social welfare final report

7/28/2019 Social Welfare Final Report

1/22

Social Welfare Function

Final Project of Applied Economics Page 1

SOCIAL WELFARE

Social welfare is about how people, communities and institutions in a society take action to

provide certain standards and certain opportunities to make living better. It is generally about

helping people that facing contingencies.

Social welfare function

In economics, a social welfare function is a real-valued function that ranks conceivable social

states (alternative complete descriptions of the society) from lowest to highest. Inputs of the

function include any variables considered to affect welfare of the society. In using welfare

measures of persons in the society as inputs, the social welfare function is individualistic in

form. One use of a social welfare function is to represent prospective patterns of collective

choice as to alternative social states. The social welfare function is analogous to an indifference-

curve map for an individual, except that the social welfare function is a mapping of individual

preferences or judgments of everyone in the society as to collective choices, which apply to all,

whatever individual preferences are. One point of a social welfare function is to determine how close

the analogy is to an ordinal utility function for an individual with at least minimal restrictions suggested

by welfare economics.

W= W(Y, I, P)

Here, we will use following variables in welfare function:

Household Consumption Inequality Poverty Real GDP per Capita

Real GDP Per capita:

The concept of real GDP per capita is related to all economic indicators that are calculated, usually at the

end of a fiscal year. The phenomenon of modern economies is the basis of calculation of these economic

indicators. Real GDP divided by Population is known as Real GDP per Capita. This is the "average" outputof the economy per person measured in a base year prices. This ratio is often used as a measure of

standard of living in comparisons over time of one country, or between different countries when

measured in the same currency. The measure is expressed in currency units per person (for example,

U.S. dollars per person, or British pounds per person, Pakistan Rupees per person).It is positively related

to consumption function.


2/22



Inequality:

Income inequality is a term that is used to describe an uneven distribution of wealth within a definedgeographic area. When this type of economic inequality is high, this means that a small number of

individuals living in the area receive the majority of the income generated during a specified period,

while a low rate of income inequality would mean that the overall income generated was more evenly

distributed among each of the households established in the area. There are a number of different tools

and strategies used to measure this type of economic disparity, with approaches like the Hoover Index,

the Atkinson Index, the Gini Coefficient, and the Theil Index being some of the more common examples.

It is negatively related to welfare function.

Poverty:

Poverty can usually be thought of as the state of lacking resources that would provide people with basicnecessities, or that force people to go without certain needed things like three meals a day or shelter.

Yet it ought to be understood that people can still have some of these things, like a roof over their

heads, and yet not enough of other things, like food, money to seek medical treatment, or to purchase

adequate clothing. And a main problem that most countries facing is drinking clean water that is most

severe in poor countries. As our former President Musharaf said: The next wars will be battled on

water. In many countries, poverty may be defined by income only. Countries, states or even counties

may set poverty lines. People who live below these lines or just above them might be considered

impoverished, while those who live well above the line are clearly not. While this may prove one helpful

way to evaluate how to help those with providing basic needs, there is significant debate about where

these lines should be set. When great changes in a countrys economic structure occur, current

valuations of poverty may change drastically. It is negatively related to welfare function.

Household Consumption:

We will use it as proxy of welfare.Household consumption expenditure is a transaction of the national

account's use of income account representing consumer spending. It consists of the expenditure

incurred by resident households on individual consumption goods and services, including those sold at

prices that are not economically significant. It also includes various kinds of imputed expenditure of

which the imputed rent for services of owner-occupied housing (imputed rents) is generally the most

important one. The household sector covers not only those living in traditional households, but alsothose people living in communal establishments, such as retirement homes, boarding houses and

prisons.

In this project, we will analyze the welfare function of Pakistan and China. Here, we will use

different tools such as multiple regression and Hypothesis analysis to know about welfare

function.


3/22



Data of Different variables of Pakistan

Years

HC ratio at $

1.25 Gini coefficient

Real GDP/

Capita($)

Real GDP/ Capita

$ (Million)1987 23.93 0.358 254.0342 0.000254034

1991 23.23 0.4099 285.5537 0.000285554

1993 4.19 0.3937 295.2262 0.000295226

1997 11.7 0.3598 308.7557 0.000308756

1999 6.28 0.4187 313.4261 0.000313426

2002 7.92 0.4129 324.2032 0.000324203

2005 4.35 0.331 368.9435 0.000368944

Years Household Consumption $

(Million) CPI

Real Consumption per

Capita $

Population

1987 105933.2179 25.21 42.07 99953232.23

1991 121333.9951 36.07 30.37 110750019.26

1993 140070.1974 43.44 26.29 116444164.85

1997 173185.3627 67.41 20.00 128457310.83

1999 188956.1705 84.57 18.80 134790000

2002 193432.7777 82.92 16.09 144902409.43

2005 241479.4975 100(Base year) 15.50 155772000

Sources:

We took the data of Head count ratio, Real GDP per capita, and household consumption from

Trading economics, Data of CPI also fromTrading economics and Data ofGini coefficient

fromthefinance division.


