UGC NET Economics Book in Hindi PDF [Sample]
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Unit-1: Micro Economics
DIWAKAR EDUCATION HUB
DIWAKAR EDUCATION HUB
Unit-1: Micro Economics
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S. N. TOPIC
Unit-1: Micro Economics
PAGE NO.
1.
Theory of Consumer Behaviour
4-125
2.
Theory of Production and Costs
126 -200
3.
Decision making under uncertainty
Attitude towards Risk and Market
Structures, competitive and non-
competitive equilibria and their
efficiency properties
201-262
4.
Game Theory – Non Cooperative games
263-266
5.
Factor Pricing
267-272
6.
General Equilibrium Analysis
273-276
7.
Efficiency Criteria: Pareto-Optimality,
Kaldor – Hicks and Wealth
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S. N. TOPIC
Unit-1: Micro Economics
PAGE NO.
1.
Theory of Consumer Behaviour
4-125
2.
Theory of Production and Costs
126 -200
3.
Decision making under uncertainty
Attitude towards Risk and Market
Structures, competitive and non-
competitive equilibria and their
efficiency properties
201-262
4.
Game Theory – Non Cooperative games
263-266
5.
Factor Pricing
267-272
6.
General Equilibrium Analysis
273-276
7.
Efficiency Criteria: Pareto-Optimality,
Kaldor – Hicks and Wealth
Unit-1: Micro Economics
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Maximization and Welfare Economics:
Fundamental Theorems , Social
Welfare Function
277-297
8.
Asymmetric Information: Adverse
Selection and Moral Hazard
298-300
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Maximization and Welfare Economics:
Fundamental Theorems , Social
Welfare Function
277-297
8.
Asymmetric Information: Adverse
Selection and Moral Hazard
298-300
Unit-1: Micro Economics
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What is Theory of Consumer Behaviour ?
Theory of Consumer Behaviour
Microeconomic theory tends to assume that individuals are the
economic agents exercising the act of consumption, the decision to
purchase goods and services. The consumer is assumed to choose
among the available alternatives in such a manner that the
satisfaction derived from consuming commodities (in the broadest
sense) is as large as possible.
This implies that he is aware of the alternatives facing him and is
capable of evaluating them. All the information pertaining to the
satisfaction that the consumer derives from various quantities of
commodities is contained in his ‘utility function’.
We assume that each consumer or family unit has complete
information on all matters pertaining to its consumption decision. A
consumer knows precisely what his money income will be during
the planning period. ‘Utility’ refers to subjective satisfaction derived
from consumption of commodities.
The 19th century economists, namely W. Stanley Jevons, Leon
Walras and Alfred Marshall came up with the cardinal theory of
consumer behaviour. They considered utility is measurable just as
the weight of objects. The consumer is assumed to possess a
cardinal measure of utility when he is able to assign every
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What is Theory of Consumer Behaviour ?
Theory of Consumer Behaviour
Microeconomic theory tends to assume that individuals are the
economic agents exercising the act of consumption, the decision to
purchase goods and services. The consumer is assumed to choose
among the available alternatives in such a manner that the
satisfaction derived from consuming commodities (in the broadest
sense) is as large as possible.
This implies that he is aware of the alternatives facing him and is
capable of evaluating them. All the information pertaining to the
satisfaction that the consumer derives from various quantities of
commodities is contained in his ‘utility function’.
We assume that each consumer or family unit has complete
information on all matters pertaining to its consumption decision. A
consumer knows precisely what his money income will be during
the planning period. ‘Utility’ refers to subjective satisfaction derived
from consumption of commodities.
The 19th century economists, namely W. Stanley Jevons, Leon
Walras and Alfred Marshall came up with the cardinal theory of
consumer behaviour. They considered utility is measurable just as
the weight of objects. The consumer is assumed to possess a
cardinal measure of utility when he is able to assign every
Unit-1: Micro Economics
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commodity, a number representing the amount or degree of utility
associated with it.
Under this theory, it is possible to measure marginal utility (MU) of a
commodity, whereby by MU we mean a change in utility due to a
change in per unit of consumption of a commodity. Another property
is the existence of Law of Diminishing Marginal Utility (LDMU).
This means as a consumer keeps on consuming successive units of
the same commodity, consumption of other commodities held fixed,
marginal utility diminishes. Total utility increases at a decreasing
rate for successive units of consumption of a particular commodity.
Cardinal Utility is the idea that economic welfare can be directly
observable and be given a value.
For example, people may be able to express the utility that
consumption gives for certain goods. For example, if a Nissan car
gives 5,000 units of utility, a BMW car would give 8,000 units. This
is important for welfare economics which tries to put values on
consumption. For example, allocative efficiency is said to occur
when Marginal cost = Marginal Utility.
One way to try and put values on goods utility is to see what price
they are willing to pay for a good.
If we are willing to pay £5,000 for a second-hand Nissan Car, we
can infer we must get 5,000 utils. In other words, the value of
cardinal utility is related to the price we are willing to pay.
The idea of cardinal utility is important to rational choice theory. The
idea consumers make optimal choices to maximise their utility.
Demand curve showing cardinal utility
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commodity, a number representing the amount or degree of utility
associated with it.
Under this theory, it is possible to measure marginal utility (MU) of a
commodity, whereby by MU we mean a change in utility due to a
change in per unit of consumption of a commodity. Another property
is the existence of Law of Diminishing Marginal Utility (LDMU).
This means as a consumer keeps on consuming successive units of
the same commodity, consumption of other commodities held fixed,
marginal utility diminishes. Total utility increases at a decreasing
rate for successive units of consumption of a particular commodity.
Cardinal Utility is the idea that economic welfare can be directly
observable and be given a value.
For example, people may be able to express the utility that
consumption gives for certain goods. For example, if a Nissan car
gives 5,000 units of utility, a BMW car would give 8,000 units. This
is important for welfare economics which tries to put values on
consumption. For example, allocative efficiency is said to occur
when Marginal cost = Marginal Utility.
One way to try and put values on goods utility is to see what price
they are willing to pay for a good.
If we are willing to pay £5,000 for a second-hand Nissan Car, we
can infer we must get 5,000 utils. In other words, the value of
cardinal utility is related to the price we are willing to pay.
The idea of cardinal utility is important to rational choice theory. The
idea consumers make optimal choices to maximise their utility.
Demand curve showing cardinal utility
Unit-1: Micro Economics
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Cardinal utility is an important concept in utilitarianism and neo-
classical economics. Jeremy Bentham talked about utility as
maximising pleasure and minimising pain.
William Stanley Jevons, Léon Walras, and Alfred Marshall all
developed concepts of utility, usually linked to market prices.
However, proving exact measurement of utility proved elusive.
Ordinal Utility
In ordinal utility, the consumer only ranks choices in terms of
preference but we do not give exact numerical figures for utility.
For example, we prefer a BMW car to a Nissan car, but we don’t
say by how much.
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Cardinal utility is an important concept in utilitarianism and neo-
classical economics. Jeremy Bentham talked about utility as
maximising pleasure and minimising pain.
William Stanley Jevons, Léon Walras, and Alfred Marshall all
developed concepts of utility, usually linked to market prices.
However, proving exact measurement of utility proved elusive.
Ordinal Utility
In ordinal utility, the consumer only ranks choices in terms of
preference but we do not give exact numerical figures for utility.
For example, we prefer a BMW car to a Nissan car, but we don’t
say by how much.
Unit-1: Micro Economics
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It is argued this is more relevant in the real world. When deciding
where to go for lunch, we may just decide I prefer an Italian
restaurant to Chinese. We don’t calculate the exact levels of utility.
Carl Menger, an Austrian economist, developed concepts of utility
which rested on ranked preferences.
In 1906 Vilfredo Pareto in 1906 concentrated on an indifference
curve map. This placed preferences on bundles of goods but did not
attempt to say how much.
John Hicks and Roy Allen in 1934 first produced a paper which
mentioned ordinal utility.
Behavioural economics and utility
Recent developments in utility theory have tended to downplay the
role of cardinal utility. The ability of consumers to make exact
evaluations of utility is not clear.
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It is argued this is more relevant in the real world. When deciding
where to go for lunch, we may just decide I prefer an Italian
restaurant to Chinese. We don’t calculate the exact levels of utility.
Carl Menger, an Austrian economist, developed concepts of utility
which rested on ranked preferences.
In 1906 Vilfredo Pareto in 1906 concentrated on an indifference
curve map. This placed preferences on bundles of goods but did not
attempt to say how much.
John Hicks and Roy Allen in 1934 first produced a paper which
mentioned ordinal utility.
Behavioural economics and utility
Recent developments in utility theory have tended to downplay the
role of cardinal utility. The ability of consumers to make exact
evaluations of utility is not clear.
Unit-1: Micro Economics
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One more way to measure utility:
Utils cannot be taken as a standard unit for measurement as it will
vary from individual to individual. Hence, several economists
including Marshall, suggested the measurement of utility in
monetary terms. It means, utility can be measured in terms of
money or price, which the consumer is willing to pay.
In the above example, suppose 1 util is assumed to be equal to Rs.
1. Now, an ice-cream will yield utility worth Rs. 20 (as 1 util = Rs. 1)
and chocolate will give utility of Rs. 10. This utility of Rs. 20 from the
ice-cream or f I0 from the chocolate is termed as value of utility in
terms of money.
The advantage of using monetary values instead of utils is that it
allows easy comparison between utility and price paid, since both
are in the same units.
