1h − p2 q 2h
)
(3)
22
Optimization
(
)
(
)
(
)
∂L q1h , q1h , λh
B1h
h
=
−
λ
p1 = 0
h
h
h
∂q1
q1 − γ 1
(4)
∂L q1h , q1h , λh
B2h
h
=
−
λ
p2 = 0
h
h
h
∂q2
q1 − γ 1
(5)
∂L q1h , q1h , λh
= y h − p1q1h − p2 q2h = 0
h
∂λ
Rearrange (4) to get
(6)
(
(
)
)
pq = pγ +
h
1 1
h
1 1
B1h
(7)
λh
Similarly rearrange (5) to get
p 2 q = p 2γ +
h
2
h
2
B2h
(8)
λh
Now using (7) and (8) in (6) to get
y − pγ −
h
B1h + B2h
λ
h
h
1 1
B1h
λh
− p 2γ −
= y h − p1γ 1h − p2γ 2h or
h
2
1
λ
h
B2h
λh
=0
= y h − p1γ 1h − p2γ 2h
(9)
23
Demands for Fuel and Non-Fuel Products
(
)
Put (9) into (7) p1q1h = p1γ 1h + B1h y h − p1γ 1h − p2γ 2h tot get
(
B1h h
q =γ +
y − p1γ 1h − p2γ 2h
p1
h
1
h
1
)
Similarly put (9) into (8) p2 q2h = p2γ 2h + B2h ( y h − p1γ 1h − p2γ 2h )
(
B2h h
q =γ +
y − p1γ 1h − p2γ 2h
p2
h
2
h
2
(10)
to get
)
(11)
1) Household h below the point A in above diagram if (yh − p1γ 1h − p2γ 2h ) < 0 .
This household faces fuel poverty and is in vulnerable situation.
2) The household’s budget constraint just allows to meet minimum requirement if
(yh − p1γ1h − p2γ 2h ) = 0 . It is at point A in the above diagram. Such household just manages to be out
of fuel poverty.
3) Household is above the point A in the above diagram if (yh − p1γ1h − p2γ 2h ) > 0 ,
where the household needs not to bother about the minimum needs as this household consumes above
the basic needs.
24
Fi gur e 2
I nc ome Gr owt h P r oc e ss of Lowe st , M e di a n a nd H i ghe st I nc ome D e c i l e H ouse hol ds
( Of f i c e of N a t i ona l S t a t i st i c s)
700.00
Highest
600.00
500.00
400.00
300.00
Median
200.00
lowest 10th
100.00
0.00
Y ear s
25
Solutions of Fuel Poverty
• Transfer payments
– winter fuel payments
– Fuel subsidies
• Home improvement measures
–
–
–
–
–
–
–
–
–
Draught proofing (£100)
Cavity insulation (£300)
Loft insulation (£200)
Gas central heating (£2000)
Boiler replacement (£1000)
Oil fired central heating (£3500)
CHP Community heating (£5000)
Solid wall external £4000
Electric storage (£900)
government estimates on
fuel poverty white paper:
but
Seems to be too
conservative
from the perspective of the
British Gas.
26
Dynamic Macroeconomic Supply
Side Model of Fuel Poverty
Dynamic Programming for
Determining the Optimal
accumulation and Welfare
27
C2
Future Consumption relative to current consumption
Energy White Paper aims to eliminate fuel poverty in UK by 2016
Steady
state
Figure 5
Optimal Saving and Consumption Trajectory in Ramsey Model
.
Low discount factor
Target Level
in year T
High saving and investment path
More preference for
future consumption
CH path
GAP
CM path
Equal Preference for current
and Future consumption
High discount for future
CL Path
Low saving and investment pat
More preference for
Current consumption
C1
Time
What is Optimal Saving and Consumption to Maximise Life Time Utility?
28
Application of Dynamic Programming Model for Analysing Fuel Poverty
∞
Max U = ∑ β t ln C t
t
0
<
β
<
1
subject to
K t +1 + C t = AK tα
In the context of fuel poverty Ct is composite of q1h and q 2h , quantities of fuel and
non fuel products. Similarly the output Yt = AK tα also is composite of these two
products, q1,t and q 2,t .