4/22



Head Count Ratio of Pakistan

Explanation:

This graphs shows headcount ratio in different years. If we see in 1987, the headcount ratio was

much higher than other years. Mr. Junajo was the prime Minister of that time. He was followingthe military rules of General Zia-Ul-Haq. On the other side if we see in 1993, headcount ratio

was much lower than other years. It was regime of Benzair Bhoto; her government was taking

steps to reduce the poverty. We noted that in 1987 and 1991 the headcount ratio was high. In

1991, poverty was high because large number of people came from Iraq and Kuwait due to war

and those people were Jobless. So, this factor is great hurdle in the way of Social welfare.

Total

0

5

10

15

20

25

30

1987 1991 1993 1997 1999 2002 2005

Total

Sum of HC Ratio

Years


5/22



Gini coefficient of Pakistan

Explanation:

This graph tells the Gini coefficient for different years. If we see in 2005, the income distribution

in Pakistan was relatively equitable distribution. It means that income distribution in 2005

among the Pakistani people was relatively equal because this value of Gini coefficient (0.331) is

between 0.20 0.35. But in other years, income distribution in Pakistan was highly unequal

because in these years value of Gini coefficient occurs between 0.35 0.70. In 1999 and 2002

income inequality was high because it was regime of dictator and main jobs and posts were

available only to limited people. Except in 2005, the Gini coefficient was high that is why, Social

welfare was impossible.

Total

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

1987 1991 1993 1997 1999 2002 2005

Total

Sum of Gini coefficient

Years


6/22



Real Household consumption (welfare) of Pakistan

Explanation:

This graphs shows real household consumption per capita of Pakistans people in different

years. If we see in 1987, the real household consumption per capita was $ 42.04. So, we can say

that social welfare in 1987 was much better than other years, and in 2005 real household

consumption per capita was $ 15.50. So we can say welfare in 2005 was much lower than otheryears. From 1987 to 2005 the real household consumption per capita is decreasing gradually

because our economys performance is becoming very poor day by day. We used consumption

as proxy of Welfare. The greater the real consumption per capita then there will be greater

welfare in the country.

Total

0

5

10

15

20

25

30

35

40

45

1987 1991 1993 1997 1999 2002 2005

Total

Sum of R. Consumption/ Capita

Years


7/22



Real GDP per Capita of Pakistan

Explanation:

This graph shows the Real GDP per Capita of Pakistan in different years. . If we see in 1987, the

real GDP per Capita was $ 254.034 and in 2005 real GDP per Capita was $ 368.9435. From 1987

to 2005 the Real GDP per Capita is increasing gradually. In 2005 real GDP per capita was highbecause huge foreign aid had come into Pakistan due to Earthquake. If the real GDP per Capita

will be greater then there will be huge chances of welfare in the country.

Total

0

50

100

150

200

250

300

350

400

1987 1991 1993 1997 1999 2002 2005

Total

Sum of Real GDP per Capita

Years


8/22



Real GDP Per Capita and Social Welfare of Pakistan

Interpretation:

Real GDP usually have positive relation with social welfare but in our case it

represents inverse relation on Pakistan data analysis. There are some reasons for its inverserelation. First one is that inaccurate data availability in Pakistan causes this conflict. In our data

analysis on Pakistan real GDP increases but social welfare decreases. There is another reason

for this situation is at Pakistans population dont contribute productive programs and other

factors contribute to its real GDP growth like foreign aid.

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00


9/22



GINI Coefficient and Social Welfare of Pakistan

Interpretation:

GINI coefficient normally has inverse relationship with social welfare that every

country try to reduce the ratio to escape the individuals from misery and unequal emotions. In

Pakistan data GINI coefficient or inequality ratio is somewhat decreases but not so much as

social welfare increases therefore Pakistan also not achieving the high social welfare to bring

prosperity in country.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.36 0.41 0.39 0.36 0.42 0.41 0.33


10/22



Head Count Ratio and Social Welfare of Pakistan

Interpretation:

Head count ratio represents the poverty in a country that also has negativerelationship with social welfare and should reduce to achieve better outcomes. In Pakistan data

analysis initially the poverty decreased so much and in further years decreases but not that

ratio that initially decrease. Poverty is an important element in any countrys social welfare and

should reduce to improve living standard of individuals.

