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MFE ECONOMICS
创建日期：2024-04-02 14:29:15
所属分类：经济Economics
标签： ECONOMICS
MFE ECONOMICS
MFE ECONOMICS
MID-YEAR ASSESSMENT
Please answer all questions in Part A and exactly one question from Part B.
Part A is worth 60% of the marks (each question’s weight is 15%), Part B is worth 40%.
Please, start the answer to each question on a separate page. Time allowed: 2 hours.
PART A: Please answer each question.
Question A1. In the context of the NK model studied in class, what is the natural real rate
of interest? What might cause it to fall and why?
Answer:
• Flexible prices
– They should refer to it being the real rate of interest that prevails in equilibrium
in the flexible price (θ = 0) special case of the NK model. They may refer to the
flexible price case indirectly by saying that all firms have their prices at the ‘desired’
markup but in this case I would dock a small amount of credit as it’s ambiguous
what they mean.
• Causes of a decline
– The best students will hopefully distinguish shock stories from longer run structural
change
– Shocks: An increase in ‘patience’/‘precaution’ (preference shock discussed in class
- though extra marks if they mention that a similar effect might arise from tighter
bank lending - which isn’t explicitly modeled in the basic NK setup) or anticipation
of weaker growth in the short/medium run (smoothing)
– Long run influences: An ‘increase in β’ (if they get the sign wrong but clearly
understand the intuition then only a small deduction) which may capture, say, a
decline in the trend growth rate of the economy (great if they mention slower tech
growth, some of the secular stagnation debates), longer retirements, Asian glut of
savings, regulatory-induced demand for safe assets. . . (they don’t need to name them
all)
– Would be great to see the student refer to the decline in r∗ is recent decades and
even some of the research on it
• Why?
– Generally all these influences act by increasing desired saving at a given real rate (in
the flex price economy). The reduced saving in equilibrium at the ‘initial’ rate may
not be consistent with consumption and output/labor supply decisions etc. such
that for the households to be optimizing and for the other equilibrium requirements
to be satisfied, a lower r is required to disincentivize savings (i.e. market terms of
trade must reach different equilibrium values to reflect a change in ex ante ‘desire
to save’).
1
Question A2. Forward guidance is always at play in monetary policy, but especially at the
zero lower bound. Discuss.
Answer:
• Dynamic IS Curve
– They should likely agree with this statement - and the ‘always’ bit hopefully should
elicit references to the dynamic IS curve and how it can be iterated forwards to
obtain a connection between the output gap (I don’t really mind if they are a
bit loose about the output gap concept or simply think of it as real activity) and
expected future paths of nominal interest rates (tool of policy) the natural real rate
and inflation
– Also, if they have most of what I have written below but then simply seem to believe
that forward guidance is just as important away from ZLB as at the ZLB then they
shouldn’t be docked marks - it’s ok to disagree with the statement as long as they
understand the issues and (a matter of taste really) weigh them up.
– If they write out equations they should be something like (if they explain in words
equivalently, that’s fine too)
y˜t = Et [y˜t+1]− 1
σ
(it − Et [pit+1]− rnt )
= − 1
σ
∞∑
k=0
Et[rt+k − rnt+k]
= − 1
σ
∞∑
k=0
Et[it+k − (rnt+k + pit+k+1)]
• Conventional monetary policy
– They should note that forward guidance most typically is thought of in terms of
guidance about nominal interest rates - additionally though, they can refer to trying
to influence inflation expectations via some credible method (extra marks if they
note that influencing expectations in a rational expectations context is a subtle
concept - double extra marks if they then allude to specific reasons why rational
expectations might not hold)
– Once they have established that setting up a credible commitment to pursue some
form of interest rate policy in the future can be an important element of conventional
monetary policy - even away from the ZLB
– Great if they allude to Williams/Rudebusch ‘secrets of the temple’ intuition too
(where central banks’ aims and preferences may be somewhat latent to the private
sector - justifying extra communication)
• ZLB/Unconventional monetary policy
– Should note that the DIS shows that if one can lower expectations of future short
rates (great if they refer to ‘lower for longer’ and slow tightening after liftoff from
2
ZLB) then even if the short rates / short maturity yields are stuck at the ZLB, real
activity can be influenced. Would be nice to see references to Williams and Swanson
AER paper, but not necessary.