It must be noted that it is impossible to measure satisfaction of a
person as it is inherent to the individual and differs greatly from
person-to-person. Still, the concept of utility is very useful in
explaining and understanding the behaviour of consumer.
Total Utility (TU):
Total utility refers to the total satisfaction obtained from the
consumption of all possible units of a commodity. It measures the
total satisfaction obtained from consumption of all the units of that
good. For example, if the 1
st
ice-cream gives you a satisfaction of 20
utils and 2
nd
one gives 16 utils, then TU from 2 ice-creams is 20 +
16 = 36 utils. If the 3
rd
ice-cream generates satisfaction of 10 utils,
then TU from 3 ice-creams will be 20+ 16 + 10 = 46 utils.
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One more way to measure utility:
Utils cannot be taken as a standard unit for measurement as it will
vary from individual to individual. Hence, several economists
including Marshall, suggested the measurement of utility in
monetary terms. It means, utility can be measured in terms of
money or price, which the consumer is willing to pay.
In the above example, suppose 1 util is assumed to be equal to Rs.
1. Now, an ice-cream will yield utility worth Rs. 20 (as 1 util = Rs. 1)
and chocolate will give utility of Rs. 10. This utility of Rs. 20 from the
ice-cream or f I0 from the chocolate is termed as value of utility in
terms of money.
The advantage of using monetary values instead of utils is that it
allows easy comparison between utility and price paid, since both
are in the same units.
It must be noted that it is impossible to measure satisfaction of a
person as it is inherent to the individual and differs greatly from
person-to-person. Still, the concept of utility is very useful in
explaining and understanding the behaviour of consumer.
Total Utility (TU):
Total utility refers to the total satisfaction obtained from the
consumption of all possible units of a commodity. It measures the
total satisfaction obtained from consumption of all the units of that
good. For example, if the 1
st
ice-cream gives you a satisfaction of 20
utils and 2
nd
one gives 16 utils, then TU from 2 ice-creams is 20 +
16 = 36 utils. If the 3
rd
ice-cream generates satisfaction of 10 utils,
then TU from 3 ice-creams will be 20+ 16 + 10 = 46 utils.
Unit-1: Micro Economics MCQs
MCQs
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MCQs
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Unit-1: Micro Economics MCQs
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1. Any individual who purchases
goods and services from the market
for his/her end-use is
called a..................
(1) Customer
(2) Purchaser
(3) Consumer
(4) All these
Answer: 1
2. ------------ is nothing but
willingness of consumers to
purchase products and services as
per their taste, need and of course
pocket.
(1) Consumer behavior
(2) Consumer interest
(3) Consumer attitude
(4) Consumer perception
Answer: 2
3. ------------- is a branch which deals
with the various stages a consumer
goes through before
purchasing products or services for
his end use.
(1) Consumer behavior
(2) Consumer interest
(3) Consumer attitude
(4) Consumer perception
Answer: 1
4. -------------- refers to how an
individual perceives a particular
message
(1) Consumer behavior
(2) Consumer interest
(3) Consumer attitude
(4) Consumer interpretation.
Answer: 4
5. “----------- is the action and
decisions process or people who
purchase goods and services for
personal consumption.”
(1) Consumer behavior
(2) Consumer interest
(3) Consumer attitude
(4) Consumer interpretation.
Answer: 1
6. ________________ emphasize(s)
that profitable marketing begins
with the discovery and
understanding of consumer needs
and then develops a marketing mix
to satisfy these needs.
(1) The marketing concept
(2) The strategic plan
(3) The product influences
(4) The price influences.
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1. Any individual who purchases
goods and services from the market
for his/her end-use is
called a..................
(1) Customer
(2) Purchaser
(3) Consumer
(4) All these
Answer: 1
2. ------------ is nothing but
willingness of consumers to
purchase products and services as
per their taste, need and of course
pocket.
(1) Consumer behavior
(2) Consumer interest
(3) Consumer attitude
(4) Consumer perception
Answer: 2
3. ------------- is a branch which deals
with the various stages a consumer
goes through before
purchasing products or services for
his end use.
(1) Consumer behavior
(2) Consumer interest
(3) Consumer attitude
(4) Consumer perception
Answer: 1
4. -------------- refers to how an
individual perceives a particular
message
(1) Consumer behavior
(2) Consumer interest
(3) Consumer attitude
(4) Consumer interpretation.
Answer: 4
5. “----------- is the action and
decisions process or people who
purchase goods and services for
personal consumption.”
(1) Consumer behavior
(2) Consumer interest
(3) Consumer attitude
(4) Consumer interpretation.
Answer: 1
6. ________________ emphasize(s)
that profitable marketing begins
with the discovery and
understanding of consumer needs
and then develops a marketing mix
to satisfy these needs.
(1) The marketing concept
(2) The strategic plan
(3) The product influences
(4) The price influences.
Unit-1: Micro Economics MCQs
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Answer: 1
7. ________________ is one of the
most basic influences on an
individual’s needs, wants, and
behaviour.
(1) Brand
(2) Culture
(3) Product
(4) Price
Answer: 2
8. In terms of consumer behaviour;
culture, social class, and reference
group influences have been related
to purchase and _______________.
(1) Economic situations
(2) Situational influences
(3) Consumption decisions
(4) Physiological influences
Answer: 3
9. Many sub-cultural barriers are
decreasing because of mass
communication, mass transit, and a
___________________.
(1) Decline in the influence of
religious values
(2) Decline in communal influences
(3) Strong awareness of brands in
the market
(4) Strong awareness of pricing
policies in the market.
Answer: 1
10. ___________ develop on the
basis of wealth, skills and power.
(1) Economical classes
(2) Purchasing communities
(3) Competitors
(4) Social classes.
Answer: 4
11. _____________ (is) are
transmitted through three basic
organizations: the family, religious
organizations, and educational
institutions; and in today’s society,
educational institutions are playing
an increasingly greater role in this
regard.
(1) Consumer feedback
(2) Marketing information systems
(3) Market share estimates
(4) Cultural values.
Answer: 4
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Answer: 1
7. ________________ is one of the
most basic influences on an
individual’s needs, wants, and
behaviour.
(1) Brand
(2) Culture
(3) Product
(4) Price
Answer: 2
8. In terms of consumer behaviour;
culture, social class, and reference
group influences have been related
to purchase and _______________.
(1) Economic situations
(2) Situational influences
(3) Consumption decisions
(4) Physiological influences
Answer: 3
9. Many sub-cultural barriers are
decreasing because of mass
communication, mass transit, and a
___________________.
(1) Decline in the influence of
religious values
(2) Decline in communal influences
(3) Strong awareness of brands in
the market
(4) Strong awareness of pricing
policies in the market.
Answer: 1
10. ___________ develop on the
basis of wealth, skills and power.
(1) Economical classes
(2) Purchasing communities
(3) Competitors
(4) Social classes.
Answer: 4
11. _____________ (is) are
transmitted through three basic
organizations: the family, religious
organizations, and educational
institutions; and in today’s society,
educational institutions are playing
an increasingly greater role in this
regard.
(1) Consumer feedback
(2) Marketing information systems
(3) Market share estimates
(4) Cultural values.
Answer: 4
Unit-1: Micro Economics MCQs
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12. In large nations, the population
is bound to lose a lot of its
homogeneity, and thus
_________________ arise.
(1) Multilingual needs
(2) Cultures
(3) Subcultures
(4) Product adaptation requirements
Answer: 3
13. _______________ are based on
such things as geographic areas,
religions, nationalities,
ethnic groups, and age.
(1) Multilingual needs
(2) Cultures
(3) Subcultures
(4) Product adaptation
requirements.
Answer: 3
14. Marketing managers should
adapt the marketing mix to
___________________ and
constantly monitor value changes
and differences in both domestic
and global markets.
(1) Sales strategies
(2) Marketing concepts
(3) Cultural values
(4) Brand images.
Answer: 3
15. _____________ has become
increasingly important for
developing a marketing strategy in
recent years.
(1) Change in consumers’ attitudes
(2) Inflation of the dollar
(3) The concept and the brand
(4) Age groups, such as the teen
market, baby boomers, and the
mature market.
Answer: 4
16. Two of the most important
psychological factors that impact
consumer decision-making
process are product _____________
and product involvement.
(1) Marketing
(2) Strategy
(3) Price
(4) Knowledge
Answer: 4
17. Which of the following is the
most valuable piece of information
for determining the social
class of your best friend's parents?
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12. In large nations, the population
is bound to lose a lot of its
homogeneity, and thus
_________________ arise.
(1) Multilingual needs
(2) Cultures
(3) Subcultures
(4) Product adaptation requirements
Answer: 3
13. _______________ are based on
such things as geographic areas,
religions, nationalities,
ethnic groups, and age.
(1) Multilingual needs
(2) Cultures
(3) Subcultures
(4) Product adaptation
requirements.
Answer: 3
14. Marketing managers should
adapt the marketing mix to
___________________ and
constantly monitor value changes
and differences in both domestic
and global markets.
(1) Sales strategies
(2) Marketing concepts
(3) Cultural values
(4) Brand images.
Answer: 3
15. _____________ has become
increasingly important for
developing a marketing strategy in
recent years.
(1) Change in consumers’ attitudes
(2) Inflation of the dollar
(3) The concept and the brand
(4) Age groups, such as the teen
market, baby boomers, and the
mature market.
Answer: 4
16. Two of the most important
psychological factors that impact
consumer decision-making
process are product _____________
and product involvement.
(1) Marketing
(2) Strategy
(3) Price
(4) Knowledge
Answer: 4
17. Which of the following is the
most valuable piece of information
for determining the social
class of your best friend's parents?
