Seminar on Equity and Inequalities presented by KC LAM 20080505
(Please DO NOT QUOTE)
Outline
I. Introduction to the topic on Equity and Efficiency
1. Relevance and importance of the topic

Polls in HK have consistently indicated inequalities as one of the top social concerns

CE listed the issue of inequalities and poverty as one of his five main policy concerns
2. In relation to the rationale, aims and objectives of the new Economics syllabus

“giving students a more comprehensive understanding of contemporary issues facing our society
and the country”

“participate as informed and responsible citizens in the decision-making processes of a modern
democratic society”

“students develop skills to evaluate information, arguments, proposals and policies from different
economic perspectives and make informed judgements”; and

“to communicate economic ideas and informed judgements, in a clear, logical and appropriate
form”
3. Connection with other topics in the syllabus

For whom to produce

Positive and normative statements

Market intervention

Market structure: perfect competition, monopoly power

Limitation of national income statistics

Growth and development e.g. marketization in Chinese economy
II. Equity and Efficiency in the market economy
1. Are market outcomes efficient?

Why market may fail?

Market power

Externalities

Public goods

Incomplete information

Apart from market failures listed above, inefficiencies may result from government policies like
taxes, subsidies & quota
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2. Does efficiency imply equity?
The Utility Possibilities Frontier
Karen’s
Utility
OJ – James has zero utility
OK – Karen has zero utility
E, F, G – points on contract
curve
H – inefficient – can do better
in shaded area
L - unobtainable
OJ
L
E
F
H
G
OK
James’ Utility
Source: Pindyck & Rubenfeld

Some efficient allocations may be more fair than others

Difficult to say what is the most equitable allocation

There is no reason to believe that efficient allocation from competitive markets will give an
equitable allocation.

Utility possibilities frontier (In Depth)

An inefficient allocation may be regarded as more equitable than the efficient ones

Social welfare functions: weights are applied to individual’s utility to determine what is socially
desirable. Different social welfare functions represent different views of equity

Some views of equity do not assign weights, and cannot be represented by a welfare function
3. Equity and perfect competition
Q. Must a society that wants to be more equitable necessarily operate in an inefficient world?
A. Second Theorem of Welfare Economics

If individual preferences are convex, then every efficient allocation (every point on the contract
curve) is a competitive equilibrium for some initial allocation of goods.

In other words, any equilibrium that is equitable can be achieved by redistributing resources and
may be efficient

However, typical ways to redistribute goods are costly and cause inefficiencies
III. Different views of Equity
 Many principles (but not all) can broadly be classified as those focusing on results (#1,2,3 ) and
those focusing on rules or processes (#4)
1. Utilitarian
 the principle states we should strive for the greatest happiness for the greatest number
 founded by English philosophers Jeremy Bentham and John Stuart Mill
 All humans have the same basic needs and the same desire to enjoy life
 The principle of diminishing marginal utility suggests that the entire society would gain utility if
there was a transfer of income until the marginal utility per dollar of income was equal across all
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households.
Marginal benefit (units)
Utilitarian - example
Clara
a
3
c
2
Maximum
total
benefit
Jack
b
1
MB
0
5
25
45
Income (thousands of dollars)
 Conceptual problem: different people have different utility function, problem of interpersonal
comparison
 Welfare economics
2. Rawlsian
 A contemporary view on utilitarianism originally developed by John Rawls of Harvard University
 Government should choose policies deemed to be just, as evaluated by an impartial observer
behind a “veil of ignorance”
 Public policy should be based on maximin criterion, which seeks to maximize the utility or
well-being of the worst-off person in society.
 Would allow for the redistribution of income as a form of social insurance
 However, this view would argue that any shrinking of the economic pie that would decrease the
well being of the poorest would not be fair.
3.
Egalitarian

An egalitarian view believes that goods should be equally shared by all individuals in society

more productive people thereby producing more goods and then having more to reallocate to all
of society
4. Equalizing Opportunities (Libertarian)

The symmetry principle is the requirement that people in similar situations be treated similarly

this would be an equality of opportunity principle, rather than an equality of income principle

Rules must be created and enforced such that individuals have equal economic opportunity

The state must enforce laws that establish and protect private property

Private property may be transferred from one person to another only by voluntary exchange

Fair rules will lead to equal opportunity, but not equal distribution of goods and/or income
because households have different preferences

Taxes for redistribution are not seen as fair, since they are an involuntary transfer of private
property
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
Challenges: initial endowments may not result from fair acquisition; opportunities are rarely
equal in real world; claim to private property may not be absolute because of social nature of
activities
5. Other views of justice
(i) Social responsibilities

The rich have responsibilities to take care of the poor and the needy by transfers