0 <α <1
The market clearing condition implies that
h
q
∑ 1,t = q1,t and
h
h
q
∑ 2,t = q2,t . Capital
h
stock is similarly divided in producing fuel and non-fuel products, K t = K 1,t + K 2,t .
29
Value Function Iterations
V1 (K ) = max{ln C + β ln (V0 (K '))}
k
K T +1 = 0
C t + K ' = AK
(
C t = AK α
α
)
V1 (K ) = ln C = ln AK α = ln A + α ln K
(
)
V2 (K ) = ln C + β ln (V1 (K ')) = ln C + β (ln A + α ln K ) = ln AK α − K ' + β (ln A + α ln K )
(
)
V2 (K ) = ln AK − K ' + β (ln A + α ln K )
α
K'
30
Dynamic Programming Model : Optimality Conditions
∂V2 (K )
βα
1
=−
+
=0
α
∂K
AK − K ' K '
1
α
AK − K '
=
(
βα
K'
α
K ' = βα AK − K '
K ' (1 + βα ) = βα AK
)
α
βα
α
K'=
AK
(1 + βα )
31
Dynamic Programming Model : Second Iteration of Value Function
βα
C = AK −
AK α
(1 + βα )
α
1
α
C=
AK
(1 + βα )
⎤
⎡ 1
V2 (K ) = ln C + βV1 AK α = ln ⎢
AK α ⎥ + β (ln A + α ln K ')
⎣ (1 + βα )
⎦
(
)
⎛ βα
⎡ 1
α⎤
α ⎞
V2 (K ) = ln ⎢
AK ⎥ + β ln A + βα ln⎜⎜
AK ⎟⎟
⎝ (1 + βα )
⎠
⎣ (1 + βα )
⎦
⎡ 1
⎤
⎞
⎛ βα
V2 (K ') = ln ⎢
A⎥ + β ln A + βα ln⎜⎜
A ⎟⎟ + α (1 + αβ ) ln K '
⎣ (1 + βα ) ⎦
⎝ (1 + βα ) ⎠
32
Third Iteration of the Value Function
( )
V3 (K ) = ln C + β V2 K '
(
)
V3 (K ) = ln AK α − K ' + β (α (1 + αβ ) ln K ')
max k
∂V3 (K )
1
βα (1 + αβ )
=−
+
=0
α
∂K
K'
AK − K '
max k
1
=
α
AK − K '
(βα + α
β2)
K'=
AK α
2 2
(1 + βα + α β )
βα (1 + αβ )
K'
(
)
2
⎤
⎡
βα + α 2 β 2
α
C = AK − K ' = ⎢ AK −
AK α ⎥
2 2
1 + βα + α β
⎣
⎦
(
)
α
(
C=
)
1
AK α
2 2
1 + βα + α β
(
)
⎡ ⎡ 1
⎤
⎡
⎞
⎤
⎛ βα
1
α⎤
⎟
⎜
(
)
+
+
V3 (K ') = ln ⎢
AK
β
A
β
A
βα
A
α
αβ
K
+
+
+
ln
ln
ln
1
ln
'
⎢ ⎢
⎥
⎥
⎥
⎜ (1 + βα ) ⎟
2 2
(
)
βα
1
+
βα
α
β
1
+
+
⎠
⎦
⎝
⎣
⎣
⎦
⎣
⎦
(
)
⎛
⎡ A ⎤
⎛ βα A ⎞
A
2
2
⎜
⎜
⎟
V3 (K ') = β ln ⎢
β
A
β
α
+
ln
+
ln
+
ln
⎥
⎜ (1 + βα ) ⎟
⎜ 1 + βα + α 2 β 2
⎣ (1 + βα )⎦
⎝
⎠
⎝
(
)
+ α 1 + βα + α 2 β 2 ln K '
(
)
(
(
)
⎞
⎡ βα + α 2 β 2 A ⎤
⎟⎟ + βα (1 + αβ ) ln ⎢
2
2 ⎥
⎠
⎣ 1 + βα + α β ⎦
)
33
Forth Iteration of Value Function
( )
(
) (
)
V4 (K ) = ln C + β V3 K ' = ln AK α − K ' + α 1 + βα + α 2 β 2 ln K '
C=
1
1 + αβ + α 2 β 2 + α 3 β 3
AK α
⎡
⎡ A ⎤
⎛ βα A ⎞
⎟⎟
+ β 2 ln A + β 2α ln⎜⎜
⎢ β ln ⎢
⎥
(
)
(
)
+
+
1
βα
1
βα
⎠
⎣
⎦
⎝
⎢
⎢
⎛
⎞
⎡ βα + α 2 β 2 A
⎡
1
A
α ⎤
⎢
⎟ + βα (1 + αβ ) ln ⎢
V 4 (K ') = ln ⎢
AK ⎥ + β + ln⎜⎜
2
2
3 3
2
2 ⎟
2
2
⎢
+
+
+
+
+
1
1
βα
α
β
αβ
α
β
α
β
⎣
⎦
⎝
⎠
⎣ 1 + βα + α β
⎢
⎡ βα + α 2 β 2 + α 3 β 3
⎢
α ⎤
2
2
+
+
+
1
ln
α
βα
α
β
AK
⎢
⎥
2
2
3 3
⎢
⎣1 + αβ + α β + α β
⎦
⎣
(
)
(
⎛
⎡
⎤
1
A
⎜
+
ln
β
V 4 (K ') = ln ⎢