0

5

10

15

20

25

30

23.93 23.23 4.19 11.7 6.28 7.92 4.35


11/22



MULTIPLE REGRESSIONS OF PAKISTAN

W= W (P, I, Y)

1 1 2 2 3 3y a b x b x b x

Where

y

= social welfare

a = fixed welfare (intercept)

a = 24.21-49255.26-81.31-0.0000039

a = -49149.66

1b =change in social welfare due to per unit change in

1x (Poverty)

1b

=4227.921

1x = Poverty

2b = change in social welfare due to per unit change in

2x (Income inequality)

2b = -212.296

2x = Income inequality


3x (Real GDP/Capita)

3b

=-0.01303018

3x = Real GDP/Capita

y

= -49149.66+4227.921-212.296-0.01303018

y

= -45134.048


12/22



We used these equations to findb, b and b:

1 1 2 2 3 3y na b x b x b x

2

1 1 1 1 2 1 2 3 1 3

x y a x b x b x x b x x

2

2 2 1 1 2 2 2 3 2 3x y a x b x x b x b x x

INTERPRETATION:

a is fixed welfare of Pakistan. If there is no poverty, income inequality and GDP growth then

the welfare of Pakistan will be

= -45134.048

So without poverty, income inequality and GDP growth, Pakistan is having a negative social

welfare of $ -45134.048.

According to data and calculation, poverty has negative impact on Pakistan s Social welfare i.e.

in 1987, when poverty was 23.93 and per unit change in poverty was 4227.921 and then social

welfare was $101174.15.

According to data and calculation, income inequality has positive impact on Pakistans Social

welfare i.e. in 1987, when income inequality was 0.36 and per unit change in income inequality

was -212.296, and then social welfare was $ -76.42656.

According to data and calculation, GDP growth has positive impact on Pakistan s Social welfare

i.e. in 1987, when GDP growth was $ 0.000254034 and per unit change in GDP growth was

$-0.01303018 and then social welfare was $-3310110.

By taking aggregate effect of Poverty, Income Inequality and GDP growth, we calculated the

Social welfare of Pakistanis $-45134.048. One reason of negative answer of social welfare is

data conflict, second reason is increase in population but consumption is on unnecessary goods

and capital stocks, that is why, GDP growth is not consistent with social welfare.


13/22



Data of China

Years HC ratio at $ 1.25 Gini coefficient

R.GDP/Capita(Million)

$

1987 18.51 0.17 0.000311

1991 20.72 0.20 0.000392

1993 17.65 0.24 0.000476

1997 10.73 0.21 0.000716

1999 11.08 0.24 0.000827

2002 8.66 0.28 0.001021

2005 3.95 0.28 0.001323

CPI RealConsumption/capita $Y

32.37 13.8

48.54 10.71

59.14 11.2

95.65 9.08

93.51 10.43

93.46 12.08

100 13.37

Sources:

We took the data of Head count ratio, Real GDP per capita, household consumption,

Data of CPI also fromTrading economics and data of Gini coefficient from

www.bwpi.manchester.ac.uk/resources/Working.../bwpi-wp-10910.pdf(China Gini).
http://www.bwpi.manchester.ac.uk/resources/Working.../bwpi-wp-10910.pdf(China%20Gini)http://www.bwpi.manchester.ac.uk/resources/Working.../bwpi-wp-10910.pdf(China%20Gini)http://www.bwpi.manchester.ac.uk/resources/Working.../bwpi-wp-10910.pdf(China%20Gini)


14/22



Head Count Ratio of China

Explanation:

This graphs shows headcount ratio of China in different years. If we see in 1991, the headcount

ratio of China was much higher than other years because the rate of growth was

not high enough to reduce poverty for the majority of the rural poor and mining operations

were generally detached from local supply chains. On the other hand head count ration in 2005was much lower than other years. So, this factor is great hurdle in the way of Social welfare.

Total

0

5

10

15

20

25

1987 1991 1993 1997 1999 2002 2005

Total

Sum of HC ratio at $ 1.25

Years


15/22



Gini coefficient of China

Explanation:

This graph tells the Gini coefficient for different years. If we see in 1987, the income distribution

in China was relatively equitable distribution than other years. In this year income Inequality

was very low that was 0.17. In this year income gap was not high. Although income inequality in

others was high than 1987, but it was relatively equal distribution. So, we can conclude that

income distribution in china is relatively equitable distribution.

