FREE IGNOU MEC
102 MICRO ECONOMIC
ANALYSIS SOLVED ASSIGNMENT
2024-25
SECTION
A
Answer
the following questions in about 700 words each.
1.a. The production function of a small factory that produces and
sells toys is: ๐ = 5. √๐ฟ.๐พ Where Q is the number of
toys produced each day, L is the labour hours and k is the machine hours.
Suppose 9 labour hours and 9 machine hours are used every day, what is the
maximum number of toys that can be produced in a day? Calculate the marginal product
of labour when 9 labour hours are used each day together with 9 machine hours.
Suppose the firm doubles both the amount of labour and machine hours used per
day. Calculate the increase in output. Comment on the returns to scale in the
operation. b. Define the term ‘Shepard’s lemma’. Assume that the production
function of a producer is given by Q=5L0.5 K 0.3, where Q,L and K denote
output, labour and capital respectively. If labour cost ₹ 1 per unit and
capital ₹2, find the least cost combination of inputs (L&K)
1. a. Production Function and Calculations
The
given production function for the toy factory is:
Q=5L⋅KQ
= 5 \sqrt{L} \cdot KQ=5L⋅K
where:
- QQQ = Number of toys produced
per day
- LLL = Labour hours
- KKK = Machine hours
 |
| FREE IGNOU MEC 101 MICRO ECONOMIC ANALYSIS SOLVED ASSIGNMENT 2024-25 |
Substitute
L=9L = 9L=9 and K=9K = 9K=9 into the production function:
Q=59⋅9Q
= 5 \sqrt{9} \cdot 9Q=59⋅9 Q=5×3×9=5×27=135Q = 5 \times 3 \times 9 = 5 \times 27 =
135Q=5×3×9=5×27=135
So,
the maximum number of toys that can be produced in a day is 135.
1.2. Marginal Product of Labour (MPL)
The
marginal product of labour (MPL) is the additional output produced by using an
additional unit of labour while keeping all other inputs constant.
The
MPL can be found by taking the partial derivative of the production function
QQQ with respect to LLL:
MPL=∂Q∂LMPL = \frac{\partial
Q}{\partial L}MPL=∂L∂Q
Given:
Q=5L⋅K=5L0.5KQ
= 5 \sqrt{L} \cdot K = 5 L^{0.5} KQ=5L⋅K=5L0.5K
The
partial derivative with respect to LLL is:
MPL=5K⋅∂(L0.5)∂LMPL
= 5 K \cdot \frac{\partial (L^{0.5})}{\partial L}MPL=5K⋅∂L∂(L0.5) MPL=5K⋅(0.5L−0.5)MPL
= 5 K \cdot \left(0.5 L^{-0.5}\right)MPL=5K⋅(0.5L−0.5)
MPL=5K2LMPL = \frac{5K}{2 \sqrt{L}}MPL=2L5K
Substitute
L=9L = 9L=9 and K=9K = 9K=9:
MPL=5⋅929MPL
= \frac{5 \cdot 9}{2 \sqrt{9}}MPL=295⋅9
MPL=452⋅3=456=7.5MPL = \frac{45}{2 \cdot 3} = \frac{45}{6} =
7.5MPL=2⋅345=645=7.5
So,
the marginal product of labour when 9 labour hours are used each day together
with 9 machine hours is 7.5.
1.3. Increase in Output When Labour and Machine Hours are
Doubled
If
both labour and machine hours are doubled:
L′=2L=18,K′=2K=18L' = 2L = 18, \quad K' = 2K = 18L′=2L=18,K′=2K=18
The
new output Q′Q'Q′ is:
Q′=5L′⋅K′Q'
= 5 \sqrt{L'} \cdot K'Q′=5L′⋅K′ Q′=518⋅18Q' = 5 \sqrt{18} \cdot 18Q′=518⋅18 Q′=5×18×18Q' = 5 \times \sqrt{18} \times 18Q′=5×18×18
Q′=5×(32)×18Q' = 5 \times (3 \sqrt{2}) \times 18Q′=5×(32)×18 Q′=5×542Q' = 5
\times 54 \sqrt{2}Q′=5×542
Now,
let's find the value:
Q′=2702≈270×1.414≈382.5Q' = 270
\sqrt{2} \approx 270 \times 1.414 \approx 382.5Q′=2702≈270×1.414≈382.5
The
new output is approximately 382.5 toys.
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2. Consider a Cobb-Douglas utility function U (X, Y) = Xฮฑ Y (1- ฮฑ) ,
Where X and y are the two goods that a consumer consumes at per unit
prices of Px and Py respectively. Assuming the income of the consumer to be ₹M,
determine:
a. Marshallian demand function for goods X and Y.
b. Indirect utility function for such a consumer.
c. The maximum utility attained by the consumer where ฮฑ =1/2, Px =₹
2, Py = ₹ 8 and M= ₹ 4000.
d. Derive Roy’s identity.