– May also note (likely these are the students who wrote out the equations) that
something like price level targeting or some other nominal commitment (such as
debated in recent times) could also be interpreted as a form of forward guidance
- and extra marks if they connect this to the fact that the ZLB is particularly
damaging/constraining when inflation and inflation expectations are low, since it
limits how low short real rates can go. . .
– . . . which is another reason why effective policy at the ZLB is especially important
- they should show they understand that in theory - and in recent times in the
real world - the economy may perform very badly if unconventional policy is not
introduced in a low r∗ and low pi environment
– Extra marks if they say something like - since quantitative easing is an alternative -
maybe forward guidance isn’t so vital at ZLB (that may or may not be correct but
that’s an issue for AER papers. . . ) and double extra marks if they note that some
people (e.g. Rudebusch and Bauer) have argued that LSAPs can enhance forward
guidance on rates through the signaling channel
Question A3. Bank liquidity and solvency are completely distinct concepts. Discuss.
Answer:
• Ways in which they are distinct
– I want them to understand the concept of solvency: value of assets > value of
external liabilities. Capital is a loss absorbing buffer etc.
– I want them to understand the concept of liquidity: can sell or borrow against
assets quickly and easily at a reasonable price (not firesale, or at a price below
fundamentals)
– Formally, you can be solvent and have illiquid assets or be illiquid (hard to raise
money quickly) and you can be liquid and insolvent - all your assets are in cash but
you don’t have enough to cover your obligations
– So they should convey the idea that they are somewhat distinct in theory
• Ways in which they are related
– Would be nice to see some Diamond-Dybvig allusions here - especially since it makes
explicit how banks can create liquidity (promising demand deposits or offering lia-
bilities to, say, money market funds, that can be swiftly liquidated) and how beliefs
about solvency can make it optimal to demand liquidity ‘prematurely’ (i.e. to run)
if those beliefs are negative (in DD those beliefs are not irrational but they may
also make the point about irrational beliefs). Here the illiquidity of the long term
asset means that early sale does impair solvency. So this simple model shows so-
phisticated interactions between liquidity and solvency so even if they are formally
distinct, they are often correlated in practice.
3
– Taking a less formal approach, the students may alternatively (or, for the best marks,
additionally) describe some of the events of the recent financial crisis - especially
the run on repo, how that might induce firesales prices that could (from a mark to
market perspective) impair solvency, and how doubts about solvency arising from
opaque derivatives etc. on the balance sheet made it more difficult to raise funds
(liquidity) via haircuts on collateral. Liquidity in the sense of ‘fair price’ asset sales
and liquidity in the sense of ‘fair rate’ ability to borrow are very closely related in
the world of collateralized lending.
– On the last point, there is a lot of irrelevant stuff they could write about the financial
crisis - but the point is for them to focus on the nub of the question (if they talk
about run on repo, the size of the positions being rolled overnight and the losses
incurred by banks through bad performance of loan pools or through mark to market
of opaque products then those are indications they’ve understood the question)
Question A4. Can markets overcome the problems associated with polluting firms, or is there
a need for government intervention?
Answer: A good answer might begin by laying out the First Welfare Theorem, and ex-
plaining why we expect complete, competitive markets to allocate resources (Pareto) efficiently.
Unchecked pollution by firms is a violation of the conditions underlying the First Welfare the-
orem; there is a failure of the complete markets assumption. Hence it is possible that markets
are inefficient. Good answers will set up the very simple quasilinear model of a polluting firm
and a consumer seen in lectures, illustrating that the firm does indeed pollute more than the
efficient amount.
To discuss whether there is a need for government intervention, students should explain
the insight of the Coase Theorem. The best answers will walk through the model to show
that when the parties can write contracts over pollution (and there is a property right defining
outside options), we should expect them to bargain to an efficient outcome.
A discussion of the extent to which the Coase Theorem implies no need for government
intervention might include (i) the need for low transactions costs (including no significant
asymmetries of information, and the ability of all affected parties to enter the bargain); (ii)
why there was not a market for the pollution in place to start with (potential free-rider problems
with many consumers); (ii) the need for at least a minimal role of government in supporting
enforcement of contracts and defining property rights.
