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Unformatted text preview: THE UNIVERSITY OF HONG KONG
School of Economics & Finance 20072008 2“d Semester Examination Economics: ECONZlOl
Microeconomic Theory
Dr M Lo May 8, 2008 9:3011:30a.rn. Candidates may use any selfcontained, silent, batteryoperated and pocket—sized
calculator. The calculator should have numeraldisplay facilities only and should be used only for the purposes of calculation. It is the candidate’s responsibility to ensure that his
calculator operates satisfactorily. Candidates must record the name and type of their calculators on the front page of their
examination scripts. Final Exam of Microeconomic Theory (ECON2101)
May 8, 2008 The Instructor: Peiyu Melody LO Instructions: This is a closed book and closed notes exam. You have 2 hours to work on it. There are 100
points in total. Q5 Q9 are true/false explain type of questions. No credits will be given to answers without
the process. Partial credits will be given if you write down the correct equation to solve for the answer. You
can use the following mathematical formula to work out some questions in the exam. Mathematical formula 0 Let f (z) = aﬁ Where a is a constant. Then f’ z: 23;. 0 Let f (9:) = ax'aL where a is a constant. Then f’ (11:) = 1. (25 pts) Consider a perfectly competitive industry with a large number of ﬁrms and no entry barrier.
1 1 Every ﬁrm in this industry has the production function f (331, 2:2) = $15 $25 . Price of input 1 is $1/ unit
and price of input 2 is $4/unit. Level of input 2 can only be changed yearly. 15 . sip13.2173, 10.35131
r" #3 A.
’1. 10 —AG when 32:1
warno when 12:3
 MI: when 3.12:1
“NH“Mt: when x2=3 ﬂ AC intersects MC
4‘ 2 AC curves
513] 0.5 1 1.5 2 2.5 Y Figure 1: Cost Functions (3.) (2 pts) Write down a mathematical expression of a typical ﬁrm’s short run total cost as a function
of output level 3/ and level of the ﬁxed input .12. (b) (2 pts) Alby Inc. is a typical ﬁrm in this industry and currently operates at x2 : 1. Write down
the short run individual supply function of Alby Inc.. What is its short run shut down point? (c) (1 pt) Suppose a typical firm in this industry can only choose between a low level of input 2,
$2 = l, and a high level of input 2, x2 = 3. Figure 1 shows a typical ﬁrm’s short run average
total cost curves and short run marginal cost curves at both levels of input 2. Suppose market
price is currently $12 per unit of output. Following Q1.b, What is Alby Inc’s proﬁt maximizing
output level in the short run? (d) (2 pts) Following Q1.c, suppose Alby now has a chance to reevaluate its level of input 2. Assume
that market price will remain $12 for the coming year, shall Alby expand its level of input 2
to 3 units or exit the market? If Alby expands, what’s the proﬁtmaximizing output level?
(16\/3 m 27.71) What is its maximal proﬁts at p = 12? (e) (2 pts) What is the minimal output price for Alby Inc. to optimally choose a high level of input
2? Write down the equation without solving it. (f) (2 pts) Will the market price for the output remain $12 in the long run? Why or why not? (g) (3 pts) What is the minimal output price for Alby Inc. to stay in the market? (Hint: use the
cost ﬁgure provided.) (h) (3 pts) Assume that the solution to Q1.e is 10.3513, and Alby’s short run marginal cost when the
ﬁxed input :52 = 3 at y = 3.2173 is equal to 10.3513. Draw Alby’s long run average cost curve.
