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MEC-001: Microeconomic Analysis AssignmentCourse Code:
MEC-001Assignment Code: MEC-001/TMA/2011-12Marks: 100
Note:Answer all the questions. While questions in Section A
carry 20 marks each, those of Section B carry 12 marks each.Section
A1.Explain the concept of Nash equilibrium. How it is related to
(a) Dominant strategy equilibrium and (b) Sub-game perfection?
Ans.In a n player normal form game G = {S1, S2,..,Sn; u1,
u2,...,un}, the strategies (s*1,s*2,.,s*n) constitute a Nash
equilibrium if, for each player I, si is player is best response to
the strategies specified for the (n-1) other players, (s*1,s*2,,
s*i-1, s*i+1,.,s*n) :
or U1 (s*1,s*2,, s*i-1, s*i, s*i+1,.,s*n) U1 (s*1,s*2,, s*i-1,
s*i, s*i+1,.,s*n) where i = 1,2,,n
or, for every feasible strategy si in Si; that is s*i solves
max U1 (s*1,s*2,, s*i-1, s*i, s*i+1,.,s*n)s*2S*i
Nash equilibrium is strategically stable and self-enforcing
because no single player wants to deviate from her predicted
strategy.
Dominant Strategy A player in a simultaneous move game may have
nay finite number of pure strategies at her disposal. One of these
strategies called as dominant strategies if it outperforms all of
her other strategies, no matter what any other player does.In the
normal form game G = {S1, S2,..,Sn; u1, u2,...,un}, let s1i and
s11i be feasible strategies for the player I (i.e s1i and s11i are
members of Si). Strategy s11i strictly dominates strategy s1i, if
for each possible combination of other players strategies, is
payoff from playing s1i is strictly less than i's payoff from
playing s11i. Symbolically,
U1 (s1,s2,, si-1, s1i, si+1,.,sn) < U1 (s1,s2,, si-1, s11i,
si+1,.,sn)for each (s1,s2,, si-1, si+1,.,sn) that can be
constructed from other players strategy spaces (S1,S2,, Si-1,
Si+1,.,Sn). Strategy s11i is called strictly dominant strategy for
player i. The dominance is said to be weak when there is a weak
inequality ( rather than 1, implies increasing returns to scale a+b
< 1, implies decreasing returns to scale
To determine the elasticity of substitution in Cobb-Douglas
production function, let us use Allens definition
= q/L.( q/k) / q (2q/LK)
When q = AKaL1-a
= [(1-a).(q/L).a(q/K)] / [q2.{(1-a)(a)/LK)}] = 1The Cobb-Douglas
function is linear in logarithms, i.e, log q = log A + a log K + b
log L.
As a result, the constant a in above equation is the elasticity
of output with respect to capital output, and b is the elasticity
of output with respect to labour input. To get the result, take
eq,K = q/K . (K/q) = log q / log K) such thateq,K = a from above
eqn. Similarly, we get eq,L = b
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4.What are the recommendations of Coase to solve the problem of
externalities?
Ans.Ronald Coase asserted that under perfect competition private
and social cost will be equal and addressed a well known problem of
market externalities, known as the Spillover Effect. This occurs
when someone other than the buyer must share the benefits or costs
of a product. The classic example of such a perception is
pollution. Factories can either treat pollution which costs money-
or dump it into the air or water for free. If they choose to dump,
they may save their customers some money, but citizens who live
near the factory will also pay a price in higher death and disease
rates, less fertile land, environmental catastrophes, etc.
Sometimes the spillover effect is both positive and negative. An
airport benefits its customers, but it also subjects the local
neighborhood to various externalities eg. noise pollution.
Coase argued that individuals could organise bargains so as to
bring about an efficient outcome and eliminate externalities
without without government intervention. The government should
restrict its role to facilitating bargaining among the affected
groups or individuals and to enforcing any contracts that result.
This result, often known as the Coase Theorem requires that:
property rights are well defined; the number of people involved
is small; and bargaining costs are very small
Only if all three conditions, apply then individual bargaining
will solve the problem of externalities. All that is needed is a
common law or statutory rule, which assigns rights over the
externality to one party or another. The market/pricing mechanism
will then function in the same way as it does for the ordinary
goods and services over which rights clearly defined.
Thus Coases theorem has helped in the emergence of numerous
policy formulations in the welfare imperatives of societies.
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5.Explain Arrows Impossibility Theorem.
Ans.The democratic procedure for reaching a social choice or
group decision is the expression of their preferences by
individuals through free voting. Social choice will be determined
by the majority rule. But Arrow has demonstrated through his
impossibility theorem that consistent social choices cannot be made
without violating the consistency or transitivity condition. The
social choice on the basis of majority rule may be inconsistent
even if individual preferences are consistent. Arrow first
considers a simple case of two alternative social states and proves
that in this case group decision or social choice through a
majority rule yields a social choice, which can satisfy all the
five conditions. But when there are more than two alternatives,
majority rule fails to yield a social choice without violating at
least one of the five conditions. Thus, Arrows theorem says that if
the decision-making body has at least two members and at least
three options to decide among, then it is impossible to design a
social choice function that satisfies all these conditions at
once.