PART B: Please answer exactly one question.
Question B1.
A region (‘the North’) is soon to hold a referendum over whether it should leave or remain
in the ‘Seven Kingdoms’. Refer to the outcome that the North remains as ‘state 1’ and the
outcome that it leaves as ‘state 2’. In the Seven Kingdoms, there is only one good (consumption)
and two agents: agent a, who has a wealth of ωa, and agent b , who has a wealth of ωb (measured
in units of the consumption good). Let agents’ aggregate wealth be ω¯. Agent a believes that
the probability of the North leaving is pia2 . Agent b believes the probability of ‘leave’ is pib2.
4
The outcome of the referendum will not affect any individual’s endowment. If agent i’s
consumption in state k as cik, for i = a, b, her final utility from consumption in state k is
ui(c
i
k) = ln c
i
k
Assume no individual is important enough to influence the outcome of the referendum –
i.e. they take their beliefs about the outcome as given.
a.) Are the agents risk averse, risk neutral or risk loving? If pia2 = pib2 =
1
2
, explain
intuitively (no maths) whether there will be any economic gains to introducing a
market for speculating on the outcome of the referendum? [5%]
b.) Write down an expression for the expected utility of agent i as a function of cik, k =
1, 2, and pii2. Show that agent i’s marginal rate of substitution between consumption
in state 1 and state 2 is
MRSi21 = −
1− pii2
pii2
ci2
ci1
.
[10%]
Now suppose that pia2 =
2
3
, pib2 =
1
3
.
c.) Find an expression for the contract curve (i.e., ca2 in terms of ω¯ and ca1). Illustrate,
using an Edgeworth box with state-2 consumption on the vertical axis. [25%]
Before the referendum, there are two markets for state-contingent consumption. In market 1,
agents can buy rights to state-1 consumption. In market 2, agents can buy the right to state-2
consumption. Let p be the price of a unit of state-2 consumption and normalize the price of
(a unit of) state-1 consumption to 1.
d.) Derive a’s demand for consumption in each state as a function of p and ωa. Simi-
larly, find b’s demands. (Hint: are utilities Cobb-Douglas?) [25%]
e.) Solve for Walrasian equilibrium prices and consumption as a function of ωa and ωb.
Is the equilibrium efficient? [20%]
f.) Suppose the ‘true’ probability of leave is 1
2
. What distribution of wealth is required
for the relative market ‘implied probability’ of state 2, p
1−p , to equal
1
2
? [10%]
g.) Briefly discuss the validity of using market ‘implied probabilities’ for predicting
risky events. [5%]
Solution to B1.
(a) ui(c) is concave. Hence, both a and b are risk-averse. Since both are risk-averse and
initially face no risk to their own consumption as a result of the referendum, if both agents also
had the same beliefs about the outcome of the referendum there would be no gains to trade
(i.e. the no trade outcome is already on the contract curve and hence Pareto efficient).
(b) From definition in lecture notes, expected utility: U(ci1, ci2) = pii1ui(ci1) + pii2ui(ci2) =
pii1 ln c
i
1 + (1− pii1) ln ci2. Given this, we can apply the definition of i’s MRS to find:
MRSi21 = −
MU1
MU2
= − pi
i
1/c
i
1
(1− pii1)/ci2
= − pi
i
1
(1− pii1)
ci2
ci1
.
5
(c) Contract curve is all the set of all Pareto efficient allocations. Can be found by equating
MRS across agents:
MRSa21 = MRS
b
21,
which from (b) gives for the case pia1 =
1
3
, pib1 =
2
3
:
1
2
ca2
ca1
= 2
cb2
cb1
.
We also know that in an efficient allocation, aggregate allocations are exhausted in each state:
cbk = ω¯ − cak, for k = 1, 2. Plugging in to the MRS condition and rearranging gives:
ca2 =
4ω¯ca1
ω¯ + 3ca1
.
Since ω¯ ≥ ca1, the contract curve always lies above the 45 degree line in the Edgeworth box
(and touches it only at ca1 = 0, ω¯). It is increasing and concave (check:
dca2
dca1
is positive, but
decreasing). The endowment by contrast is on the 45 degree line. With the two extreme
exceptions, consuming the endowment is no longer efficient (in contrast to part (a.)).