Mark the coordinates of the kinky points. Draw on the same graph Alby’s long run individual
supply curve. Mark the price level of all kinky or discontinuous points. (Hint: No calculations
are necessary. All the information you need has either been provided in the previous subquestions
or in ﬁgure 1.) (i) (2 pts) Draw the long run industry supply curve on the same graph as in Q1.h, assuming that all
ﬁrms have access to the same technology and input prices remain constant as ﬁrms enter and exit
this industry. Clearly label it and mark the interception with the vertical axis and the slope. (j) (2 pts) Suppose the industry has adjusted to its long run equilibrium. Now the government
imposes a $1 quantity tax per unit. In the long run (after entry and exit stops), how much tax
will the consumers pay per unit? (k) (2 pts) Answer the question assuming there is no tax. Suppose in the long run equilibrium, there
are 1000 ﬁrms in the industry. The government decides to regulate the industry by requiring a
license to legally operate and issues a license to every existing ﬁrm including ﬁrm Alby. Suppose
demand has increased and pushed the equilibrium price up to $12 /unit. If the government does
not issue new licenses in the long run, what will ﬁrm Alby’s long run proﬁt be? What will be the
price of a license? (Hint: You have answered questions about Alby Inc.’s optimal choice when
p = 12.) (1) (2 pts) Suppose Alby Inc. can choose any nonnegative level of input 2. Write down its long run
total cost as a function of output level y. 2. (20 pts) Ali Mobile is the only mobile service provider in a small island country. There is a constant
marginal cost of 40 cents per minute provided and no ﬁxed cost. Market demand for mobile services
is given by Q = 320 — 0.5P, where P is price per minute in cent. All mobile services are considered
the same by consumers. (a) (3 pts) If Ali Mobile aims to maximize proﬁts, what per minue price should it charge? What will
be the equilibrium number of minutes? What’s Ali Mobile’s proﬁts? (b) (2 pts) What is the Pareto efﬁcient output level in the mobile service market? (c) (4 pts) The EasyGroup is considering starting a company called Easy Mobile to enter the mobile
service market. To enter the market, it has to ﬁrst lay a network of towers to receive and transmit
signals. This will cost $10,000. Other than this ﬁxed cost, it has the same cost structure as Ali
Mobile. Suppose the two ﬁrms choose quantity simultaneously once Easy Mobile enters. What’s
Easy Mobile’s postentry proﬁts? Will Easy Mobile enter? Why or why not? (d) (4 pts) Suppose production takes no time and Ali Mobile and Easy Mobile engage in Bertrand
competition if Easy Mobile enters. What will be Easy Mobile’s postentry proﬁts? Will Easy
Mobile enter? Why or why not? (e) (5 pts) Suppose before Easy Mobile builds the towers and incurrs the ﬁxed cost, Ali Mobile can
choose whether they will engage in Bertrand competition or Gourmet competition. If Easy Mobile
does not enter, it earns 0 proﬁts and Ali Mobile remains a monopolist. Draw the game tree,
suppressing the competition stage and just write down their payoffs after Easy Mobile makes its
entry decision. Find a subgame perfect Nash equilibrium in this game. (f) (2 pts) Suppose after Easy Mobile builds the towers and incurrs the ﬁxed cost, Ali Mobile decides
whether they will engage in Bertrand competition or Cournot competition. The CEO of Ali
Mobile calls the CEO of Easy Group and says, "You should not enter the mobile service market
because if you do, I will start a price war and we will engage in Bertrand competition. You will
earn a loss as a result of entry. " Is this threat credible if the two companies are both rational and
they both know that? Why or why not? 3. (14 pts) Aaron and Ben are two brothers that share a room. Each day they spend 4 hours of their
awake time in their shared room. Aaron loves punk rock and cannot enjoy music through earphones.
Ben hates Aaron’s music and needs a quiet place in order to write his poems. Their parents give them
each $10 allowance per day. Aaron’s preference over money and hours of playing punk rock can be
represented by U A (771.4, 7') = m A + 2%, where m A is the dollar amount of money Aaron has per day
and 'r is the number of hours per day Aaron spends in the room playing punk rock. Ben’s preference
can be represented by U 3 (mg, q) = mg + 2\/§, where m B is the dollar amount of money Ben has per
day and q is the number of hours per day Ben gets to enjoy his quiet time in the room. If Aaron plays
rock music for 1" hours, then Ben enjoys q = 4 — 7" hours of quiet time. (a) (2 pts)lf playing punk rock is banned in their home, what will be the resulting allocation? Draw
this allocation in an Edgeworth box where the horizontal axis represents money and the vertical
axis represents time Aaron spends playing punk rock. Clearly lable the axes, the width and the
height of the box. Draw and label Aaron and Ben’s indifference curves that pass through this
allocation. (b) (2 pts)(m,q, m3, 1’) denotes an allocation in which Aaron has m A dollars, Ben has m 3 dollars and
Aaron plays rock music for r hours in their room. What are the necessary conditions for such an
allocation to be Pareto efﬁcient? (c) (2 pts) Find the Contract Curve. Draw the Contract Curve in the Edgeworth Box of Q3.a.