A
⎥
2
2
3 3
⎜ 1 + βα + α 2 β 2
⎣1 + αβ + α β + α β
⎦
⎝
)
(
(
(
)
)
⎤
⎥
⎥
⎤⎥
⎥⎥
⎦⎥
⎥
⎥
⎥
⎦
)
⎞
⎡ ln A ⎤
⎟⎟ + β 2 ⎢
+ β 3 ln A
⎥
⎣ (1 + βα ) ⎦
⎠
⎧
⎡ βα + α 2 β 2 + α 3 β 3 αβ A ⎤
⎡ βα + α 2 β 2 A ⎤⎫
⎡ αβ A ⎤ ⎫
2
2
2⎧
(
)
β
βα
αβ
β
βα
+ βα 1 + βα + α β ln ⎢
+
+
1
ln
ln
+
⎨
⎨
⎢
⎢ (1 + βα ) ⎥ ⎬
2
2
3 3 ⎥
2
2 ⎥⎬
βα
α
β
1
+
+
⎦⎭
⎣
⎣ 1 + αβ + α β + α β ⎦
⎣
⎦
⎩
⎩
⎭
+ α 1 + βα 1 + βα + α 2 β 2 + α 3 β 3 ln K '
) (
(
[
(
)
(
)]
)
(
(
)
)
Can this process can continue forever……Need Strategic considerations
34
Fuel Poverty Game
Central and Local
Government
Energy Providers
Housing Agencies
Rich Households
Tax payers
Fuel Poor
35
Fuel Poverty Game
Players: Fuel poor, rich and government strategy profiles = (s, l, k,)
State contingent income of poor
State contingent income of rich
p
t
y ( s, l , k )
R
t
y ( s, l , k )
π t ( s, l , k )
p
Transition probability of being rich
Probability of being poor
π ( s, l , k )
R
t
36
Expected Utility Maximisation
Proposition 1: The state contingent money metric utility of fuel poor is less than that of rich
R
R
R
(
)
(
)
(
π
(
s
,
l
,
k
)
⋅
δ
u
y
s
,
l
,
k
<
π
(
s
,
l
,
k
)
⋅
δ
u
y
∑∑∑∑ t
∑∑∑∑ t
t
t
t (s , l , k ))
s
l
k
T
s
p
s =1 l =1 k =1
p
p
t
l
k
T
s =1 l =1 k =1
t
t
Proposition 2: Transfer raises money metric expected utility of fuel poor and
reduces the utility of rich
s
l
k
T
∑ ∑ ∑ ∑π
s =1 l =1 k =1
p
t
( (s, l , k ) + T (s, l , k )) < ∑ ∑ ∑ ∑ π
( s, l , k ) ⋅ δ t u y
p
t
s
p
t
l
k
T
p
t
s =1 l =1 k =1
R
t
(
)
( s, l , k ) ⋅ δ tR u y tR (s, l , k ) − Tt p (s, l , k )
t
Condition 3: Participation and incentive compatibility requires
p
p
p
(
)
(
)
(
)
(
π
(
s
,
l
,
k
)
⋅
δ
u
y
s
,
l
,
k
+
T
s
,
l
,
k
>
π
(
s
,
l
,
k
)
⋅
δ
u
y
∑∑∑∑ t
∑∑∑∑ t
t
t
t
t (s , l , k ))
s
l
k
T
s
p
s =1 l =1 k =1
s
p
p
t
k
T
∑∑∑∑ π
s =1 l =1 k =1
t
R
t
k
s =1 l =1 k =1
t
l
l
T
p
(
)
s
l
t
k
T
(
)
( s, l , k ) ⋅ δ u y (s, l , k ) − Tt (s, l , k ) < ∑∑∑∑ π tR ( s, l , k ) ⋅ δ tR u y tR (s, l , k )
R
t
R
t
p
s =1 l =1 k =1
t
37
Condition 4: Growth requires that income of both poor and rich are rising over time:
Yt (s, l , k ) < Y
p
p
t +1
(s, l , k ) < Y (s, l , k ) < .. < Y (s, l , k
p
t +2
p
t +T
Yt R (s, l , k ) < Yt +R1 (s, l , k ) < Yt +R2 (s, l , k ) < .. < Yt +RT (s, l , k )
Tt (s, l , k ) < T
p
p
t +1
Tt (s, l , k ) > T
p
(s, l , k ) < T (s, l , k ) < .. < T (s, l , k )
p
t +1
p
t+2
p
t +T
(s, l , k ) > T (s, l , k ) > .. > T (s, l , k )
p
t +2
p
