青鸾EDU-5033精讲
ECONOMIC ANALYSIS
B y Pau l e t t e
ASSIGNMENT TUTORIAL
CONTENT
 Qu e s t i o n 1
 Qu e s t i o n 2
 Q&A
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QUESTION 1
E C O N O M I C U T I L I T Y F U N C T I O N
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QUESTION 1 (a) EXAMPLE
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Assume that Mr Nobody is a financial investor, whose wealth is given by £54. Mr
Somebody has invested 50% of their wealth in an asset, call it Beta, whose return is
usually £20 per unit of wealth invested. However, there is a positive probability, call it 1,
that Beta’s return will collapse to £10; and the probability of Beta’s return to fall to £10 is
2. The table below illustrates Beta’s returns in the three relevant states of the world along
with the corresponding probability with which each states occurs (for simplicity, three
states of the world are assumed throughout).
Rho1=0.25 Rho2=0.25 1-Rho 1-Rho 2
Beta’s returns (per £
invested)
10 0 20
Suppose that Mr Nobody is an expected utility maximiser with expected utility function
given by () = ∛� where denotes the market value of Mr Nobody’s assets.
QUESTION 1 (a) EXAMPLE
5
 £54
 50%
 () = ∛�
Rho1=0.25 Rho2=0.25 1-Rho 1-
Rho2
Beta’s returns
(per £ invested)
10 0 20
Calculate the expected value (EV_Beta) of Beta’s
returns, i.e., Beta’s average return.
Then, calculate the expected utility of the amount
of money for sure that is given by the expected
value you just calculated, i.e., calculate the
expected utility of EV_Beta with certainty.
(a) i.
EV_Beta = 0.25*10 + 0.25*0 + 0.5*20 = 12.5
Utility of EV_Beta =
3 0.25 * 10 + 0.25 * 0 + 0.5 * 20
= 2.321
REVIEW
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QUESTION 1 (a) EXAMPLE
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 £54
 50%
 () = ∛�
1=0.25 2=0.25 1- 1- 2
Beta’s returns
(per £
invested)
10 0 20
(a) ii.
Calculate the expected utility of the Beta’s
returns.
By comparing this answer to that of a.i), what
can you conclude about Mr Nobody’s risk
attitudes?
E(U(V_BETA)) = 0.25*U(w1)+0.25*U(w2) + 0.5*U(w3)
= 0.25*3 10+0.25*3 0+0.5*3 20
= 1.8958
U(EV_BETA) = 2.321 > E(U(V_BETA)) = 1.89
which means the expected utility is smaller than
the utility of the expected value of uncertain payment.
Hence, according to the relationship of the
chracteristics of a risk-averse utility function, it can be
concluded that the investor is risk-averse. That is, Mr
Nobody tends to avoid risks in investment.
REVIEW
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Risk-averse Risk-neutral Risk-seeking(loving)
CE – Certainty equivalent; 
E(U(W)) – Expected value of the utility (expected utility) of the uncertain payment W; 
E(W) – Expected value of the uncertain payment; 
U(CE) – Utility of the certainty equivalent; 
U(E(W)) – Utility of the expected value of the uncertain payment; 
U(W0) – Utility of the minimal payment; 
U(W1) – Utility of the maximal payment; 
W0 – Minimal payment; 
W1 – Maximal payment; 
RP – Risk premium
QUESTION 1 (a) EXAMPLE
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 £54
 50%
 () = ∛�
1=0.25 2=0.25 1- 1- 2
Beta’s returns
(per £
invested)
10 0 20
(a) iii.
Provide an example of risk preferences [in the
form of an expected utility function] that would
induce Mr Nobody to be indifferent between
holding Beta Asset and having an amount of
money for sure equal to £EV_Beta.