Clearly label it and mark the intercept with the vertical axis and the slope. ((1) Suppose their parents decide to give the right to quiet time to Ben and Ben can do whatever he
wants with his right, including selling it to Aaron for Aaron to play punk rock. Suppose Aaron
and Ben are both price takers in the money market and the noise market. Normalize price of
money to $1. Let pr denote price per hour of punk rock. Assume that both Aaron and Ben
choose their most preferred affordable bundle. 1. (1 pt) Given that price per hour of punk rock is p,, how many hours is Aaron willing to buy? 2. (1 pt) Given that price per hour of punk rock is pr, how many hours is Ben willing to sell to
Aaron? 3. (1 pt) Write down the market clearing condition. 4. (1 pt) Find the competitive equilibrium price p; and the competitive equilibrium allocation
(m2, m3, r‘). 5. (2 pt) Draw in the Edgeworth Box of Q3.a the equilibrium consumption bundle, Aaron and
Ben’s indifference curves that pass through it, and their budget lines. (e) (2 pts) Suppose their parents give the right to play music to Aaron and Aaron can do whatever
he wants with his right, including selling it to Ben. How will that change the equilibrium amount
of time Aaron plays punk rock? Does Ben prefer to be assigned the right to quiet time or does
he prefer that Aaron is assigned the right, or is he indifferent? 4. (13 pts) An airport is located next to a large tract of land owned by a housing developer. The developer
would like to build houses on this land, but noise from the airports reduces the value of the land. The
more planes that ﬂy, the lower is the amount of proﬁts that the developer makes. Let X be the number
of planes that ﬂy per day to or from the airport and let Y be the number of houses that the developer
builds. The airport’s total proﬁts are 26X — X 2 and the developer’s total profits are 22Y — Y2 — X Y (a) (3 pts) Suppose one single proﬁtmaximizing company owns both airports and the housing devel
opement. What is the optimal number of landings in the airport and the number of houses? (b) (3 pts) Suppose the airport and the housing development are owned by different proﬁtmaximizing
ﬁrms. If noise cannot be contracted upon, that is, if the right to quietness is not welldeﬁned
by law, find out the number of landings in each airport and the number of houses built by the
developer. Are these levels Pareto efﬁcient? Why or why not? (c) (3 pts) If the government decides to levy a tax t per landing on the airport, how large should it
be for the equilibrium level of landings to be efﬁcient? (d) (4 pts) If the government does not know the airport’s cost function, what measure can the gov
ernment take so that the resulting alocation is Pareto efﬁcient? State the assumptions you need
and the theorem you use. 5. (5 pts) Can a price ceiling be pareto improving? If yes, give an example when it is Pareto improving.
State the assumptions about the market. 6. Currently Hong Kong and Kowlong Ferry Ltd. is the only one that operates ferry services between
Hong Kong Island and Lemma Island. (a) (4 pts) For the slow ferry services, HKK charges $11.80 one way on weekdays and $15.60 on
weekends. Many residents of Lamma Island work in Hong Kong and thus need to use the ferry
on weekdays, while toursists go mostly on weekends. Suppose HKK is a proﬁtmaximizer, what
does its pricing strategy tell you about price elasticity of demand of ferry service for commuters
and tourists? (b) (4 pts) What assumptions about the ferry service market can give efficiency ground for Hong
Kong government to regulate ferry fares between Hong Kong and Lamrna? 7. (5 pts) " Perfect price discrimination by a monopolist should be banned because it decreases welfare."
Is the above statement true or false? If true, give an example such that it is the case. If false,
graphically explain how perfect price discriminiation does not decrease welfare. 8. (5 pts) According to the Kyoto Treaty, EU members have to reduce their green house gas emissions
by 2012 by about a collective average of 15% below their expected green house gas emission in 2008.
To achieve this collective average reduction, different member states have different obligation: more
developed member states have a higher required reduction rate than less developed ones. Under What
assumptions is this arrangement Pareto improving from requiring all EU member states to achieve the
same reduction rate? 9. (5 pts) "To improve the efﬁciency of health care allocation, we simply need a perfectly competitive
health insurance market because competitive market equilibrium is Pareto efﬁcient according to the
First Fundamental Theorem of Welfare Economics." Is the above statement true or false? Why?
Instructions. Replace this text by the instructions to the students. The fixed vertical spaces for each
question were entered using Insert Spacing, Vertical, and then choosing the Custom option. To adjust
the amount of space set aside for each question, place the insertion point to the right of the vertical space (the large green down arrow that’s visible at the end of each question when View Invisibles is
turned on). End of paper ...
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