t +T
It partly depends on the state contingent poverty line:
p
1
Yt +pT (s, l , k ) ≥ ∑ Yt +pT (s, l , k )
2 p =1
38
Cooperative Solutions of Fuel Poverty Problem
YR
Income of
Rich and
poor
Yp
Is it possible?
Time
39
Working and poor??
How government is solving the poverty problem in UK?
Bi = Ei − tb ( yi − y )
Bi is amount of annual benefit,
Ei is the total entitlement that constitutes of child
tax credit and working family tax credit and
tb is the tax back rate,
yi is the annual household income that includes
W
y
income of husband y and wife i and other
O
y
incomes such as the interest rate earning i and
hs
i
y the threshold income.
40
CTC and WFTC components of benefit entitlements for
a family with dependent children
Ei = E F ,i + ECH ,i N CH ,i − 0.7CCi + E B,i + (ECP,i or E LP,i ) + E30
where EF ,i is the family entitlement,
ECH ,i the entitlement per child
NCH ,i the number of dependent children in the
family, CC child care cost, EB entitlement for
family,
ECP,i or ELP,i the entitlement for couples or lone
parent and E the entitlement for working more
than 30 hours.
30h,i
41
hs
i
W
y
equal to £15,000, i equal to
For a family with y
£10,000 and net y iO of £60 with three dependent
children the DWP’s benefit entitlement for fiscal
year 2007 is calculated as
E i = E F , i + E CH , i N CH , i − 0 . 7 CC i + E B , i + (E CP , i or E LP , i ) + E 30 h , i
= 545 + 3 × 1690 + 1620 + 1595 + 660 = £ 9490 .
Thus the annual amount of benefit
is B = E − t ( y − y ) = 9490 − 0 . 37 (25060 − 5220 ) = £ 2149 . 20
which amounts to £41.33 per week.
i
i
b
i
Generally WFTC provides more benefits to a
couple with many children and implicitly
encourages at least one parent to remain at home to
take care of children.
42
Various Transfers to Alleviate Poverty in the UK
Armed
force
allowance
(£62.25-£41.65),
bereavement entitlement (£84.25),
care taker allowance (£46.95),
disability allowance (£62.25),
housing benefit (7.5% to 25%),
incapacity benefit (£78.50),
income support (single £57.45; couple £90.10),
hospital rates (£46.75),
industrial injuries (£127.10),
job seekers’ allowance (£34.60 to £45.58),
maternity allowance (£108.85),
pension credit (£114.05), state pension (£84.25),
severe disablement allowance (£47.45),
widow benefit (£84.25),
winter fuel allowance (lump sum £200),
national insurance ( £84.01 - £97.00)
43
Households:
Income:
Income distribution:
i = 1,2, …, N.