REVIEW
10
Risk-neutral (Risk-indifferent)
CE – Certainty equivalent; 
E(U(W)) – Expected value of the utility (expected utility) of the uncertain 
payment W; 
E(W) – Expected value of the uncertain payment; 
U(CE) – Utility of the certainty equivalent; 
U(E(W)) – Utility of the expected value of the uncertain payment; 
U(W0) – Utility of the minimal payment; 
U(W1) – Utility of the maximal payment; 
W0 – Minimal payment; 
W1 – Maximal payment; 
RP – Risk premium
QUESTION 1 (b) EXAMPLE
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QUESTION 1 (b.i, b.ii)
HINT ON THE ASSIGNMENT
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QUESTION 1 (b.iii) EXAMPLE
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(1) Calculate �� of x=0 and x=20 according to � = �(�)
(2) Calculate the expected values of Alpha and Beta:
EVA = p(�A1)+(1-p)(�A2),
EVB = p(�B1)+(1-p)(�B2).
(3) Calculate the standard deviations of Alpha and Beta:
�� = (푉� − �(푉�))2 * 푃
�� = (푉� − �(푉�))2 * 푃
(4) Calculate the covariance of A and B:
�ov(A, B) = (푉� − �푉� )(푉� − �푉� ) * 푃
(5) Calculate the correlation coefficient of A and B:
��, � = �ov(A, B)/σAσB
S U M M A R Y
 Make sure to show every step of your calculation.
 Add connotations to help better explaining your reasoning.
 Double check your results with calculator or Excel.
QUESTION 2
M A R K E T S T R U C T U R E
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QUESTION 2
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Critically discuss how different market structures affect the relationship between marginal
revenues and prices when the market is in equilibrium. Specifically, your discussion shall
include:
1) An outline of the firm’s profit maximisation problem in general (i.e., by abstaining from
assuming a specific market structure).
2) An explanation of the first-order conditions for a maximum, inclusive of a definition of
marginal revenue.
3) A discussion of how marginal revenues relate to the market price under at least two
market structures, one of which must be perfect competition and the other a market
structure of your choice that is different from perfect competition, such as monopoly or
Cournot oligopoly.
The word limit for answering this question 250 words (no exceptions).
1. MARKET STRUCTURE
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1. MARKET STRUCTURE
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(1) Perfect Competition
Perfect competition occurs when there is a large number of small companies competing
against each other. They sell similar products (homogeneous), lack price influence over the
commodities, and are free to enter or exit the market.
Consumers in this type of market have full knowledge of the goods being sold. They are aware
of the prices charged on them and the product branding. In the real world, the pure form of
this type of market structure rarely exists. However, it is useful when comparing companies
with similar features. This market is unrealistic as it faces some significant criticisms described
below.
•No incentive for innovation: In the real world, if competition exists and a company holds a
dominant market share, there is a tendency to increase innovation to beat the competitors and
maintain the status quo. However, in a perfectly competitive market, the profit margin is fixed,
and sellers cannot increase prices, or they will lose their customers.
•There are very few barriers to entry: Any company can enter the market and start selling the
product. Therefore, incumbents must stay proactive to maintain market share.
1. MARKET STRUCTURE
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(2) Monopolistic Competition
Monopolistic competition refers to an imperfectly competitive market with the traits of both
the monopoly and competitive market. Sellers compete among themselves and can
differentiate their goods in terms of quality and branding to look different. In this type of
competition, sellers consider the price charged by their competitors and ignore the impact of
their own prices on their competition.
When comparing monopolistic competition in the short term and long term, there are two
distinct aspects that are observed. In the short term, the monopolistic company maximizes its
profits and enjoys all the benefits as a monopoly.
The company initially produces many products as the demand is high. Therefore, its Marginal
Revenue (MR) corresponds to its Marginal Cost (MC). However, MR diminishes over time as
new companies enter the market with differentiated products affecting demand, leading to less
profit.
1. MARKET STRUCTURE
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(3) Oligopoly
An oligopoly market consists of a small number of large companies that sell differentiated or
identical products. Since there are few players in the market, their competitive strategies are
dependent on each other.