Aim not at complete equality but poverty reduction
(ii) Merit & Contribution
(iii) Justice & rights vs compassion & charity
IV. Measuring inequalities
(Cowell 1995)
1. Normative or positive?
 What is fair is a normative issue, but the measurement and causes of inequalities involve positive
analyses; while the choice of measures involves both normative and positive considerations. The
major discussions in our syllabus involve positive analyses
2. Three basic elements of an inequality measure
(i). Inequality of what?
 Description of Attribute: e.g. wealth vs income
(ii). Specification of an individual social unit: household vs person
(iii). Method of representation of the allocation of income or wealth
 e.g. a scalar numerical representation (3rd element) of the interpersonal differences (2nd element) in
income (1st element) within a given population
3. Four basic principles of inequalities measures
(i). Principle of transfer: a hypothetical transfer of income from a rich person to a poor person should
reduce measured inequality
(ii). Scale independence: The measured inequality of the slices of the cake should not depend on the
size of the cake e.g. if income of all people has doubled, inequality measure should remain the same.
(iii). Population principle: the inequality of the cake distribution should not depend on the number of
cake-receivers
(iv). Decomposability: there should be a coherent relationship between inequality in the whole society
and inequality in its constituent parts
4. Different measures of inequalities
 Want a way of looking at inequality that reflects both the depth of poverty of the ‘have nots’ and
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the height of well-being of the ‘haves’
 Three broad categories of methods to present income distribution: (A) diagrams, (B) inequality
measures and (C) rankings
A. Diagrams
Data often presented in frequency tables
( e.g.Table 3.2 of 2006 census report on income distribution )
http://www.censtatd.gov.hk/products_and_services/products/publications/statistical_report/population_
and_vital_events/index_cd_B1120045_dt_latest.jsp
(1) Frequency distribution of income. Number of households/persons within a certain income
bracket ( e.g. Plot Table 3.2 of 2006 census report )
Frequency Distribution
800,000
600,000
Frequency
Distribution
400,000
200,000
0
0
10,000 20,000 30,000 40,000 50,000
Frequency distribution of Monthly Income from Main Employment of
working Population in HK, 2006
Note: Income Distribution is skewed
(2) Cumulative frequency distribution
(2) Cumulative frequency distribution
cumulative frequency
100
80
60
cumulative
frequency
40
20
0
0
10,000
20,000
30,000
40,000
50,000
Cumulative Frequency Distribution of Monthly Income from Main Employment, 2006
(3) The Lorenz curve
 imagine that you lined up all the households in ascending order of incomes
 divided the households into 10 equal groups (bottom decile, … top decile)
 computed the share of the total income that each group of household received.
 Plotted cumulative % of income against cumulative % of households
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Cumulative Share of aggregate monthly household income (%) 2006
(Data from 2006 census report on income distribution)
% of
households
1st
cumulative
households
0.8
cumulative
income share
10
0.8
2nd
2.1
20
2.9
3rd
4th
3.2
4.3
30
40
6.1
10.4
5th
5.5
50
15.9
6th
7th
8th
7.0
8.8
11.3
60
70
80
22.9
31.7
43
9th
10th
15.6
41.4
90
100
58.6
100
Income share
 if income were equally distributed across all households, each decile (10%) of families would
receive one-tenth (10%) of total income
 line of perfect equality : diagonal
 in reality, always convex toward the origin
Cumulative % of income / wealth
Lorenz Curves for Income & Wealth
100
e
80
60
40
20
0
d
Line of
equality
Income
c
a
20
Wealth
b
40
60
80
100
Cumulative % of households
(e.g. can be computed from Table 3.4 of 2006 census report)
 if Lorenz curve is farther away from the line of equality everywhere, inequality is greater
 greatest inequality, one person gets 100% of total income
 difficulties in interpretation when two Lorenz curves cross over
B. Inequality measures
(1). Range R = ymax – ymin
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(2). Gini coefficient G
Let A=area between the line of equality and the Lorenz curve,
B = area of the lower triangle
Then G = A/B
 Absolute equality; implies A=0 and G=0
 absolute inequality; implies A=B and G=1
 Lorenz curve above indicates that Gini coefficient of wealth distribution is greater than Gini of
income distribution

advantages: independent of income scale & population size; range in [0,1] interval

Limitations : Weak principle of transfer; not decomposable

Limitations in interpreting the size of Gini Coefficient and its changes in HK (ref. CoP paper
no.20 & 22)

Adjusted Gini coefficient is smaller: adjusted for taxes, education, medical & housing benefit,
CSSA

changes over time affected by changes in household size, higher education, prolonged economic
downturn
(3). Variance V

V = 1/n ∑ [yi – y‾]2

Measures deviations from the sample mean

Satisfies strong principle of transfer; decomposable

Unsatisfactory; doubling everyone’s income and V would quadruple.