Unit-2 : Macro Economics
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Unit-2 : Macro Economics
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S. N. TOPIC
Unit-2 : Macro Economics
PAGE NO.
1.
National Income: Concepts and
Measurement
4-21
2.
Determination of output and employment:
Classical & Keynesian Approach
22-38
3.
Consumption Function
39-58
4.
Investment Function
59-70
5.
Multiplier and Accelerator
71-91
6.
Demand for Money
92-122
7.
Supply of Money
123-
147
8.
IS – LM Model Approach
148-
164
9.
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S. N. TOPIC
Unit-2 : Macro Economics
PAGE NO.
1.
National Income: Concepts and
Measurement
4-21
2.
Determination of output and employment:
Classical & Keynesian Approach
22-38
3.
Consumption Function
39-58
4.
Investment Function
59-70
5.
Multiplier and Accelerator
71-91
6.
Demand for Money
92-122
7.
Supply of Money
123-
147
8.
IS – LM Model Approach
148-
164
9.
Unit-2 : Macro Economics
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Inflation and Phillips Curve Analysis 165-
174
10.
Business Cycles
175-
208
11.
Monetary and Fiscal Policy
209-
236
12.
Rational Expectation Hypothesis and its
critique
237-
243
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Inflation and Phillips Curve Analysis 165-
174
10.
Business Cycles
175-
208
11.
Monetary and Fiscal Policy
209-
236
12.
Rational Expectation Hypothesis and its
critique
237-
243
Unit-2 : Macro Economics
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What is National Income: Concepts and
Measurement ?
National Income: Concepts and Measurement
National Income is total amount of goods and services produced
within the nation during the given period say, 1 year. It is the total of
factor income i.e. wages, interest, rent, profit, received by factors of
production i.e. labour, capital, land and entrepreneurship of a
nation.
Concepts of National Income
There are various concepts of National Income, such as GDP, GNP,
NNP, NI, PI, DI, and PCI which explain the facts of economic
activities.
National of India
National income of India constitutes total amount of income earned
by the whole nation of our country and originated both within and
outside its territory during a particular year. The National Income
Committee in its first report wrote, “A national income estimate
measures the volume of commodities and services turned out
during a given period, without duplication.”
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What is National Income: Concepts and
Measurement ?
National Income: Concepts and Measurement
National Income is total amount of goods and services produced
within the nation during the given period say, 1 year. It is the total of
factor income i.e. wages, interest, rent, profit, received by factors of
production i.e. labour, capital, land and entrepreneurship of a
nation.
Concepts of National Income
There are various concepts of National Income, such as GDP, GNP,
NNP, NI, PI, DI, and PCI which explain the facts of economic
activities.
National of India
National income of India constitutes total amount of income earned
by the whole nation of our country and originated both within and
outside its territory during a particular year. The National Income
Committee in its first report wrote, “A national income estimate
measures the volume of commodities and services turned out
during a given period, without duplication.”
Unit-2 : Macro Economics
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Estimates of National Income during Pre-Independence Period:
During the British period, several estimates of national income were
made by Dadabhai Naoroji (1868), Willium Digby (1899), Findlay
Shirras (1911, 1922 and 1934), Shah and Khambatta (1921),
V.K.R.V. Rao (1925-29) and R.C. Desai (1931-40).
Among all these pre-independence estimates of national income in
India, the estimates of Naoroji, Findlay Shirras and Shaw and
Khambatta have computed the value of the output raised by the
agricultural sector and then added some portion of the income
earned by the non-agricultural sector. But these estimates were
having no scientific basis of its own.
National Income Committee and C.S.O. Estimates:
During the post-independence period, the estimate of national
income was primarily conducted by the National Income Committee.
Later on, it was carried over by the Central Statistical Organisation.
For the estimation of national income in India the National Income
Committee applied a mixture of both ‘Product Method’ and
the ‘Income Method’. This Committee divided the entire economy
into 13 sectors. Income from the six sectors, viz., agriculture, animal
husbandry, forestry, Fishery, mining and factory establishments was
estimated by the output method.
But the income from the remaining seven sectors consisting of small
enterprises, commerce, transport and communications, banking and
insurance, professions, liberal arts, domestic services, house
property, public authorities and rest of the world was estimated by
the income methods.
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Estimates of National Income during Pre-Independence Period:
During the British period, several estimates of national income were
made by Dadabhai Naoroji (1868), Willium Digby (1899), Findlay
Shirras (1911, 1922 and 1934), Shah and Khambatta (1921),
V.K.R.V. Rao (1925-29) and R.C. Desai (1931-40).
Among all these pre-independence estimates of national income in
India, the estimates of Naoroji, Findlay Shirras and Shaw and
Khambatta have computed the value of the output raised by the
agricultural sector and then added some portion of the income
earned by the non-agricultural sector. But these estimates were
having no scientific basis of its own.
National Income Committee and C.S.O. Estimates:
During the post-independence period, the estimate of national
income was primarily conducted by the National Income Committee.
Later on, it was carried over by the Central Statistical Organisation.
For the estimation of national income in India the National Income
Committee applied a mixture of both ‘Product Method’ and
the ‘Income Method’. This Committee divided the entire economy
into 13 sectors. Income from the six sectors, viz., agriculture, animal
husbandry, forestry, Fishery, mining and factory establishments was
estimated by the output method.
But the income from the remaining seven sectors consisting of small
enterprises, commerce, transport and communications, banking and
insurance, professions, liberal arts, domestic services, house
property, public authorities and rest of the world was estimated by
the income methods.
Unit-2 : Macro Economics
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CSO’s Revised 2004-05 Based Net National Product (NNP)
Series:
The Central Statistical Organisation (CSO) has released the new
2004-05 based NNP series. Let us now look into the trends in the
national income figures and per capita income figures of India both
at current and constant prices obtained through CSO’s new series
with 2004-05 as base year.
Again the national income (NNP) of India at current prices increased
from Rs 9,464 crore in 1950-51 to Rs 2,629,198 crore in 2004-05
and then to Rs 9,171,045 crore in 2013-14 (P) registering a growth
of nearly 969 times during the last 64 years.
Again the per capita income figure at constant (2004-05) prices
increased from 7,114 in 1950-51 to Rs 24,143 in 2004-05 and then
to Rs 39,904 in 2013-14 (P) registering a growth rate of 560 per
cent during the last 64 years. Moreover, the per capita income at
current prices also increased from Rs 264 in 1950- 51 to Rs 24,143
in 2004-05 and then to Rs 74,380 in 2013-14 registering growth of
281 times during the last 64 years.
CSO’s Revised 2011-12 Based NNP Series:
The Central Statistical Organisation (CSO) has released the new
2011-12 based NNP series. Let us now look into the trends of
national income figures and per capita income figures of India both
at current and constant prices obtained through CSO’s new series
with 2011-12 as base year. This new estimate is prepared as Net
National Income at market prices instead of Net National Income at
factor cost.
Rates of Growth of National Income in India:
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CSO’s Revised 2004-05 Based Net National Product (NNP)
Series:
The Central Statistical Organisation (CSO) has released the new
2004-05 based NNP series. Let us now look into the trends in the
national income figures and per capita income figures of India both
at current and constant prices obtained through CSO’s new series
with 2004-05 as base year.
Again the national income (NNP) of India at current prices increased
from Rs 9,464 crore in 1950-51 to Rs 2,629,198 crore in 2004-05
and then to Rs 9,171,045 crore in 2013-14 (P) registering a growth
of nearly 969 times during the last 64 years.
Again the per capita income figure at constant (2004-05) prices
increased from 7,114 in 1950-51 to Rs 24,143 in 2004-05 and then
to Rs 39,904 in 2013-14 (P) registering a growth rate of 560 per
cent during the last 64 years. Moreover, the per capita income at
current prices also increased from Rs 264 in 1950- 51 to Rs 24,143
in 2004-05 and then to Rs 74,380 in 2013-14 registering growth of
281 times during the last 64 years.
CSO’s Revised 2011-12 Based NNP Series:
The Central Statistical Organisation (CSO) has released the new
2011-12 based NNP series. Let us now look into the trends of
national income figures and per capita income figures of India both
at current and constant prices obtained through CSO’s new series
with 2011-12 as base year. This new estimate is prepared as Net
National Income at market prices instead of Net National Income at
factor cost.
Rates of Growth of National Income in India:
Unit-2 : Macro Economics
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In order to study the extent of changes in the national income during
different periods it is quite essential to study the annual average
growth rate of national income and per capita income in India. Table
3.2 reveals a clear picture about the annual average rates of growth
of both national income and per capita income in India during
different plan periods as well as during different decades.
During the three Ad-hoc Annual Plans, the economy of the country
gradually started to pick up resulting in increase in the growth rates
of national income and per capita income to 3.7 per cent and 1.5
per cent respectively.
During the Fourth Plan, the annual average growth rate, of both
national income and per capita income gradually declined to 3.2 per
cent and 0.9 per cent respectively and the same rates again
gradually increased to 4.9 per cent and 2.6 per cent respectively
during the Fifth Plan showing an improvement in its performance.
Thus GDP at Factor Cost = Net value added + Depreciation.
Causes for Slow Growth of National Income in India:
The growth rate of national income in India remained all along poor
particularly in the first half of our planning process. Between First
plans to Fourth Plan, the annual average growth rate of national
income varied between 2.6 per cent to 4.1 per cent. During the Fifth,
Sixth and Eighth Plan, the annual average growth rate of national
income also ranges between 4.9 per cent, 5.4 per cent and 6.7 per
cent respectively.