For example, if one of the actors decides to reduce the price of its products, the action will
trigger other actors to lower their prices, too. On the other hand, a price increase may
influence others not to take any action in the anticipation consumers will opt for their products.
Therefore, strategic planning by these types of players is a must.
In a situation where companies mutually compete, they may create agreements to share the
market by restricting production, leading to supernormal profits. This holds if either party
honors the Nash equilibrium state and neither is tempted to engage in the prisoner’s dilemma.
In such an agreement, they work like monopolies. The collusion is referred to as cartels.
1. MARKET STRUCTURE
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(4) Monopoly
In a monopoly market, a single company represents the whole industry. It has no competitor,
and it is the sole seller of products in the entire market. This type of market is characterized by
factors such as the sole claim to ownership of resources, patent and copyright, licenses issued
by the government, or high initial setup costs.
All the above characteristics associated with monopoly restrict other companies from entering
the market. The company, therefore, remains a single seller because it has the power to
control the market and set prices for its goods.
WHEN INTRODUCING STRUCTURES...
(1) How many competitors are
there?
(2) Are they producing
differentiated or identical
products?
(3) Does any own the right to
determine prices?
2. PROFIT MAXIMISATION
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We assume that the goal of firms is to maximize profits. We could compare total
revenue and total cost at every level of output in order to find the profit maximizing
level of output. An alternative is to compare marginal revenue and marginal cost.
Marginal cost
Additional cost of producing one more unit of output
Marginal revenue
Additional revenue obtained from selling one more unit of output
As long as the marginal revenue from selling a unit of output is greater than the
marginal cost of producing that unit of output the firm will make a profit on that
unit of output.
If MR > MC --> produce more output to increase profits
If MR < MC --> costs more to produce another unit of output than the firm can
sell it for --> produce less output to increase profits
A profit maximizing firm will continue to expand production as long as marginal
revenue is greater than marginal cost. In calculus terms, the requirement that the
optimal output have higher profit than adjacent output levels is that:
where R is the total revenue, C is the total cost, and Q the quantity.
2. PROFIT MAXIMISATION -
E.G., MONOPOLY
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For a monopoly like the graph shown on the
left, marginal revenue decreases as it sells
additional units of output. The marginal cost
curve is upward-sloping. The profit-
maximizing choice for the monopoly will be to
produce at the quantity where marginal
revenue is equal to marginal cost: that is, MR
= MC. If the monopoly produces a lower
quantity, then MR > MC at those levels of
output, and the firm can make higher profits
by expanding output. If the firm produces at a
greater quantity, then MC > MR, and the firm
can make higher profits by reducing its
quantity of output.
3. FIRST ORDER CONDITION AND MARGINAL
REVENUE
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PERFECT COMPETITION ANSWER
EXAMPLE
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Market Structure
introduction
MR and P
relationship
Profit maximisation
solution
ANSWER SUGGESTIONS
Introduction
The four market structures are ..... In all market structures, the general profit maximisation problem refers to...
It is obvious that maximising profit is tighly correlated with marginal revenue, market price, and marginal cost.
Marginal revenue refers to...
Structure details
(1) Perfect Competition: definition, characteristics, mr?p, profit maximisation solution
(2) Your preferred structure: same as (1)
(3) structure 3: definition, mr?p
(4) structure 4: definition, mr?p
Conclusion
Above all, ....
* If you have problems with introducing the sturctures explicitly or there is still a long way before 250 words,
feel free to use examples.
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SUMMARY
(⑴) Introduce all types of market structures (what).
(⑵) Introduce marginal revenue using the first-
order condition theory.
(⑶)Introduce the firm’s profit maximization
problem(better with solution) in each structure.
(⑷)Select two scenarios and indicate the
relationship between MR and P as well as the
rationale (short run vs. long run); For the other
two structures, only reveal MR?P without
rationale.
THANK YOU.