**Unformatted text preview: **Econ 450 Autumn 2015 HW I . Assuming no government intervention or provision, brieﬂy discuss
why public education may be underprovided if financed exclusively
by private contributions. 5 points. If education has positive externalities, or aspect of a public good, the
social marginal benefit Will lie above the private marginal benefit, and
the quantity provided in a market will be less than the optimal quan—
tity. . Define and explain the Cease Theorem, and relate it to the First Welfare
Theorem. 5 points. The Coase theorem states that in the absence of transaction costs, and
With fully speciﬁed property rights, private bargaining will lead to ef-
ficient outcomes even in the presence of externalities; essentially pri-
vate bargaining will internalize the externality. This is equivalent to
the efﬁciency requirement in the First Welfare Theorem that markets
exist for every good. . Define and explain what a Pareto improvement is, using an Edgeworth
Box. 5 points. A Pareto improvement is an alternative to the status quo that leaves
at least one person better off and no one worse off; in a two-good
exchange economy, as depicted by an edgeworth box (see attached),
the set of pareto improvements is the shaded lens area. . Consider the following market for a private good, where Anne and
Beverly's inverse demand curves are given by PA = 500 e Q
PB m 500 — 262
The marginal cost of this good is
M C = 2Q (a) Calculate the market demand curve 2 points.
For a private good we sum quantities to get the market demand
curve. 50 we sum
500 — p Qa-l-Qs =500np+ 2
QM m500-10+250——.510
QM 2750—151; (b) (C) (d) (e) (0 Solving for p, we get the inverse market demand curve: P,” 2 750— mm?» = 500 m go. Depict this market graphically. 3 points.
See attached. Calculate the market price and quantity that will be produced,
assuming this market is perfectly competitive. 3 points. Setting the inverse market demand equal to inverse supply, we
Solve for the market quantity: 500 w = 2Q
Q“ : 187.5 and the market price is 375. Argue that this outcome is Pareto Efficient. 2 points. At the price of 375, the quantities consumed by A and B are
375 = 500“ QA => (2,4 = 125 and 375 = 500m 2623 => Q3 2
62.5. At these quantities their marginal utilities are M UA
500 — QA 2 375, M U B = 500 — ZQB = 375, so marginal util—
ities are equal, so no further pareto improvements via trading
are possible. Furthermore, when the market quantity is 187.5,
the marginal cost of another unit is MC = 2 * 187.5 x 375, so
marginal utilities are equal to marginai cost, so no further pareto
improvements via production are possible. Therefore the out-
come is efficient. Suppose instead that this good is a pure public good. Costs and
utilities are the same. What wouid the outcome of private pro-
vision of this good be in that case? 5 points. In this case, B would free-ride on A, since A demands more of
the good. A would purchase 500 — q = 2r] => Q* : 166% units. What would the efficient level of production be in that case? 5
points. In this case the social marginal benefit is the sum of the marginal
utilities, or Sit/I B = 1000 — 3Q. This is equal to marginal cost
when 1000 —- 3Q = 262 => Q8 = 200. 5. Arturo, Bashir, and Carl share a house in Fremont, and each has his own bedroom. They heat the house with a shared wood—burning
stove. Arturo values one hour of heating at 6.5 dollars, Bashir at 8 dollars, and Carl at 10 dollars (with one hour of heating being as
vaiuable as the next). Suppose heat from the stove is a pure public good that can be produced at a constant marginal cost of 20 dollars
per hour of heating (a) What is the efficient quantity of hours (H) of heating per day (of
course, there are 24 hours in a day)? 5 points.
The sum of the marginal benefits is 6.5 + 8 + 10 = 24.5 > 20 =
M (3’. Since benefits exceed costs for all hours of the day, the
efﬁcient number of hours to provide is 24. Now assume that each of the housemates must choose between three
options. Option 1: Continue to fuel the wood-burning stove. All
of the housemates who choose Option 1 will split the stove heating
bill equally. Option 2: Each housemate may bring in his own electric
heater (costiessly) from his parent’s house. An electric heater pro-
vides heat only for the bedroom of the housemate who brought it. If
he turns it on, he will have to privately pay 7 dollars per hour to op-
erate it. Under this option, they make no contribution to the common
stove. Option 3: Neither; they can choose to neither fuel the stove,
nor use their owner heater. (b) Which of the three options will each of the housemates choose in equilibrium? 10 points. Suppose all three choose to participate in the cost sharing scheme.
This cannot be an equilibrium. To see why, note that the cost of
of Arturo Wili be > 6.5, so that costs exceed his benefits. So
he will opt out. If only two participate , cost shares Wili rise, so
Arturo cannot be one of the two. So it can only be Bashir and
Cari. Their shares will be § 2 10 > 8, so Bashir will opt out.