It is only during the Ninth Plan, the annual rate of growth of national
income in India touched the level of 5.5 per cent. Again in 2004-05,
the rate of growth of national income plunged down to 6.6 per cent
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In order to study the extent of changes in the national income during
different periods it is quite essential to study the annual average
growth rate of national income and per capita income in India. Table
3.2 reveals a clear picture about the annual average rates of growth
of both national income and per capita income in India during
different plan periods as well as during different decades.
During the three Ad-hoc Annual Plans, the economy of the country
gradually started to pick up resulting in increase in the growth rates
of national income and per capita income to 3.7 per cent and 1.5
per cent respectively.
During the Fourth Plan, the annual average growth rate, of both
national income and per capita income gradually declined to 3.2 per
cent and 0.9 per cent respectively and the same rates again
gradually increased to 4.9 per cent and 2.6 per cent respectively
during the Fifth Plan showing an improvement in its performance.
Thus GDP at Factor Cost = Net value added + Depreciation.
Causes for Slow Growth of National Income in India:
The growth rate of national income in India remained all along poor
particularly in the first half of our planning process. Between First
plans to Fourth Plan, the annual average growth rate of national
income varied between 2.6 per cent to 4.1 per cent. During the Fifth,
Sixth and Eighth Plan, the annual average growth rate of national
income also ranges between 4.9 per cent, 5.4 per cent and 6.7 per
cent respectively.
It is only during the Ninth Plan, the annual rate of growth of national
income in India touched the level of 5.5 per cent. Again in 2004-05,
the rate of growth of national income plunged down to 6.6 per cent
Unit-2 : Macro Economics
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after reaching 8.2 per cent in 2003-04 and then increased to 9,4 per
cent in 2006-07 and then declined to 7,4 per cent in 2014-15.
Sectoral Contribution or Distribution of National Income by the
Industrial Origin:
Sectoral contribution of national income depicts a clear picture
about the composition or distribution of national income by industrial
origin. Thus it shows the contribution made by different sectors
towards the national income of the country.
In India, among the different sectors, the primary sector and more
particularly agriculture still plays a dominant role in contributing the
major portion of the national income of the country.
Share of Government Sector in Net Domestic Product (NDP):
The share of government sector in the net domestic product of India
has been gradually increasing with the increasing participation of
the government in various economic activities connected with
enlargement of administrative services and expansion of public
sector.
The share of the government sector in net domestic product
gradually increased from 7.6 per cent in 1950-51 to 10.7 per cent in
1960-61 and then again increased to 24.9 per cent in 19.87-88.
The factors which were responsible for increase in the share of non-
departmental enterprises included setting up of new industries,
expansion of existing enterprises, nationalisation of banks,
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after reaching 8.2 per cent in 2003-04 and then increased to 9,4 per
cent in 2006-07 and then declined to 7,4 per cent in 2014-15.
Sectoral Contribution or Distribution of National Income by the
Industrial Origin:
Sectoral contribution of national income depicts a clear picture
about the composition or distribution of national income by industrial
origin. Thus it shows the contribution made by different sectors
towards the national income of the country.
In India, among the different sectors, the primary sector and more
particularly agriculture still plays a dominant role in contributing the
major portion of the national income of the country.
Share of Government Sector in Net Domestic Product (NDP):
The share of government sector in the net domestic product of India
has been gradually increasing with the increasing participation of
the government in various economic activities connected with
enlargement of administrative services and expansion of public
sector.
The share of the government sector in net domestic product
gradually increased from 7.6 per cent in 1950-51 to 10.7 per cent in
1960-61 and then again increased to 24.9 per cent in 19.87-88.
The factors which were responsible for increase in the share of non-
departmental enterprises included setting up of new industries,
expansion of existing enterprises, nationalisation of banks,
Unit-2: Macro Economics MCQs
DIWAKAR
EDUCATION
HUB
DIWAKAR EDUCATION HUB
DIWAKAR
EDUCATION
HUB
DIWAKAR EDUCATION HUB
Unit-2: Macro Economics MCQs
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1. Which of the following
statement is inconsistent with
Say’s Law
(1) The economy has flexible
wages and prices.
(2) The economy’s level of
investment solely depends on
the level of income.
(3) The economy will produce
at full employment level of
output.
(4) The economy has an
environment of”laissez faire”.
Answer: 2
2. Marginal Propensity to
Consume is
(1) Increase in consumption due
to one unit increase in income.
(2) Total consumption divided
by total income.
(3) Both (1) and (2) .
(4) Neither (1) nor (2) .
Answer: 1
3. In explaining the level of
unemployment, Keynes
emphasized,-
(1) Changes in technology.
(2) Aggregate demand.
(3) Inflationary expectations.
(4) Lending by financial
institutions.
Answer: 2
4. Assume that the consumption
function is of the form, C=
50+.8Y. If income is Rs 1000/-
then
consumption is,-
(1) Rs 50/-
(2) Rs 1050/-
(3) Rs 50/-
(4) Rs 850/-.
Answer: 4
5. In the simple Keynesian
model consumption is a
function of,
(1) Rate of interest.
(2) Level of income.
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1. Which of the following
statement is inconsistent with
Say’s Law
(1) The economy has flexible
wages and prices.
(2) The economy’s level of
investment solely depends on
the level of income.
(3) The economy will produce
at full employment level of
output.
(4) The economy has an
environment of”laissez faire”.
Answer: 2
2. Marginal Propensity to
Consume is
(1) Increase in consumption due
to one unit increase in income.
(2) Total consumption divided
by total income.
(3) Both (1) and (2) .
(4) Neither (1) nor (2) .
Answer: 1
3. In explaining the level of
unemployment, Keynes
emphasized,-
(1) Changes in technology.
(2) Aggregate demand.
(3) Inflationary expectations.
(4) Lending by financial
institutions.
Answer: 2
4. Assume that the consumption
function is of the form, C=
50+.8Y. If income is Rs 1000/-
then
consumption is,-
(1) Rs 50/-
(2) Rs 1050/-
(3) Rs 50/-
(4) Rs 850/-.
Answer: 4
5. In the simple Keynesian
model consumption is a
function of,
(1) Rate of interest.
(2) Level of income.
Unit-2: Macro Economics MCQs
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(3) Price level.
(4) None of the above.
Answer: 2
6. In the simple Keynesian
model investment is
(1) Fixed.
(2) A function of level of
income.
(3) Either fixed or a function of
level of income.
(4) None of the above.
Answer: 3
7. Which of the following
statement is incorrect,-
In simple Keynesian model,-
(1) MPC+MPS=1
(2) APC+ APS=1
(3) Both (1) and (2)
(4) Neither (1) nor (2) .
Answer: 4
8. In simple Keynesian model,
stability of equilibrium exists, if
(1) APC is less than one.
(2) APS is less than one.
(3) MPC is less than one.
(4) None of the above.
Answer: 1
9. Keynesian analysis is
(1) A short run analysis.
(2) Long run analysis.
(3) Both short and long run
analysis.
(4) Neither short nor long run
analysis.
Answer: 1
10. The average propensity to
consume is measured by
(1) C/Y
(2) C=Y
(3) Y/C
(4) C+Y
Answer: 1
11. An increase in marginal
propensity to consume will
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(3) Price level.
(4) None of the above.
Answer: 2
6. In the simple Keynesian
model investment is
(1) Fixed.
(2) A function of level of
income.
(3) Either fixed or a function of
level of income.
(4) None of the above.
Answer: 3
7. Which of the following
statement is incorrect,-
In simple Keynesian model,-
(1) MPC+MPS=1
(2) APC+ APS=1
(3) Both (1) and (2)
(4) Neither (1) nor (2) .
Answer: 4
8. In simple Keynesian model,
stability of equilibrium exists, if
(1) APC is less than one.
(2) APS is less than one.
(3) MPC is less than one.
(4) None of the above.
Answer: 1
9. Keynesian analysis is
(1) A short run analysis.
(2) Long run analysis.
(3) Both short and long run
analysis.
(4) Neither short nor long run
analysis.
Answer: 1
10. The average propensity to
consume is measured by
(1) C/Y
(2) C=Y
(3) Y/C
(4) C+Y
Answer: 1
11. An increase in marginal
propensity to consume will
Unit-2: Macro Economics MCQs
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(1) Lead to the consumption
function becoming steeper.
(2) Shift the consumption
function upwards.
(3) Shift the consumption
function downwards.
(4) Shift the savings function
upwards.
Answer: 1
12. If the Keynesian
consumption function is,
C=10+.8Y, if income is Rs 1000/-
what is total
consumption.
(1) Rs .8/-
(2) Rs 800/-
(3) Rs 810/-
(4) Rs .81/-
Answer: 3
13. An increase in consumption
at any given level of income will
lead to
(1) Higher aggregate demand.
(2) An increase in exports.
(3) A fall in taxation revenue.
(4) A decrease in import
spending.
Answer: 1
14. Lower interest rates are
likely to
(1) Decrease consumption.
(2) Increase cost of borrowing.
(3) Encourage saving.
(4) Increase borrowing and
spending.
Answer: 4
15. The marginal propensity to
consume is equal to
(1) Total spending/Total
consumption
(2) Total consumption/ Total
income.
(3) Change in consumption/
Change in income
(4) Change in consumption/
Change in savings.
Answer: 3
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(1) Lead to the consumption
function becoming steeper.
(2) Shift the consumption
function upwards.
(3) Shift the consumption
function downwards.
(4) Shift the savings function
upwards.