yi ≠ y j
∀i
y1 < y 2 < .. < y N
y
y=∑
N
N
Average income:
i
i
Poverty line
Depth of Poverty:
1
z= y
2
n
∑ ( yi − z )
I=
i
44
z.n
Measuring Poverty in a hypothetical economy
y
10
20
30
40
50
60
90
100
200
400
N
1
1
1
1
1
1
1
1
1
1
cy
10
30
60
100
150
210
300
400
600
1000
cp
1
2
3
4
5
6
7
8
9
10
yshre
0.01
0.02
0.03
0.04
0.05
0.06
0.09
0.10
0.20
0.40
cyshre
0.01
0.03
0.06
0.10
0.15
0.21
0.30
0.40
0.60
1.00
pshre
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
cpshre
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Triangle
0.0005
0.001
0.0015
0.0020
0.0025
0.0030
0.0045
0.0050
0.0100
0.0200
Rectangle
0.000
0.001
0.003
0.006
0.010
0.015
0.021
0.030
0.040
0.060
Area
0.0005
0.0020
0.0045
0.0080
0.0125
0.0180
0.0255
0.0350
0.0500
0.0800
45
ygap
-90
-80
-70
-60
-50
-40
-10
0
100
300
Sen(1996) Measure of Poverty
P = H .I + H (1 − I )G
1
z = y = 50
2
n
I=
∑ (y
i
− z)
i
z.n
40 + 30 + 20 + 10 100
=
=
= 0.5
50 ⋅ 4
200
P = H .I + (1 − I )G = 0.4 × 0.5 + 0.4(1 − 0.5)0.528 = 0.2 + 0.106 = 0.306
Poverty elimination
T1 = 40
T2 = 30
T3 = 20
Tax 9th and 10th decile 20 and 80
T4 = 10
46
Income Inequality and Lorenz Curve
Cumulative income share
1
Equality line
A
Lorenz
B
Cumulative Population share
1
47
Cumulative income share
Approximation of Area Under the Lorenz Curve
A
G=
A+ B
A
0
0.2
0.4
Cumulative Population share
0.6
0.8
1.0
48
Cumulative income share
Approximation of Area Under the Lorenz Curve
0.05015
A
0.0230
0.0146
0.0087
0.0035
0.2
0.0070
0.0997
0.0244 0.0536
0.4
Cumulative Population share
0.6
0.8
1.0
49
Computation of Gini Coefficient
Cumulative income share
1
Gini = (0.2152/0.5000) = 0.43043
ea
r
A
=
)
(A
5
0.
00
0
0
.2
0
-
8
4
8
=
52
1
2
0.
Area (B) =0.2848
Cumulative Population share
1
50
Income group Income
1st (lowest)
10186
2nd
25321
3rd
42492
4th
66939
5th (highest)
145811
Total
290749
Ishare
0.035034
0.087089
0.146147
0.23023
0.501501
CMIshare Equality pop
0.035034
0.2
0.122123
0.4
0.268269
0.6
0.498499
0.8
1
1
Total area under Lorenz
Gini
cmpop
0.2
0.2
0.2
0.2
0.2
0.2
0.4
0.6
0.8
1
Rectangle
0
0.007007
0.024425
0.053654
0.0997
Triangle
0.003503
0.008709
0.014615
0.023023
0.05015
Total area
0.003503
0.015716
0.039039
0.076677
0.14985
0.2848
0.43043
51
Projection of Old and young People in Yorksshire and Humber
1400.0
Projected Population and Dependency Ratio in Yorkshire and Humberside
1200.0
2004
2007
2009
2014
2019
2024
2029
Dependent (1-15, 65+)
2191.9
2199.7
2220.7
2362.9
Working age (16-64)
3231.2
3329
3371.7
3409.1
2521.6
2719
2902.4
3442.1
3476.8
3473.3
Dependency Ratio
0.6784
0.6608
0.6586
0.6931
0.7326
0.7820
0.8356
1260.7
Source: http://www.statistics.gov.uk/CCI/nscl.asp?ID=7595 Accessed Feb 2, 2007.
N u m b e r o f p e o p le (0 0 0 )
1000.0
800.0
5-10
11-15
16-19
65+
600.0
400.0
200.0
0.0
2004
2005
2006
2007
2008
2009
2014
2019
2024
2029
Projection years
52
53
Gas fired central heating
54
55
Woods and coals
Central Heating
56
Combi-Boilers
www.imaginationsolar.com/systems/combi.htm
57
Current
practices
Meters and fuel costs
58
59
60
Interior of House
61