2.
Cobb-Douglas Utility Function
The utility function is:
U(X,Y)=XฮฑY1−ฮฑU(X, Y) = X^{\alpha}
Y^{1 - \alpha}U(X,Y)=XฮฑY1−ฮฑ
where:
- XXX and YYY are two goods consumed by the consumer.
- ฮฑ\alphaฮฑ is a parameter (with 0<ฮฑ<10 < \alpha
< 10<ฮฑ<1).
- PXP_XPX and PYP_YPY are the per-unit prices of goods
XXX and YYY, respectively.
- MMM is the consumer's income.
a.
Marshallian Demand Function for Goods X and Y
c. Maximum Utility with Given Values
d. Derive Roy’s Identity
SECTION B
Answer the following questions in about 400
words each. Each question carries 12marks.
3. a.) What do you mean by market failure? What are its causes?
Market failure occurs
when the allocation of goods and services by a free market is not efficient. In
other words, market failure happens when the market, operating on its own, does
not lead to a socially optimal outcome, resulting in a loss of economic
welfare. Market failure is a situation where market forces of supply and demand
do not lead to the most efficient distribution of resources, causing a net
social welfare loss. This can result in overproduction, underproduction, or a
misallocation of resources.
Causes
of Market Failure
Externalities
An
externality occurs when a third party, not directly involved in an economic
transaction, is affected by it. Externalities can be positive or negative.
Negative Externalities:
These occur when a transaction causes a cost to a third party. For example,
pollution from a factory affects the health and environment of those living
nearby, but the costs of pollution are not reflected in the price of the
factory's products. This leads to overproduction of goods that generate
negative externalities.
Positive Externalities:
These occur when a transaction provides benefits to a third party. For example,
education not only benefits the individual who receives it but also society as
a whole through increased productivity, lower crime rates, and more informed
citizens. However, since individuals do not account for these societal
benefits, education may be underprovided by the market.
Public
Goods
Public
goods are goods that are non-excludable and non-rivalrous.
Non-Excludable: It is not
possible to exclude anyone from using the good. For example, street lighting is
available to everyone, and no one can be excluded from its use.
Non-Rivalrous: The use of
the good by one person does not diminish its availability to others. For
instance, one person benefiting from street lighting does not reduce the amount
available to others.
Because no one can be
excluded from using public goods and one person’s use does not reduce the
availability for others, firms may find it unprofitable to provide them. This
results in underproduction or no production of public goods, leading to market
failure.
Information Asymmetry
Information asymmetry
occurs when one party in a transaction has more or better information than the
other. This can lead to adverse selection and moral hazard:
Adverse Selection: This
occurs when buyers or sellers have information that the other party does not
have, leading to a selection of products or services that are less favorable.
For example, in the health insurance market, individuals with higher health
risks are more likely to buy insurance, leading to higher premiums and
potentially pushing healthy individuals out of the market.
Moral Hazard: This occurs
when one party takes more risks because they do not bear the full consequences
of those risks. For example, a person with car insurance might drive less
cautiously, knowing that any damage is covered by the insurer.
Market Power and Monopoly
Market power refers to
the ability of a firm to influence or control the price and output of a product
in the market. When a single firm (monopoly) or a small group of firms
(oligopoly) has significant market power, they can set prices above the
competitive level, leading to inefficiency and welfare loss.
Monopoly: A single firm
controls the entire market supply, which allows it to set prices higher than in
competitive markets, resulting in reduced consumer surplus and potential
deadweight loss.
Oligopoly: A few firms
dominate the market and can collude to set prices or output, reducing
competition and leading to market inefficiencies.
Imperfect Competition
Imperfect competition
refers to market structures that deviate from the ideal conditions of perfect
competition, which include monopolistic competition and oligopoly:
Monopolistic Competition:
A market structure where many firms sell differentiated products, leading to
non-price competition. This may result in excessive advertising, branding, and
other expenses that do not necessarily improve the product but lead to higher
prices and reduced consumer welfare.
Oligopoly: A market
structure dominated by a few large firms that have significant control over
price and output. These firms may collude to reduce output and keep prices
high, leading to inefficiencies and reduced consumer welfare.
Lack of Property Rights
When property rights are
not well-defined or enforced, resources can be overused or misused. For
example, in the case of common resources like air or water, individuals or
firms may overuse them because they do not own them and bear the full cost of
their actions. This can lead to overexploitation and depletion of resources, a
situation known as the "tragedy of the commons."
Government Intervention
and Regulatory Failure
Government intervention
is often needed to correct market failures, but in some cases, it can cause new
market failures, known as regulatory failures:
Price Controls: Setting
price floors (minimum prices) or price ceilings (maximum prices) can lead to
shortages or surpluses. For example, rent control can lead to a shortage of
rental properties as landlords may find it unprofitable to rent at controlled
prices.