Answer: 1
12. If the Keynesian
consumption function is,
C=10+.8Y, if income is Rs 1000/-
what is total
consumption.
(1) Rs .8/-
(2) Rs 800/-
(3) Rs 810/-
(4) Rs .81/-
Answer: 3
13. An increase in consumption
at any given level of income will
lead to
(1) Higher aggregate demand.
(2) An increase in exports.
(3) A fall in taxation revenue.
(4) A decrease in import
spending.
Answer: 1
14. Lower interest rates are
likely to
(1) Decrease consumption.
(2) Increase cost of borrowing.
(3) Encourage saving.
(4) Increase borrowing and
spending.
Answer: 4
15. The marginal propensity to
consume is equal to
(1) Total spending/Total
consumption
(2) Total consumption/ Total
income.
(3) Change in consumption/
Change in income
(4) Change in consumption/
Change in savings.
Answer: 3
DIWAKAR EDUCATION HUB
Unit- 3 : Statistics and
Econometrics
Unit- 3 : Statistics and
Econometrics
Unit- 3: Statistics and Econometrics
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S. N. TOPIC
Unit- 3 : Statistics and Econometrics
PAGE NO.
1.
Probability Theory: Concepts of probability,
Distributions, Moments, Central Limit
theorem
4-28
2.
Descriptive Statistics – Measures of Central
tendency & dispersions, Correlation, Index
Numbers
29-125
3.
Sampling methods & Sampling Distribution
126-
145
4.
Statistical Inferences, Hypothesis testing
146-
205
5.
Linear Regression Models and their
properties – BLUE
206-
224
6.
Identification Problem
225-
226
7.
Simultaneous Equation Models – recursive
and non-recursive
227-
234
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S. N. TOPIC
Unit- 3 : Statistics and Econometrics
PAGE NO.
1.
Probability Theory: Concepts of probability,
Distributions, Moments, Central Limit
theorem
4-28
2.
Descriptive Statistics – Measures of Central
tendency & dispersions, Correlation, Index
Numbers
29-125
3.
Sampling methods & Sampling Distribution
126-
145
4.
Statistical Inferences, Hypothesis testing
146-
205
5.
Linear Regression Models and their
properties – BLUE
206-
224
6.
Identification Problem
225-
226
7.
Simultaneous Equation Models – recursive
and non-recursive
227-
234
Unit- 3: Statistics and Econometrics
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8.
Discrete choice models
235-236
9.
Time Series Analysis
237-247
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8.
Discrete choice models
235-236
9.
Time Series Analysis
237-247
Unit- 3: Statistics and Econometrics
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What is Probability Theory: Concepts of
probability, Distributions, Moments, Central
Limit theorem
Theory Probability Theory: Concepts of probability,
Distributions, Moments, Central Limit theorem
Probability theory is foundational for economics and econometrics.
Probability is the mathematical language used to handle
uncertainty, which is central for modern economic theory.
Probability theory is also the foundation of mathematical statistics,
which is the foundation of econometric theory. Probability is used to
model uncertainty, variability, and randomness. When we say that
something is uncertain we mean that the outcome is unknown. For
example, how many students will there be in next year’s Ph.D.
entering class at your university? By variability we mean that the
outcome is not the same across all occurrences. For example, the
number of Ph.D. students fluctuate from year to year. By
randomness we mean that the variability has some sort of pattern.
For example, the number of Ph.D. students may fluctuate between
20 and 30, with 25 more likely than either 20 or 30. Probability gives
us a mathematical language to describe uncertainty, variability, and
randomness.
Classical (sometimes called "A priori" or "Theoretical")
This is the perspective on probability that most people first
encounter in formal education (although they may encounter the
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What is Probability Theory: Concepts of
probability, Distributions, Moments, Central
Limit theorem
Theory Probability Theory: Concepts of probability,
Distributions, Moments, Central Limit theorem
Probability theory is foundational for economics and econometrics.
Probability is the mathematical language used to handle
uncertainty, which is central for modern economic theory.
Probability theory is also the foundation of mathematical statistics,
which is the foundation of econometric theory. Probability is used to
model uncertainty, variability, and randomness. When we say that
something is uncertain we mean that the outcome is unknown. For
example, how many students will there be in next year’s Ph.D.
entering class at your university? By variability we mean that the
outcome is not the same across all occurrences. For example, the
number of Ph.D. students fluctuate from year to year. By
randomness we mean that the variability has some sort of pattern.
For example, the number of Ph.D. students may fluctuate between
20 and 30, with 25 more likely than either 20 or 30. Probability gives
us a mathematical language to describe uncertainty, variability, and
randomness.
Classical (sometimes called "A priori" or "Theoretical")
This is the perspective on probability that most people first
encounter in formal education (although they may encounter the
Unit- 3: Statistics and Econometrics
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subjective perspective in informal education).
For example, suppose we consider tossing a fair die. There are six
possible numbers that could come up ("outcomes"), and, since the
die is fair, each one is equally likely to occur. So we say each of
these outcomes has probability 1/6. Since the event "an odd
number comes up" consists of exactly three of these basic
outcomes, we say the probability of "odd" is 3/6, i.e. 1/2.
More generally, if we have a situation (a "random process") in which
there are n equally likely outcomes, and the event A consists of
exactly m of these outcomes, we say that the probability of A is m/n.
We may write this as "P(A) = m/n" for short.
This perspective has the advantage that it is conceptually simple for
many situations. However, it is limited, since many situations do not
have finitely many equally likely outcomes. Tossing a weighted die
is an example where we have finitely many outcomes, but they are
not equally likely. Studying people's incomes over time would be a
situation where we need to consider infinitely many possible
outcomes, since there is no way to say what a maximum possible
income would be, especially if we are interested in the future.
This method is also called the axiomatic approach.
Example 1: Roll of a Die
S = {1, 2, · · · , 6}
Probabilities: Each simple event has a 1/6 chance of occurring.
Example 2: Two Rolls of a Die
S = {(1, 1), (1, 2), · · · , (6, 6)}
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subjective perspective in informal education).
For example, suppose we consider tossing a fair die. There are six
possible numbers that could come up ("outcomes"), and, since the
die is fair, each one is equally likely to occur. So we say each of
these outcomes has probability 1/6. Since the event "an odd
number comes up" consists of exactly three of these basic
outcomes, we say the probability of "odd" is 3/6, i.e. 1/2.
More generally, if we have a situation (a "random process") in which
there are n equally likely outcomes, and the event A consists of
exactly m of these outcomes, we say that the probability of A is m/n.
We may write this as "P(A) = m/n" for short.
This perspective has the advantage that it is conceptually simple for
many situations. However, it is limited, since many situations do not
have finitely many equally likely outcomes. Tossing a weighted die
is an example where we have finitely many outcomes, but they are
not equally likely. Studying people's incomes over time would be a
situation where we need to consider infinitely many possible
outcomes, since there is no way to say what a maximum possible
income would be, especially if we are interested in the future.
This method is also called the axiomatic approach.
Example 1: Roll of a Die
S = {1, 2, · · · , 6}
Probabilities: Each simple event has a 1/6 chance of occurring.
Example 2: Two Rolls of a Die
S = {(1, 1), (1, 2), · · · , (6, 6)}
Unit- 3: Statistics and Econometrics
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Assumption: The two rolls are “independent.”
Probabilities: Each simple event has a (1/6) · (1/6) =1/36 chance of
occurring.
2. Empirical (sometimes called "A posteriori" or "Frequentist")
This perspective defines probability via a thought experiment.
To get the idea, suppose that we have a die which we are told is
weighted, but we don't know how it is weighted. We could get a
rough idea of the probability of each outcome by tossing the die a
large number of times and using the proportion of times that the die
gives that outcome to estimate the probability of that outcome.
This idea is formalized to define the probability of the event A as
P(A) = the limit as n approaches infinity of m/n,
where n is the number of times the process (e.g., tossing the die) is
performed, and m is the number of times the outcome A happens.
(Notice that m and n stand for different things in this definition from
what they meant in Perspective 1.)
In other words, imagine tossing the die 100 times, 1000 times,
10,000 times, ... . Each time we expect to get a better and better
approximation to the true probability of the event A. The
mathematical way of describing this is that the true probability is the
limit of the approximations, as the number of tosses "approaches
infinity" (that just means that the number of tosses gets bigger and
bigger indefinitely).
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Assumption: The two rolls are “independent.”
Probabilities: Each simple event has a (1/6) · (1/6) =1/36 chance of
occurring.
2. Empirical (sometimes called "A posteriori" or "Frequentist")
This perspective defines probability via a thought experiment.
To get the idea, suppose that we have a die which we are told is
weighted, but we don't know how it is weighted. We could get a
rough idea of the probability of each outcome by tossing the die a
large number of times and using the proportion of times that the die
gives that outcome to estimate the probability of that outcome.
This idea is formalized to define the probability of the event A as
P(A) = the limit as n approaches infinity of m/n,
where n is the number of times the process (e.g., tossing the die) is
performed, and m is the number of times the outcome A happens.
(Notice that m and n stand for different things in this definition from
what they meant in Perspective 1.)
In other words, imagine tossing the die 100 times, 1000 times,
10,000 times, ... . Each time we expect to get a better and better
approximation to the true probability of the event A. The
mathematical way of describing this is that the true probability is the
limit of the approximations, as the number of tosses "approaches
infinity" (that just means that the number of tosses gets bigger and
bigger indefinitely).