(d) Given prices, individual i’s income is (1 + p)ωi. Since utility is Cobb-Douglas, can use
trick from lectures:
ca1 =
(1 + p)ωa
3p
; ca2 =
2
3
(1 + p)ωa
cb1 =
2
3
(1 + p)ωb
p
; cb2 =
1
3
(1 + p)ωb
(e) Equilibrium: prices clear both markets. By Walras’ law, need only find a p that clears
one of the markets. Clearing market 2:
2
3
(1 + p)ωa +
1
3
(1 + p)ωb = ω¯.
Using ω¯ ≡ ωa + ωb and rearranging for p:
p =
ωa + 2ωb
2ωa + ωb
.
Consumptions can be found by plugging prices back into the demand function.
(f) From (e), they need an equal distribution of wealth for p = 1. In this case, prices reflect
a fair gamble, exactly what we would expect if people knew the ‘true probability’ of leave were
1
2
.
(g) As part (e) shows, when people have different beliefs prices only reflect a weighted
average of the beliefs of the two agents: notice if a owns all the wealth, then p would equal
1
2
and hence the implied probability would be 1
3
; if b held all the wealth the implied market
probability would be 2

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MOEC0021 STA 106 ENGG 1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A PHIL2617 PHYS3116 MIE250 BCPM0008 ECN 620 QBUS6830 ECSE-415 ECON5102 MGMT20005 MAT 653 ECO 480 COMP 5/600 CSSE 5600 ME 571 7CCMMS61 CS 550 COMP2865 MATH3075 STATS 506 QTM 220 ISYS2120 FIT5106 STAT 153 MKTG3112 ECON2102 ELE2018 COMP3031 MSIN0010 SCC461 MATH237 CS246 CSC3065 CSE 101 ICTWEB411 COMP9313 ECOS 2025 FN620 MATH11111 MATH 3018 KE1068 FINA 6112 C++ MISM 6202 MSIN0105 CSC8631 MECO6935 COMP4121 ACCT2011 DPBS1150 EEL 3701C F19PL OPM 661 CSE 310 CS918 BIOL30001 ACCT3563 BANK3600 MET CS622 MATH367 ACCT5907 Continuing COMP5048 COMP61021 CS3334 GSOE9210 CSCI-570 COMP 5322 HW 2 ALY-6020 IEOR 4706 DATA 200 EBUS504 CGE12412 COMP4108 7SSMM800 ECMM171P MATE50002 CS225 RS 6003 BH2274 ELEC3111 MAT6669 ECON-UA 227 PHIL 1012 7SSMM603 TB028A P6 ECS708 CSC 427 CS6476 CSE 250A A1A2 ITS61504 EECS 376 model HW6 UV0010 ECON 6074 MG4F7 CMP-7030Y INFO3008 BFIP013 ECON 5068 MATH6002 CS3483 PSTAT 131 C31FM CSOR W4246 AAEC 5307 DATA ELEC362 COMSM0047 ECN6006 MA20224 BST351 MATH 323 MATH323 AA2021 COMP3811 COMP2013 IB9X60 INVP001 EMATM0051 COMP220 BLAW1002 E20 TCP8001 ECON61001 EART40005 ECONM1022 MATH 365 MATH 367 ELEC6218 COMP 5812M EDUC 5061M ELEC ENG 1101 equation MATH6174 ST334 C4 EC9570 A33648 EBUS603 ECON47815 stata WFMS0001 PEM102 INF6060 ionically ELECTRICAL MATH 375 MMW 12 MKTG860 ECON60401 ALY6010 SOST20131 Introduction COM3524 MME2 GGR305 JNB 538 EECS101 COMM5030 IEOR E4601 2B CSC336 EN2315 LAW 432 CSC263 MATH2001 OLET1143 CSCB63 SIT772 COMM1170 STAT 441 MS930 INFT3050 GLBH0030 Stat 120B