Subsidies and Taxes:
While subsidies and taxes can correct certain market failures, they may also
lead to unintended consequences, such as overproduction of subsidized goods or
underproduction of taxed goods.
Macroeconomic Instability
Macroeconomic factors,
such as inflation, unemployment, and recession, can also contribute to market
failure. For example, during a recession, demand for goods and services falls,
leading to underutilization of resources and unemployment. Conversely, inflation
can distort prices and lead to inefficient allocation of resources.
Inadequate Market
Structure
Inadequate market
structures, such as underdeveloped financial markets, lack of competition, or
weak legal systems, can lead to market failure by limiting access to
information, credit, or opportunities for competition. This can prevent
efficient resource allocation and hinder economic growth.
Incomplete Markets
An incomplete market
occurs when not all goods or services are provided by the market, or there is a
lack of insurance markets for certain risks. For example, markets for health
insurance, environmental risks, or long-term care might be incomplete, leading
to suboptimal provision of these services.
Coordination Failures
Coordination failure
occurs when agents in the market do not coordinate their actions, resulting in
suboptimal outcomes. For instance, multiple firms may fail to invest in a new
technology that is beneficial to all because each firm waits for the others to
take the first step. This can lead to stagnation and market failure.
Equity and Income
Distribution Issues
Markets may fail to
achieve an equitable distribution of income and wealth, which is considered a
market failure from a societal perspective. While markets may allocate
resources efficiently, they may not do so fairly, leading to significant
inequality. For instance, basic necessities like food, healthcare, and
education may not be accessible to everyone due to unequal distribution of
income, even though they are efficiently provided in the market.
Conclusion
Market failure represents
a situation where free markets, on their own, fail to achieve an efficient and
socially desirable outcome. The causes of market failure are diverse and can
include externalities, public goods, information asymmetry, market power, and
government intervention. Understanding these causes is essential for
policymakers to design interventions that correct these failures and enhance
overall economic welfare. By addressing the root causes of market failure, such
as through regulation, taxation, subsidies, or the provision of public goods,
societies can aim to achieve a more efficient and equitable allocation of
resources.
b) What are the two principles of justice as mentioned by the philosopher Rawls?
Philosopher
John Rawls, in his seminal work "A Theory of Justice" (1971),
introduced two fundamental principles of justice that form the basis of his
theory of "justice as fairness." Rawls’ principles are designed to
ensure a fair and equitable distribution of goods, rights, and opportunities
within a society. His framework aims to establish a just social order, where
each individual is treated fairly and given a fair chance to succeed,
irrespective of their social or economic background. The two principles of
justice, according to Rawls, are:
1. The Principle of Equal Liberty:
The
First Principle of Justice is the principle of equal liberty,
which states:
- “Each person has an equal right
to a fully adequate scheme of equal basic liberties, which is compatible
with a similar scheme of liberties for all.”
This
principle emphasizes that every individual in society should have the same set
of basic rights and liberties. These liberties include, but are not limited to,
freedom of speech, freedom of conscience, freedom of assembly, the right to
vote, and the right to personal property. According to Rawls, these liberties
must be guaranteed to everyone in an equal measure and should be protected to
the maximum extent.
This
principle takes precedence over other considerations; it means that basic
rights cannot be sacrificed or compromised, even for social or economic
advantages. Rawls insists that any infringement of these basic liberties cannot
be justified, even if it results in overall societal benefit. The priority
given to equal basic liberties is meant to ensure that individual freedoms are
preserved and respected as the foundation of a just society.
2. The Difference Principle and the Principle of Fair
Equality of Opportunity:
The
Second Principle of Justice is divided into two parts: the Difference
Principle and the Principle of Fair Equality of Opportunity.
- a. The Difference Principle:
The
Difference Principle asserts that social and economic inequalities are only
justified if they benefit the least advantaged members of society. In other
words, any inequalities in the distribution of wealth, income, or social status
are acceptable only if they work to the advantage of those who are worst off.
According to this principle, societal resources should be allocated in a way
that improves the situation of the most disadvantaged members, ensuring that
any benefits of inequality ultimately contribute to the overall well-being of
everyone. Rawls argues that this principle helps create a system where the
benefits of social cooperation are distributed fairly and equitably.
- b. The Principle of Fair
Equality of Opportunity:
The
Principle of Fair Equality of Opportunity requires that everyone should have a
fair chance to attain positions of advantage, such as jobs, education, or
political offices, regardless of their background or social status. Rawls
argues that social and economic inequalities should be arranged so that
positions and offices are open to all, under conditions of fair equality of
opportunity. This principle goes beyond mere formal equality, which only
prohibits overt discrimination; it requires that individuals have genuinely
equal opportunities to develop their talents and abilities, regardless of their
circumstances of birth, socioeconomic status, or other factors beyond their
control.