One way round is to standardize V
(4) Coefficient of variation c :

divide square root of V by mean of y
 Satisfies strong principle of transfer; decomposable;independent of income scale & population size
(5). Log variance v
 Fails principle of transfers; not decomposable;
 but independent of income and population size
C. Rankings
(1).Quantiles
 absolute value of quantiles, e.g. earnings at 10th, 50th or 90th percentile: Y10, Y50,Y90
 quantile ratio of earnings
e.g. Y90/ Y10
th
i.e. ratio of earnings at 90 percentile to earnings at 10th percentile
(e.g. Bernanke 2007; HK data 1986-2001)
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Table. Quantile Ratio of Earnings in HK,1981 – 2001
‘81
1986
1991
1996
2001
Y90/Y10
3.88
4.51
4.17
5.20
6.25
Y90/Y50
2.07
2.28
2.27
2.60
2.84
Y75/Y50
1.37
1.51
1.45
1.50
1.77
Y50/Y25
1.36
1.33
1.38
1.43
1.38
Y50/Y10
1.88
1.98
1.83
2.00
2.20
Variance of
Log Earnings
0.42
0.472
0.456 0.505
0.565
(2). shares
 Share of income by a certain group of household, e.g. share of labor income vs share of capital
income
 Choice of measures often depends on the situation and what you want to study
 E.g. Gini coefficient is often used in comparing countries of different sizes, or changes over time;
the measure is widely used and available
 In public policies that involves transfers, principle of transfer is important
V. Sources of income inequalities
 Have implications on whether income inequalities are justified
Demand and supply factors in the market

Demand side: Value of marginal product: price of the product and marginal product of a factor

Supply side: e.g. immigration across the border resulting in an increase in supply of low skilled
workers may depress wages for low-skilled workers
Labor earnings
1. human capital

nature of capital investment: expenditure of resources at one point in time to raise
productivity in the future

e.g. schooling, post-schooling on the job training, health, appearances

( e.g. Table 3.6 of 2006 census report on income distribution.)

Current income vs lifetime income

Observed income of a young worker is lower since he is investing a greater share of his earnings
potential at young age, and also his accumulated human capital is smaller

Implication: observed current income differentials cannot be interpreted as unfair
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2. Compensating differentials – differences in tastes and job characteristics

a difference in wages that arises from non-monetary characteristics of different jobs.

E.g. higher pay for risky jobs

Free choice of occupation as a result of matching tastes of workers and productivity of firms

Implication: earnings differentials are not unfair
3. discrimination

meaning: the marketplace offers different opportunities to similar individuals who differ only by
race, ethnic group, sex, age or other personal characteristics (unrelated to market productivity)
(Mankiw)

type of discrimination: competitive vs non-competitive

competitive: prejudice of consumers, employers and workers; statistical discrimination
2. Statistical Discrimination (In Depth)
The Screening Problem-
No personal prejudice

non-competitive: crowding (e.g. women crowded into low pay jobs); collusive behavior

difficulties in measuring discrimination : observe wages, but other things are not the same, there
may be unobservables or left out variables so that earnings differentials may be the result of
unobserved skills or qualities (e.g. better work ethics, higher EQ)

How significant is discrimination in a competitive market?

For competitive discrimination: firms that do not discriminate will be more profitable than those
firms that do discriminate, thus competitive markets tend to limit the impact of discrimination on
wages

Non-competitive discrimination may persist due to social custom or market power; call for
government intervention
4. Ability, effort, attitude and chance
5. Signaling

Sheep skin effect

Firms use educational attainment as a way of sorting between high-ability and low-ability
workers.
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
i.e. productivity is not raised by education as claimed by human capital theory

It is rational for firms to interpret a college degree as a signal of ability.
6. The superstar phenomenon

Every customer in the market wants to enjoy the good supplied by the best producer

The good is produced with a technology that makes it possible for the best producer to supply
every customer at a low cost
Other non-labor income: rent, interest, profit

unequal ownership of capital or initial wealth
Q. Are inequalities listed above ‘fair’?
Considerations:
1. What kind of inequality ?
2. What are the underlying principles of equity?
3. Should compare like with like
4. Family income depends on resource prices, resource endowment and choices
5. Changes in income thus depends on the changes of the these factors
6. Mobility, intergeneration mobility and inequalities
7. Inequalities vs poverty : not possible to eliminate relative poverty
VI. Different views on equity have different implications on policies

E.g. those emphasizing equal opportunities may think it’s fair that some people who have
invested a lot on human capital or work harder earn higher wages, with a possible implication
that redistribution is neither needed nor desirable

People emphasizing charity may vote for policies for economic transfers to the needy who are in
absolute poverty for whatever reasons

Policies are not the subject of discussion in this seminar
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References

Mankiw, N. Gregory, Principles of Microeconomics,4 ed. chapters 19,20.

Parkin, Michael, Economics 7 ed., Addison Wesley

Cowell, Frank, Measuring Inequalities, 2nd ed. Prentice Hall/Harvester Wheatheaf. 1995

Census and Statistics Department, Report of the Population Censuses

http://www.censtatd.gov.hk/products_and_services/products/publications/statistical_report/popula
tion_and_vital_events/index_cd_B1120045_dt_latest.jsp

http://www.cop.gov.hk/eng/pdf/Income%20Distribution%20of%20HK%20and%20the%20Gini%20Co
efficient.pdf

Sen, Amartya (1995), Inequality Reexamined, Harvard/Russell Sage Foundation.

Arthur, John and William H. Shaw (1991), Justice and Economic Distribution, NJ: Prentice Hall.

Bernanke, Ben S.(2007) , “The level and distribution of economic well-being”, Remarks given
before the Greater Omaha Chamber of Commerce, Omaha, Nebraska, The Federal Reserve
Board, February 6, 2007.
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