Unit- 3: Statistics and Econometrics
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Subjective
Subjective probability is an individual person's measure of belief
that an event will occur. With this view of probability, it makes
perfectly good sense intuitively to talk about the probability that the
Dow Jones average will go up tomorrow. You can quite rationally
take your subjective view to agree with the classical or empirical
views when they apply, so the subjective perspective can be taken
as an expansion of these other views.
However, subjective probability also has its downsides. First, since
it is subjective, one person's probability (e.g., that the Dow Jones
will go up tomorrow) may differ from another's. This is disturbing to
many people. Sill, it models the reality that often people do differ in
their judgments of probability.
The second downside is that subjective probabilities must obey
certain "coherence" (consistency) conditions in order to be
workable. For example, if you believe that the probability that the
Dow Jones will go up tomorrow is 60%, then to be consistent you
cannot believe that the probability that the Dow Jones will do down
tomorrow is also 60%. It is easy to fall into subjective probabilities
that are not coherent.
Axiomatic
This is a unifying perspective. The coherence conditions needed for
subjective probability can be proved to hold for the classical and
empirical definitions. The axiomatic perspective codifies these
coherence conditions, so can be used with any of the above three
perspectives.
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Subjective
Subjective probability is an individual person's measure of belief
that an event will occur. With this view of probability, it makes
perfectly good sense intuitively to talk about the probability that the
Dow Jones average will go up tomorrow. You can quite rationally
take your subjective view to agree with the classical or empirical
views when they apply, so the subjective perspective can be taken
as an expansion of these other views.
However, subjective probability also has its downsides. First, since
it is subjective, one person's probability (e.g., that the Dow Jones
will go up tomorrow) may differ from another's. This is disturbing to
many people. Sill, it models the reality that often people do differ in
their judgments of probability.
The second downside is that subjective probabilities must obey
certain "coherence" (consistency) conditions in order to be
workable. For example, if you believe that the probability that the
Dow Jones will go up tomorrow is 60%, then to be consistent you
cannot believe that the probability that the Dow Jones will do down
tomorrow is also 60%. It is easy to fall into subjective probabilities
that are not coherent.
Axiomatic
This is a unifying perspective. The coherence conditions needed for
subjective probability can be proved to hold for the classical and
empirical definitions. The axiomatic perspective codifies these
coherence conditions, so can be used with any of the above three
perspectives.
Unit- 3: Statistics and Econometrics
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The axiomatic perspective says that probability is any function (we'll
call it P) from events to numbers satisfying the three conditions
(axioms) below. (Just what constitutes events will depend on the
situation where probability is being used.)
The three axioms of probability:
0 ≤ P(E) ≤ 1 for every allowable event E. (In other words, 0 is the
smallest allowable probability and 1 is the largest allowable
probability).
I. The certain event has probability 1. (The certain event is the
event "some outcome occurs." For example, in rolling a die,
the certain event is "One of 1, 2, 3, 4, 5, 6 comes up." In
considering the stock market, the certain event is "The Dow
Jones either goes up or goes down or stays the same.")
II. The probability of the union of mutually exclusive events is the
sum of the probabilities of the individual events. (Two events
are called mutually exclusive if they cannot both occur
simultaneously. For example, the events "the die comes up 1"
and "the die comes up 4" are mutually exclusive, assuming we
are talking about the same toss of the same die. The union of
events is the event that at least one of the events occurs. For
example, if E is the event "a 1 comes up on the die" and F is
the event "an even number comes up on the die," then the
union of E and F is the event "the number that comes up on
the die is either 1 or even."
If we have a fair die, the axioms of probability require that each
number comes up with probability 1/6: Since the die is fair, each
number comes up with the same probability. Since the outcomes "1
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The axiomatic perspective says that probability is any function (we'll
call it P) from events to numbers satisfying the three conditions
(axioms) below. (Just what constitutes events will depend on the
situation where probability is being used.)
The three axioms of probability:
0 ≤ P(E) ≤ 1 for every allowable event E. (In other words, 0 is the
smallest allowable probability and 1 is the largest allowable
probability).
I. The certain event has probability 1. (The certain event is the
event "some outcome occurs." For example, in rolling a die,
the certain event is "One of 1, 2, 3, 4, 5, 6 comes up." In
considering the stock market, the certain event is "The Dow
Jones either goes up or goes down or stays the same.")
II. The probability of the union of mutually exclusive events is the
sum of the probabilities of the individual events. (Two events
are called mutually exclusive if they cannot both occur
simultaneously. For example, the events "the die comes up 1"
and "the die comes up 4" are mutually exclusive, assuming we
are talking about the same toss of the same die. The union of
events is the event that at least one of the events occurs. For
example, if E is the event "a 1 comes up on the die" and F is
the event "an even number comes up on the die," then the
union of E and F is the event "the number that comes up on
the die is either 1 or even."
If we have a fair die, the axioms of probability require that each
number comes up with probability 1/6: Since the die is fair, each
number comes up with the same probability. Since the outcomes "1
Unit- 3: Statistics and
Econometrics MCQs
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1. When we throw a coin then what
is the probability of getting head?
(A) 1/2
(B) 3
(C) 4
(D) 1
Answer: A
2. When we throw a coin then what
is the probability of getting a tail?
(A) 2
(B) 1/2
(C) 5
(D) 0
Answer: B
3. When we tossed three unbiased
coins then what is the probability of
getting at least 2 tails?
(A) 1/6
(B) 1/3
(C) 1/2
(D) 0
Answer: C
4. When we throw a dice then what
is the probability of getting the
number greater than 5?
(A) 1/5
(B) 1/6
(C) 1/2
(D) 1/3
Answer: B
5. When we throw two dice then
what is the probability of getting a
sum 9?
(A) 2/9
(B) 1/12
(C) 1/9
(D) All of these
Answer: C
6. Events which can never occur
together In probability theories then
it is classified as?
(A) mutually exclusive events
(B) collectively exclusive events
(C) mutually exhaustive events
(D) None of these
Answer: A
7. If J and K will be two variables
then the Joint probability of
independent events J and K is equal
to?
(A) P(J) + P(K)
(B) P(J) * P(K)
(C) P(J) * P(K) – P(J * K)
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1. When we throw a coin then what
is the probability of getting head?
(A) 1/2
(B) 3
(C) 4
(D) 1
Answer: A
2. When we throw a coin then what
is the probability of getting a tail?
(A) 2
(B) 1/2
(C) 5
(D) 0
Answer: B
3. When we tossed three unbiased
coins then what is the probability of
getting at least 2 tails?
(A) 1/6
(B) 1/3
(C) 1/2
(D) 0
Answer: C
4. When we throw a dice then what
is the probability of getting the
number greater than 5?
(A) 1/5
(B) 1/6
(C) 1/2
(D) 1/3
Answer: B
5. When we throw two dice then
what is the probability of getting a
sum 9?
(A) 2/9
(B) 1/12
(C) 1/9
(D) All of these
Answer: C
6. Events which can never occur
together In probability theories then
it is classified as?
(A) mutually exclusive events
(B) collectively exclusive events
(C) mutually exhaustive events
(D) None of these
Answer: A
7. If J and K will be two variables
then the Joint probability of
independent events J and K is equal
to?
(A) P(J) + P(K)
(B) P(J) * P(K)
(C) P(J) * P(K) – P(J * K)
Unit- 3: Statistics and Econometrics
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(D) P(J) * P(K) + P(J-K)
Answer: B
8. All possible outcomes for a
random experiment are called?
(A) sample space
(B) event space
(C) numerical space
(D) both b and c
Answer: D
9. What is the marginal probability
of dependent events and
independent events?
(A) one
(B) different
(C) same
(D) All of these
Answer: C
10. When we consider an event B
then non-occurrence of event B is?
(A) A is equal to zero
(B) intersection of A
(C) complement of A
(D) union of A
Answer: C
11. A and B are two events such that
P(A) = 0.4 and P(A ∩ B) = 0.2 Then
P(A ∩ B) is equal to ___________
(A) 0.4
b) 0.2
c) 0.6
d) 0.8
Answer: a
Explanation: P(A ∩ B) = P(A – (A ∩
B))
= P(A) – P(A ∩ B)
= 0.6 – 0.2 Using P(A) = 1 – P(A)
= 0.4.
12. A problem in mathematics is
given to three students A, B and (C)
If the probability of A solving the
problem is 1⁄2 and B not solving it is
1⁄4. The whole probability of the
problem being solved is 63⁄64 then
what is the probability of solving it?
(A) 1⁄8
(B) 1⁄64
c) 7⁄8
d) 1⁄2
Answer: c
Explanation:
Let A be the event of A solving the
problem
Let B be the event of B solving the
problem
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(D) P(J) * P(K) + P(J-K)
Answer: B
8. All possible outcomes for a
random experiment are called?
(A) sample space
(B) event space
(C) numerical space
(D) both b and c
Answer: D
9. What is the marginal probability
of dependent events and
independent events?
(A) one
(B) different
(C) same
(D) All of these
Answer: C
10. When we consider an event B
then non-occurrence of event B is?
(A) A is equal to zero
(B) intersection of A
(C) complement of A
(D) union of A
Answer: C
11. A and B are two events such that
P(A) = 0.4 and P(A ∩ B) = 0.2 Then
P(A ∩ B) is equal to ___________
(A) 0.4
b) 0.2
c) 0.6
d) 0.8
Answer: a
Explanation: P(A ∩ B) = P(A – (A ∩
B))
= P(A) – P(A ∩ B)
= 0.6 – 0.2 Using P(A) = 1 – P(A)
= 0.4.