If only one participates, he bears the entire cost, and 20 > 10,
so Carl will not participate on his own. So the furnace will not
be turned on in equilibrium. The cost of private heating is 7,
Carl and Bashir wiil opt for private heating, since their beneﬁts
exceed this cost, while Arturo will buy nothing and receive no
benefits, and pay no costs. (c) Is this equilibrium allocation Pareto efficient? Explain why or
why not. 10 points.
This is not pareto efficient. You can see this in a number of
ways; first, Arturo receives no heat, an in an efficient outcome he would. Therefore it is no efficient. Another way to see it is
that total welfare under this outcome is 10 + 8 —— 7 — 7 = 4, While
total welfare under an outcome where heat is provided by the
heater is is 10 + 8 + 6.5 — 20 2 4.5. Therefore the private out-
come does not maximize welfare. Yet another way is to specify
a pareto improvement; Here is one: let the furnace be turned
on. Arturo is to be charged 6 doilars, While Bashir and Carl are
each charged 7. Bashir and Carl and equally well off under this
alternative, while Aturo is strictly better off. Thus it is a pareto
improvement, so the previous arrangement was not efficient. 6. For each of the examples below, please answer the following: (a) (b) (C) Does an externality exist? If so, classify the externality as posi-
tive/ negative (or both). 2 points. If an externality exists, determine whether the Coase theorem
applies (i.e. is it possible to assign property rights and solve the
problem?) 2 points. If an extenality exists and the Coase theorem does not apply, ar-
gue which of the government’s tools are best suited to address
the issue: quantity regulation, taxes/ subsidies, tradeable per-
mits, or something else. 1 point. Consider the foilowing examples: (a) (b) British Petroleum drills for oil in the gulf coast If there is environmental damage BP does not pay for, there is
an externality. IF the damage is so widespread or outside the
jurisdiction of any one government, private bargaining will not
work, due to high transaction costs and unclear property rights.
A good way to address this would be a tax on oil equal to the
marginal damage. Carbon emissions from vehicles The externality is the pollution and climate effects from car emis-
sions. These damages are committed by drivers, of whom there
are many, and experienced globally. The Coase theorem will
probably not apply in this case. An effective response would
probably be a Carbon tax, rather than requiring drivers to pur—
chased permits, or mandated emissions goals. (c) Your upstairs neighbors throwing an awesome, but loud party
They are bothering you, and your unhappiness is the external-
ity. The coase theorem probably applies here; noise regulations
give you the right to call police, so you have the property right
to the "noise environment" and bargaining with your neighbor
is easy. Social norms Culture can also help address this prob
lem. Government intervention beyond property rights is proba~
bly not necessary. ((21) Buying a car with added safety features that prevent the driver’s
and passengers death’ 5 in the event of an accident.
The externality is the benefit to passengers who did not decide
on which safety features you purchased with your car. The ben~
eficiaries are in the future and difficult to barging with; most
people aren’t about to prey their friends to buy safer cars. An
apropriate response would be to subsidize safer cars. (e) Bringing crying babies on a plane The externality is the unhap~
piness experienced by others on the plan due to your decision
to bring the baby. The Coase theorem pay not apply here; it is
not clear who has the property right here — your right to a quiet
plane or their right to bring their baby? Bargaining may also not
be possible, if it is not possible to make arrangements ahead of
time to purchase quiet ﬂights. The amount of inefficiency may
be small, however. It is not clear that any regulatory scheme will
be worth it. 7. Suppose that the agricultural production of hogs (pigs) create wa—
ter pollution that results in serious health conditions for both hu~
mans / animals that rely on those water scurces. Specifically, assume
that the market supply function is given by H3261) where H3 is the quantity of hogs supplied to the market and P is
the market price for hogs. Similarly, assume that the market demand
function is given by H D 2: 300 — 3P Further, assume that hog production imposes total external medical
costs (M) on nearby communities, quantied as M=2H where M is measured in dollars and H is the number of hogs pro—
duced. (a) Identify the relevant externality (consumer or producer, positive
or negative). 5 points.
This is a negative production externality. (b) Sketch the market for hog production and identify the corre-
sponding DWL in the market resulting from the externality iden- tified in part (a). (Do not calculate.) 5 points.
See Attached. (c) Suppose that property rights to clean drinking water are assigned
to the neighboring communities. Further assume that hog pro—
duction is common on numerous small farms in the area. i. Briey discuss the potential Coasian outcome. 2 points. ii. Determine whether or not the private market solution is likely
to succeed in this context. 3 points.
The Coasian outcome is for the communities to agree on a
payment from the hog farmers to compensate them for their
harm. This may be difficult; if there are many farms it may
be difficult to assign the harm to a particular farmer and
compel their agreement to a bargain. (d) If imposing a price controi, what corrective Pigouvian tax T in
the hog market will lead to the socially optimal level of hog pro—
duction? 5 points. In this case the marginal damage is constant, so a tax T : 2 could
achieve the optimal level of hog production. ...

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