MAST10007 MGEC61 Machine GGR 252H1S ECON7030 Financial Marketing MGMT30019 ECON5120 SDSC 8009 CSC165H1S DSCI 551 3081W ACM41000 ECA 5304 MATH 1064 ECSE444 DATA 604 COMP7105 MIE1615 ECON4004 ENV200H1S EC481 MKT 306 EC1B1 MATH08051 ALY6140 CS260C CSE30 MSIN0226 CS4103 CSC3064 AM16 COMP11212 CSE4101 PSTAT 174 Math 380W CNT 5106C STAT 310 FIN2028 CS5014 STAT 425 COMP 4102A ELEC2140 MANF9544 QRM 9 QRM 8 ECON 457 COMPSCI 4091 MATH 523 DNSC-4211 PEAS 6000 MSIN0180 COMP2119 A2A HT 2022 IB93F0 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ACCOUNTING BUSS1040 CHEM 181 MAT136H1 GY 6183 COMP3170 AGRI90089 PHYSICS 1002 ECON10003 IEOR E4004 ACS61012 MATH 40550 MKTG2113 TELE4653 ENSC1004 ECE 232E MK726 MTRX2700 SHEET 3 CSCA08 COMP30027 Math 2XX3 statistic MMAN3200 BISM7213 ECMM109 ECON 2022 FNCE 20005 GR5067 CSCB09 ME 3017 CS 5100 PHYS 2903 COMS 4771 COMP222 COMP 1046 CSC148H1 ISYS2038 FINS2615 OT5206 COMP2048 A6 MECH5770M MA826/20 CMPT 726 STA457 INFS6071 INFS588 integral ECON 216 IRDR 0017 MA323 PA 15213 PSYC2001 ENV222 Statistics ACCT5930 ACCT12 LAND2121 ME 5405 COMM1180 TELE3113 A7 ECE 568 ACCT2019 INFS1200 ENGG1340 CS 1400 ASST3 FINM7409 SWEN30006 INFO2222 FIN20150 SOSS1000 CSSE7231 FINS5513 COMS3200 CECN 702 ECON4060H MN3515 HW2 PSYA02H3 ECON 2112 COMP90051 CS 1652 MA30059 AF1605 MKTG7501 ECO-6003B COM4521 CTM ECON3350 COMP 3804 ELEC9762 BISM 7255 ST22 MATH20014 MNE3122 COMP343 MATH5165 ELE7029 ENGR30002 SEEM3500 ECON7350 RISK5002 FINM7405 COMP90059 MOS 3320B STAT 431 BISM7221 MATH3014 MTH783P EBA 35302 ACS133 BUS2206 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FN1024 MATH0094 MANG 6554 ECOS3003 ELEC6252 C2511C PHY328 EC1060 ECON32202 COMP4002-E1 MATH3063 EFIMM0124 QBUS2310 ECON4411 FUNDAMENTALS ACCT20001 18YX RPM COMP 2711 QBUS6600 BUSS5221 ST3189 FIT1047 MAT344 EGB375 MATH60013 MATH96011 COMP3557 MAST20029 ECM159 EAE1011 ENSCEN 105 SECTION A STA 141C SOSE 2022 PAM006 COMP0048 M40007 ISOM2500 CMPE 142 A06472 MCC150 ACST 8083 GEOG6087 ECON920 FINM7008 ENVENG 4110 COMPSCI 361 ENGRCEE 21 PHYS 1112 ACF2100 ECMM108 COMPS267F MAT00050M MAST30025 CSIT970 MSCI 224 INT202 PUBL0054 MSDM5004 BMAN 21020 BMAN21020 MGMT1002 MATH11150 LAWS7023 ACTL30002 CIVL3340 MATH1002 ECON 8069 COMPSCI 351 IBUS7302 STAT4528 CHEM1101 STAT3925 BUSN 7008 Comp 3120 ECOS2040 SWEN90010 ENGN6528 ECM158 ECON20022 COMP6452 Calculation CITS1401 S1889112 BUS 351 ACTL30008 FIT2091 ECON6002 IBUS6020 PHI 001 ECON30290 MATH7501 ECON10004 MFIN7017 ISYS90043 LAWS7012 ECON30025 COMP30023 COMM1190 ECOM20001 GSBS6009 STAT 337 EMET8002 ECOM90001 ECOM30001 FINC 2012 BUSINESS ENGCV512 ECO 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