Total

0

0.05

0.1

0.15

0.2

0.25

0.3

1987 1991 1993 1997 1999 2002 2005

Total

Sum of Gini Coefficient

Years


16/22



Real GDP per Capita of China

Explanation:

This graph shows the Real GDP per Capita of Chain of different years. . If we see in 1987, the

real GDP per Capita was $ 311 and in 2005 real GDP per Capita was $ 1323. From 1987 to 2005

the real GDP per capita is increasing gradually. If the real GDP per Capita will be greater then

there will be huge chances of welfare in the country.

Total

0

200

400

600

800

1000

1200

1400

1987 1991 1993 1997 1999 2002 2005

Total

Sum of Real GDP Per Capita

Years


17/22



Real household Consumption per Capita of China

Explanation:

This graphs shows real household consumption per capita of Chainas people in different years.

Here, we used real household consumption per capita to know about welfare in country. In

1987 the social welfare was very good in China than other years. On the other side in 1987 the

social welfare was low in China than other years. The greater the real consumption per capita

then there will be greater welfare in the country.

Total

0

2

4

6

8

10

12

14

16

1987 1991 1993 1997 1999 2002 2005

Total

Sum of Real Household Consumption Per Capita

Years


18/22



Real GDP Per Capita and Social Welfare of China

Interpretation:

Social welfare is directly linked with the real GDP as the diagram depicts theresults. In shows that real GDP of one country rises the social welfare also raises like in our case

chinas social welfare increased with the growth of GDP. Therefore real GDP growth is main

aspect of social welfare and should improve real GDP growth to raise the social welfare of

country. The china received this situation of social welfare improvements and raises every year.

0

200

400

600

800

1000

1200

1400

311 392 476 716 827 1021 1323


19/22



GINI Coefficient and Social Welfare of China

Interpretation:

In social welfare function GINI coefficient has a main role to check its

performance. GINI Coefficient represent inequality in income distribution and in our data that is

collected on china GINI coefficient increases somewhat and also decreases some time. But it do

not increase so much to distort social welfare. The economist point of view some inequality is

compulsory for better social welfare and better source allocation.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.17 0.20 0.24 0.21 0.24 0.28 0.28


20/22



Head Count and Social Welfare of China

Interpretation:

Head count ratio represents the poverty in a country that is another important

element in social welfare function. It usually has inverse relation with social welfare that

elaborate as the poverty decreases the social welfare will increase and vice versa. In our data

analysis china face the same situation that we discuss above lines that poverty decreases every

year and social welfare increases.

0

5

10

15

20

25

18.51 20.72 17.65 10.73 11.08 8.66 3.95


21/22



REGRESSION

W= W (P, I, Y)

1 1 2 2 3 3y a b x b x b x

Where,

y

= social welfare

a = fixed welfare (intercept)

a = 11.52+26285.64+2.583+0.0005960

a = 26294.62

1b =change in social welfare due to per unit change in

1x (Poverty)

1b

= -2015.77

1x = Poverty


2x (Income inequality)

2b

= 11.0034

2x = Income inequality


3x (Real GDP/Capita)

3b

= 0.117664759

3x = Real GDP/Capita

y

= 26294.62-2015.77+11.0034+0.117664759

y

= 11790765


22/22



We used these equations to findb, b and b:

1 1 2 2 3 3y na b x b x b x

2

1 1 1 1 2 1 2 3 1 3x y a x b x b x x b x x

2

2 2 1 1 2 2 2 3 2 3x y a x b x x b x b x x

INTERPRETATION:

a is fixed welfare of China. If there is no poverty, income inequality and GDP growth then the

welfare of China will be:

= 26294.62

Therefore, without poverty, income inequality and GDP growth, China is still having a social

welfare of $26294.62

According to data and calculation, poverty has negative impact on Chinas Social welfare i.e. in

1987, when poverty was 18.51 and per unit change in poverty was -2015.77and then social

welfare was $ -37311.90.

According to data and calculation, income inequality has positive impact on Chinas Social

welfare i.e. in 1987, when income inequality was 0.17 and per unit change in income inequality

was 11.0034, and then social welfare was $1.870.

According to data and calculation, GDP growth has positive impact on Chinas Social welfare i.e.

in 1987, when GDP growth was $ 0.000311 and per unit change in GDP growth was $ 0.00031,

and then social welfare was $0.000037.

By taking aggregate effect of Poverty, Income Inequality and GDP growth, we calculated the

Social welfare of China is $11790765.

social welfare final report

Documents