12. A problem in mathematics is
given to three students A, B and (C)
If the probability of A solving the
problem is 1⁄2 and B not solving it is
1⁄4. The whole probability of the
problem being solved is 63⁄64 then
what is the probability of solving it?
(A) 1⁄8
(B) 1⁄64
c) 7⁄8
d) 1⁄2
Answer: c
Explanation:
Let A be the event of A solving the
problem
Let B be the event of B solving the
problem
Unit- 3: Statistics and Econometrics
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Let C be the event of C solving the
problem
Given P(A) = 1⁄2, P(~(B) = 1⁄4 and
P(A ∪ B ∪ C) = 63/64
We know P(A ∪ B ∪ C) = 1 – P(A ∪ B
∪ C)
= 1 – P(A ∩ B ∩ C)
= 1 – P(A) P(B) P(C)
Let P(C) = p
ie 63⁄64 = 1 – (1⁄2)(1⁄4)(p)
= 1 – p⁄8
⇒ P =1/8 = P(C)
⇒P(C) = 1 – P = 1 – 1⁄8 = 7⁄8.
13. Let A and B be two events such
that P(A) = 1⁄5 While P(A or (B) =
1⁄2. Let P(B) = P. For what values of
P are A and B independent?
(A) 1⁄10 and 3⁄10
(B) 3⁄10 and 4⁄5
c) 3⁄8 only
d) 3⁄10
view Answer
Answer: c
Explanation: For independent
events,
P(A ∩ (B) = P(A) P(B)
P(A ∪ (B) = P(A) + P(B) – P(A ∩ B)
= P(A) + P(B) – P(A) P(B)
= 1⁄5 + P (1⁄5)P
⇒ 1⁄2 = 1⁄5 + 4⁄5P
⇒ P= 3⁄8.
14. If A and B are two mutually
exclusive events with P(~(A) = 5⁄6
and P(B) = 1⁄3 then P(A /~(B) is equal
to ___________
(A) 1⁄4
(B) 1⁄2
c) 0, since mutually exclusive
d) 5⁄18
Answer: a
Explanation: As A and B are mutually
exclusive we have
A∩B¯
And Hence
P(A/B¯)=P(A∩B¯)P(B¯)
1−P(A¯)1−P(B¯)=1−561−13
P(A/B¯)=14
15. If A and B are two events such
that P(A) = 0.2, P(B) = 0.6 and P(A
/(B) = 0.2 then the value of P(A /~(B)
is ___________
(A) 0.2
(B) 0.5
c) 0.8
d) 1⁄3
Answer: a
Explanation: For independent
events,
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Let C be the event of C solving the
problem
Given P(A) = 1⁄2, P(~(B) = 1⁄4 and
P(A ∪ B ∪ C) = 63/64
We know P(A ∪ B ∪ C) = 1 – P(A ∪ B
∪ C)
= 1 – P(A ∩ B ∩ C)
= 1 – P(A) P(B) P(C)
Let P(C) = p
ie 63⁄64 = 1 – (1⁄2)(1⁄4)(p)
= 1 – p⁄8
⇒ P =1/8 = P(C)
⇒P(C) = 1 – P = 1 – 1⁄8 = 7⁄8.
13. Let A and B be two events such
that P(A) = 1⁄5 While P(A or (B) =
1⁄2. Let P(B) = P. For what values of
P are A and B independent?
(A) 1⁄10 and 3⁄10
(B) 3⁄10 and 4⁄5
c) 3⁄8 only
d) 3⁄10
view Answer
Answer: c
Explanation: For independent
events,
P(A ∩ (B) = P(A) P(B)
P(A ∪ (B) = P(A) + P(B) – P(A ∩ B)
= P(A) + P(B) – P(A) P(B)
= 1⁄5 + P (1⁄5)P
⇒ 1⁄2 = 1⁄5 + 4⁄5P
⇒ P= 3⁄8.
14. If A and B are two mutually
exclusive events with P(~(A) = 5⁄6
and P(B) = 1⁄3 then P(A /~(B) is equal
to ___________
(A) 1⁄4
(B) 1⁄2
c) 0, since mutually exclusive
d) 5⁄18
Answer: a
Explanation: As A and B are mutually
exclusive we have
A∩B¯
And Hence
P(A/B¯)=P(A∩B¯)P(B¯)
1−P(A¯)1−P(B¯)=1−561−13
P(A/B¯)=14
15. If A and B are two events such
that P(A) = 0.2, P(B) = 0.6 and P(A
/(B) = 0.2 then the value of P(A /~(B)
is ___________
(A) 0.2
(B) 0.5
c) 0.8
d) 1⁄3
Answer: a
Explanation: For independent
events,
Unit-4: Mathematical Economics
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Unit-4: Mathematical Economics
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S. N. TOPIC
Unit-4: Mathematical Economics
PAGE NO.
1.
Sets, functions and continuity, sequence,
series
4-131
2.
Differential Calculus and its Applications
132-
205
3.
Linear Algebra – Matrices, Vector Spaces
206-
259
4.
Static Optimization Problems and their
applications
260-
263
5.
Input-Output Model, Linear Programming
264-293
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S. N. TOPIC
Unit-4: Mathematical Economics
PAGE NO.
1.
Sets, functions and continuity, sequence,
series
4-131
2.
Differential Calculus and its Applications
132-
205
3.
Linear Algebra – Matrices, Vector Spaces
206-
259
4.
Static Optimization Problems and their
applications
260-
263
5.
Input-Output Model, Linear Programming
264-293
Unit-4: Mathematical Economics
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6.
Difference and Differential equations with
applications
294-
297
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6.
Difference and Differential equations with
applications
294-
297
Unit-4: Mathematical Economics
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What is Sets, functions and continuity, sequence,
series
Sets, functions and continuity, sequence, series
An introduction of sets and its definition in mathematics. The
concept of sets is used for the foundation of various topics in
mathematics.
To learn sets we often talk about the collection of objects, such as a
set of vowels, set of negative numbers, a group of friends, a list of
fruits, a bunch of keys, etc.
The different types of sets are explained below with examples.
Empty Set or Null Set:
A set which does not contain any element is called an empty set, or
the null set or the void set and it is denoted by ∅ and is read as phi.
In roster form, ∅ is denoted by {}. An empty set is a finite set, since
the number of elements in an empty set is finite, i.e., 0.
For example: (a) The set of whole numbers less than 0.
(b) Clearly there is no whole number less than 0.
Therefore, it is an empty set.
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What is Sets, functions and continuity, sequence,
series
Sets, functions and continuity, sequence, series
An introduction of sets and its definition in mathematics. The
concept of sets is used for the foundation of various topics in
mathematics.
To learn sets we often talk about the collection of objects, such as a
set of vowels, set of negative numbers, a group of friends, a list of
fruits, a bunch of keys, etc.
The different types of sets are explained below with examples.
Empty Set or Null Set:
A set which does not contain any element is called an empty set, or
the null set or the void set and it is denoted by ∅ and is read as phi.
In roster form, ∅ is denoted by {}. An empty set is a finite set, since
the number of elements in an empty set is finite, i.e., 0.
For example: (a) The set of whole numbers less than 0.
(b) Clearly there is no whole number less than 0.
Therefore, it is an empty set.
Unit-4: Mathematical Economics
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(c) N = {x : x ∈ N, 3 < x < 4}
• Let A = {x : 2 < x < 3, x is a natural number}
Here A is an empty set because there is no natural number between
2 and 3.
• Let B = {x : x is a composite number less than 4}.
Here B is an empty set because there is no composite number less
than 4.
Note:
∅ ≠ {0} ∴ has no element.
{0} is a set which has one element 0.
The cardinal number of an empty set, i.e., n(∅) = 0
Singleton Set:
A set which contains only one element is called a singleton set.
For example:
• A = {x : x is neither prime nor composite}
It is a singleton set containing one element, i.e., 1.
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(c) N = {x : x ∈ N, 3 < x < 4}
• Let A = {x : 2 < x < 3, x is a natural number}
Here A is an empty set because there is no natural number between
2 and 3.
• Let B = {x : x is a composite number less than 4}.
Here B is an empty set because there is no composite number less
than 4.
Note:
∅ ≠ {0} ∴ has no element.
{0} is a set which has one element 0.
The cardinal number of an empty set, i.e., n(∅) = 0
Singleton Set:
A set which contains only one element is called a singleton set.
For example:
• A = {x : x is neither prime nor composite}
It is a singleton set containing one element, i.e., 1.
Unit-4: Mathematical Economics
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• B = {x : x is a whole number, x < 1}
This set contains only one element 0 and is a singleton set.
• Let A = {x : x ∈ N and x² = 4}
Here A is a singleton set because there is only one element 2
whose square is 4.
• Let B = {x : x is a even prime number}
Here B is a singleton set because there is only one prime number
which is even, i.e., 2.
Finite Set:
A set which contains a definite number of elements is called a finite
set. Empty set is also called a finite set.
For example:
• The set of all colors in the rainbow.
• N = {x : x ∈ N, x < 7}
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• B = {x : x is a whole number, x < 1}
This set contains only one element 0 and is a singleton set.
• Let A = {x : x ∈ N and x² = 4}
Here A is a singleton set because there is only one element 2
whose square is 4.
• Let B = {x : x is a even prime number}
Here B is a singleton set because there is only one prime number
which is even, i.e., 2.
Finite Set:
A set which contains a definite number of elements is called a finite
set. Empty set is also called a finite set.
For example:
• The set of all colors in the rainbow.