Conclusion:
Together,
these two principles provide a framework for structuring a just society. The First
Principle ensures that fundamental rights and liberties are equally
protected for all, while the Second Principle ensures that any social or
economic inequalities are arranged in a manner that benefits the least
advantaged and provides fair opportunities for all. Rawls’ theory of justice is
a powerful critique of utilitarianism, focusing instead on fairness, equality,
and respect for each individual’s rights, ultimately aiming to create a more
equitable and just society.
4. a.) Define games of complete and incomplete information
Games of Complete
Information: A game is said to have complete information if all players know
the structure of the game, the strategies available to all players, and the
payoffs for each combination of strategies. This means that every player has
full knowledge of all the elements of the game, including the payoffs
associated with every possible outcome. In such games, uncertainty may exist
about the strategies other players will choose, but there is no uncertainty
about the structure of the game or the payoffs.
Games of Incomplete
Information: A game is said to have incomplete information when at least one
player does not have full knowledge about some elements of the game. This could
involve uncertainty about the payoffs, strategies, or types of other players.
In these games, players may not know certain critical aspects, such as the
payoff functions, available strategies, or preferences of the other players.
Games of incomplete information are often analyzed using concepts like Bayesian
Nash equilibrium, where players form beliefs about unknown aspects and choose
optimal strategies based on these beliefs.
b.) From the following pay-off matrix, where the payoffs (the
negative values) are the years of possible imprisonment for individuals A and
B, determine:
(i) The optimal strategy for each individual.
(ii) Do individuals A and B face a prisoner’s dilemma?
4. b.) Analysis of the Payoff Matrix
|
Individual
B Confess |
Individual
B Don't Confess |
|
|
Individual
A Confess |
(-5, -5) |
(-1, -10) |
|
Individual
A Don't Confess |
(-10, -1) |
(-2, -2) |
(i) Optimal Strategy for Each Individual
To
find the optimal strategy for each individual, we can analyze the payoffs and
determine the best choice for each player, assuming the other player's strategy
is fixed. This approach is also known as finding the Nash Equilibrium.
- Individual A’s Strategy:
- If Individual B Confesses:
- A's payoff if A confesses: -5
- A's payoff if A does not
confess: -10
- Therefore, A should Confess
(since -5 > -10).
- If Individual B Does Not
Confess:
- A's payoff if A confesses: -1
- A's payoff if A does not
confess: -2
- Therefore, A should Confess
(since -1 > -2).
- Individual B’s Strategy:
- If Individual A Confesses:
- B's payoff if B confesses: -5
- B's payoff if B does not
confess: -10
- Therefore, B should Confess
(since -5 > -10).
- If Individual A Does Not
Confess:
- B's payoff if B confesses: -1
- B's payoff if B does not
confess: -2
- Therefore, B should Confess
(since -1 > -2).
From
the analysis, both individuals A and B have a dominant strategy to Confess,
regardless of what the other does.
(ii) Do Individuals A and B Face a Prisoner’s Dilemma?
Yes,
Individuals A and B face a Prisoner's Dilemma.
Here’s
why:
- In a Prisoner's Dilemma, both
players have a dominant strategy (to confess in this case) that leads to a
worse collective outcome (-5, -5) than if they both chose to cooperate by
not confessing (-2, -2).
- Despite both players being
better off by not confessing (resulting in only 2 years of imprisonment
each), their dominant strategy leads them to confess, resulting in a worse
outcome for both (5 years each).
This
situation captures the essence of the Prisoner's Dilemma: each player's pursuit
of individual rationality leads to a collectively irrational outcome.
5. a) What are the conditions of Pareto optimality?
b) Suppose an investor is concerned about a business choice in which
there are three prospects. The probability and returns are given below:
What is the expected value of the uncertain investment? What is the
variance?
6. a.) Do you agree that by paying higher than the minimum wage,
employers can retain skilled workers, increase productivity, or ensure loyalty?
Comment on the statement in the light of efficiency wage model.
b.) There are two firms 1 and 2 in an industry, each producing
output Q1 and Q2 respectively and facing the industry demand given by P=50-2Q,
where P is the market price and Q represents the total industry output, that is
Q= Q1 + Q2. Assume that the cost function is C = 10 + 2q. Solve for the Cournot
equilibrium in such an industry.
7.
Write short notes on following:
a) vNM expected utility theory
b) Slutsky’s theorem
c) Arrow prat measure of risk averseness
d) Bergson-Samuelson Social welfare function
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Submission Date :
· 30
April 2025 (if enrolled in the July 2025 Session)
· 30th Sept, 2025 (if enrolled in the January
2025 session).
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MEC 102 MICRO ECONOMIC ANALYSIS
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