Alternative Social StatesXYZ
A321
B132
C213
Ranking of Alternatives by Individuals and Social Choices
In this table three individuals A, B and C who constitutes the
society have voted for three alternative social states X, Y and Z
by writing 3, against the most preferred alternative, 2 for the
next preferred alternative and 1 for the least preferred
alternative. Majority rule leads to inconsistent social choices
because on the one hand, X has been preferred to Z by the majority
and on the other hand, Z has also been preferred to X by majority,
which is contradictory or inconsistent.
Arrow has derived three consequences to explain his
impossibility theorem. According to Consequence I, whenever the two
individuals prefer X to Y, then irrespective of the rank of the
third alternative Z, society will prefer X to Y. According to
Consequence II, if in a given social choice, the will of individual
prevails against the opposition of individual B, then the will of A
will certainly prevail in case individual B is different or agrees
with A. According to Consequence III, if individuals A and B have
exactly conflicting interests in the choice between two
alternatives X and Y, then the society will be indifferent between
X and Y. It is interesting to note that the simple proof of the
impossibility theorem follows from Consequence III. For instance,
if individual A prefers X to Y and individual B prefers Y to Z and
if society opts for X, then A will be a dictator in as much as her
choice will always be social choice. Thus, Arrows theorem says that
if the decision-making body has at least two members and at least
three options to decide among, then it is impossible to design a
social choice function that satisfies all these conditions at once.
Arrow, therefore concludes that it is impossible to derive a social
ordering of different conceivable alternative social states on the
basis of the individual ordering of those social states without
violating at least one of the value judgments expressed in the five
conditions of social choices. This is in essence his impossibility
theorem.
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6.Discuss the concept of asymmetric information. Explain the
relation among moral hazard, adverse selection and signaling,
giving suitable examples.
Ans.Asymmetric information signifies a situation in which one
party involved in transaction with another, has more or superior
knowledge and information than the other. This is often the case
between buyer and seller, where seller has more knowledge than
buyer. However, the opposite condition can also happen at times.
The situation can potentially be harmful as the party with more
information can take advantage of others lack of knowledge and
thereby exploit the other party.
Asymmetric information is the source of two major problems such
as the following: Moral Hazard- This reflects on the immoral
behavior of a party with asymmetric information subsequent to a
transaction. For example, some people commit arson purposely to
reap benefits from the fire insurance. After being insured, a
driver may drive recklessly as damage in the event of accident will
be borne by the insurance company.
Adverse Selection In this case, the party displays immoral
behavior by taking advantage of the knowledge or asymmetric
information prior to transaction. For example, some people secure
life insurance aware of the languishing health. A bank may fail to
observe the risk-return characteristics of a project. Consequently,
it will extend credit facilities to bad projects while rationing
credit to good projects.
The presence of asymmetric information creates an adverse
selection problem: if consumers cannot tell the quality of a
product and are willing to pay only an average price for it, then
this price is more attractive for sellers who have bad products
than to seller who have good products (hence the term adverse
selection). Consequently, more bad products (i.e lemons) will be
offered than good products. Now, if consumers are rational, they
should anticipate this adverse selection and expect that at any
given price, a randomly chosen product is more likely to be a lemon
than a good product. Of course, these expectations imply a lower
willingness to pay for products and so the proportion of goods
products that is actually offered falls further. Eventually, this
process may lead to a complete breakdown of the market. Signalling
Initiative taken by individuals of informed category in markets
characterized by adverse selection to help identify their true risk
category. For example, In the lemons model if sellers of a good
product could find some activity that was less costly for them than
for seller of a bad product, then it might pay them to undertake
this activity as a signal of good quality product. The buyers, too,
would learn that the signal was associated with good quality
product.
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7.Do you agree with the proposition that a risk-averse person
will optimally buy full insurance if the insurance is actuarially
fair? Give reasons in support of your answer.
Ans.Yes a risk-averse person will optimally buy full insurance
if the insurance is actually fair as the expected utility of such
consumer rises with the purchase of insurance although expected
wealth is unchanged. Since insurance increases the consumers
welfare, she is willing to pay some positive price in excess of the
actuarially fair premium to defray risk. Thus, the agent is trying
to equate the marginal utility of wealth across states. Because,
the utility of average wealth is greater than the average utility
of wealth for a risk averse agent. The agent wants to distribute
wealth evenly across states of the world, rather than concentrate
wealth in one state. She will attempt to maintain wealth at the
same level in all states of the world, assuming that she can
costlessly transfer wealth between states of the world (which is
what actuarially fair insurance allows the agent to do).
Let a risk-averse persons decided to buy insurance by taking the
initial endowment wo and L is the amount of the loss from an
accident.
Pr(1 p):U(.) = U(wo),Pr(p) : U9.) = (wo L)
If insured, the endowment is: Pr(1 p) : U(.) = U(wo pA)
Pr(p):U(.) = U(wo pA + A L)
Expected utility is uninsured is :E(U|I = 0) = (1 p)U(wo) +
pU(wo L)
Expected utility if insured is :E(U|I = 1) = (1 p)U(wo pA) +
pU(wo L + A pA))
The optimal policy that the agent should purchase, differentiate
above eqn with respect to A,
= -p(1 p)U(wo pA) + p(1 p)U(wo L + A pA) = 0
U(wo pA) = U(wo L +A pA)
A = L,
which implies that wealth is wo L in both states of the world
(insurance claim or no claim)
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