• N = {x : x ∈ N, x < 7}
Unit-4: Mathematical Economics
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• P = {2, 3, 5, 7, 11, 13, 17, ...... 97}
Infinite Set:
The set whose elements cannot be listed, i.e., set containing never-
ending elements is called an infinite set.
For example:
• Set of all points in a plane
• A = {x : x ∈ N, x > 1}
• Set of all prime numbers
• B = {x : x ∈ W, x = 2n}
Note:
All infinite sets cannot be expressed in roster form.
For example:
The set of real numbers since the elements of this set do not follow
any particular pattern.
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• P = {2, 3, 5, 7, 11, 13, 17, ...... 97}
Infinite Set:
The set whose elements cannot be listed, i.e., set containing never-
ending elements is called an infinite set.
For example:
• Set of all points in a plane
• A = {x : x ∈ N, x > 1}
• Set of all prime numbers
• B = {x : x ∈ W, x = 2n}
Note:
All infinite sets cannot be expressed in roster form.
For example:
The set of real numbers since the elements of this set do not follow
any particular pattern.
Unit-4: Mathematical Economics
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Cardinal Number of a Set:
The number of distinct elements in a given set A is called the
cardinal number of A. It is denoted by n(A).
For example:
• A {x : x ∈ N, x < 5}
A = {1, 2, 3, 4}
Therefore, n(A) = 4
• B = set of letters in the word ALGEBRA
B = {A, L, G, E, B, R}
Therefore, n(B) = 6
Equivalent Sets:
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Cardinal Number of a Set:
The number of distinct elements in a given set A is called the
cardinal number of A. It is denoted by n(A).
For example:
• A {x : x ∈ N, x < 5}
A = {1, 2, 3, 4}
Therefore, n(A) = 4
• B = set of letters in the word ALGEBRA
B = {A, L, G, E, B, R}
Therefore, n(B) = 6
Equivalent Sets:
Unit-4: Mathematical Economics
MCQs
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MCQs
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Unit-4: Mathematical Economics MCQs
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1. If the binary operation * is
defined on a set of ordered
pairs of real number as
(a,(B) *(c,(D) = (ad+bc, b(D) and is
associative then (1,2)*(3,5)*(3,4)
equals
1. (74,40)
2. (32,40)
3. (23,11)
4. (7,11)
Answer: 1
2. If A = {1,2,3,4} . let =
{(1,2),(1,3),(4,2)}. Then is
1. Not anti-symmetric
2. Transitive
3. Reflexive
4. Symmetric
Answer: 2
3. If R ={ (1,2),(2,3),(3,3)} be a
relation defined on A= {1,2,3} then R
= R2
is
1. R itself
2. { (1,2),(2,3),(3,3)}
3. { (1,3),(2,3),(3,3)}
4. { (2,1),(1,3),(2,3)}
Answer: 3
4. A binary opearion * on a set of
integers is defined as x*y = x2
+y2
.Which one of the
following statement is true about *
1. Commutative but not associative
2. Both Commutative and
associative
3. Not Commutative but associative
4. Neither Commutative nor
associative
Answer: 1
5. How many onto (surjective )
functions are there form an n-
element(n 2) set to a 2-
elment set ?
1. 2n
2. 2n-1
3. 2n-2
4. 2(2n-2)
Answer: 1
6. What is the possible number of
reflexive relations on a set of 5
elements
1. 210
2. 215
3. 220
4. 225
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1. If the binary operation * is
defined on a set of ordered
pairs of real number as
(a,(B) *(c,(D) = (ad+bc, b(D) and is
associative then (1,2)*(3,5)*(3,4)
equals
1. (74,40)
2. (32,40)
3. (23,11)
4. (7,11)
Answer: 1
2. If A = {1,2,3,4} . let =
{(1,2),(1,3),(4,2)}. Then is
1. Not anti-symmetric
2. Transitive
3. Reflexive
4. Symmetric
Answer: 2
3. If R ={ (1,2),(2,3),(3,3)} be a
relation defined on A= {1,2,3} then R
= R2
is
1. R itself
2. { (1,2),(2,3),(3,3)}
3. { (1,3),(2,3),(3,3)}
4. { (2,1),(1,3),(2,3)}
Answer: 3
4. A binary opearion * on a set of
integers is defined as x*y = x2
+y2
.Which one of the
following statement is true about *
1. Commutative but not associative
2. Both Commutative and
associative
3. Not Commutative but associative
4. Neither Commutative nor
associative
Answer: 1
5. How many onto (surjective )
functions are there form an n-
element(n 2) set to a 2-
elment set ?
1. 2n
2. 2n-1
3. 2n-2
4. 2(2n-2)
Answer: 1
6. What is the possible number of
reflexive relations on a set of 5
elements
1. 210
2. 215
3. 220
4. 225
Unit-4: Mathematical Economics MCQs
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Answer: 3
7. For a set A , the power set of A is
denoted by 2A, . If A= {5, {6},{7}} ,
which of the
following option are true ?
1. ∈A
2. ⊆A
3. {5,{6}}∈A
4. . {5,{6}}⊆2A
Answer: 4
8. If f is a function from A to B ,
where O(A) = m & O(B) = n , then
total number of
distinct functions are
1. n
m
2. nm
3. m
n
4. m+n
Answer: 2
9. A function f from N to N defined
by f(n)= 2n+5 ∈ is
1. many –one function
2. into function
3. onto function
4. bijective function
Answer: 2
10. If 63% of persons like banana ,
where 76% like apple. What can be
said about the
percentage of persons who like both
banana & apples ?
1. 40
2. 39
3. 27
4. 24
Answer: 2
11. The number of binary relation
on a set with n elements is
1. n2
2. 2n
3. m
n
4. None of these
Answer: 3
12. The number of equivalence
relations of the set {1,2,3,4} is
1. 4
2. 15
3. 16
4. 24
Answer: 1
13: If R = ((1, 1), (3, 1), (2, 3), (4, 2)),
then which of the following
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Answer: 3
7. For a set A , the power set of A is
denoted by 2A, . If A= {5, {6},{7}} ,
which of the
following option are true ?
1. ∈A
2. ⊆A
3. {5,{6}}∈A
4. . {5,{6}}⊆2A
Answer: 4
8. If f is a function from A to B ,
where O(A) = m & O(B) = n , then
total number of
distinct functions are
1. n
m
2. nm
3. m
n
4. m+n
Answer: 2
9. A function f from N to N defined
by f(n)= 2n+5 ∈ is
1. many –one function
2. into function
3. onto function
4. bijective function
Answer: 2
10. If 63% of persons like banana ,
where 76% like apple. What can be
said about the
percentage of persons who like both
banana & apples ?
1. 40
2. 39
3. 27
4. 24
Answer: 2
11. The number of binary relation
on a set with n elements is
1. n2
2. 2n
3. m
n
4. None of these
Answer: 3
12. The number of equivalence
relations of the set {1,2,3,4} is
1. 4
2. 15
3. 16
4. 24
Answer: 1
13: If R = ((1, 1), (3, 1), (2, 3), (4, 2)),
then which of the following
Unit-4: Mathematical Economics MCQs
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represents R2, where R2 is R
composite R?
A. ((1, 1), (3, 1), (2, 3), (4, 2))
B. f(1, 1), (9, 1), (4, 9), (16, 4))
C. 1(1, 3), (3, 3), (3, 4), (3, 2))
D. ((1, 1), (2, 1), (4, 3), (3, 1))
Option: D
14. If A & B are sets and A B = A ∪ B
, then
1. A =
2. B =
3. A = B
4. None of these
Answer: 4
15. The domain & range are same
for
1. constant function
2. Identity function
3. absolute value function
4. Greatest integer function
Answer: 2
16. Set A has 3 elements & set B has
4 elements . The number of
injections that can be
defined from A into B
1. 144
2. 12
3. 24
4. 64
Answer: 3
17. The number of bijective
functions from set A to itself when A
contains 106 elements is
Is
1. 106
2. 106
2
3. 106 !
4. 2
106
Answer: 3
18. Let Z denote the set of all
integers define f by f(x)= x/2 , if x is
even
x , if x is odd then f is
1. Onto but not one-one
2. One-one but not onto
3. One-one & onto
4. Neither one-one nor onto
Answer: 1
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represents R2, where R2 is R
composite R?
A. ((1, 1), (3, 1), (2, 3), (4, 2))
B. f(1, 1), (9, 1), (4, 9), (16, 4))
C. 1(1, 3), (3, 3), (3, 4), (3, 2))
D. ((1, 1), (2, 1), (4, 3), (3, 1))
Option: D
14. If A & B are sets and A B = A ∪ B
, then
1. A =
2. B =
3. A = B
4. None of these
Answer: 4
15. The domain & range are same
for
1. constant function
2. Identity function
3. absolute value function
4. Greatest integer function
Answer: 2
16. Set A has 3 elements & set B has
4 elements . The number of
injections that can be
defined from A into B
1. 144
2. 12
3. 24
4. 64
Answer: 3
17. The number of bijective
functions from set A to itself when A
contains 106 elements is
Is
1. 106
2. 106
2
3. 106 !
4. 2
106
Answer: 3
18. Let Z denote the set of all
integers define f by f(x)= x/2 , if x is
even
x , if x is odd then f is
1. Onto but not one-one
2. One-one but not onto
3. One-one & onto
4. Neither one-one nor onto
Answer: 1
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इस ?वषय का हमारा पूरा अययन
नोट्स खरीद
अ?धक जानकारी के ?लए कॉल कर या
हाट्सएप 7310762592
(ये ?कताब के कुछ पेज ह, पूण 10
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