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Unformatted text preview: EEP 101/Econ 125
Spring 2010
GSIs: Biswo, Diana Problem Set 1
Due on Tuesday, February 161th at lecture.
Late assignments will not be accepted. Numerical Questions 1. (40 Points) Suppose the industry for rambutans (a fruit) has a demand curve given
by Q = 60 — %P, where P is the price in dollars, and Q is the quantity. The marginal
private cost (MP0) of production is MP0 2 20 + Q, and the marginal external cost
of production (MEC) is given by MEC = 2Q. (a) Determine the socially optimal level of output (Q*). Calculate the total external
cost (TEC*), consumer surplus (08*), producer surplus (PS*), and total social
welfare (SW*) at this level of output. Figure not drawn to scale The socially optimal quantity occurs where MSC=MSB.
MSC=MEC+MPC=20+3Q
MSB=MEB+MPB=0+MPB Rearranging demand, we have MPB=1202Q 120—2Q220—l—3Q Q*=20
P*=80 TEC* = 09* MECdQ = ff" 2QdQ = Q2 30 = 400 *=f0Q( 62* (—MPB 13*) Mg) 2 f0Q*(120 — 2Q — 80)dQ
— CSfoQ( (40 262) dc): (4062 — Q2)3° = 40(20) — 202 = 800 — 400 = 400 *=ff( Q*( —)MPC )dQ = fOQ‘(80 _ (20 + Q))dQ
_ PS‘MO (—60 P)Q )dQ: (60Q — Q72”? 2 1200 — 200 = 1000 SW" 203* + PS* — TEC* = 400 + 1000 — 400 = 1000 Calculate the quantity produced if the market is in perfect competition and only private
costs are accounted for (the externality associated with production is NOT taken into
account). What is the quantity produced (QC)? Calculate the total external cost (TECC),
consumer surplus (CSC), producer surplus (PSC), total social welfare (SW6) and
dead—weight loss (DWLC) at this level of output. Figure not drawn to scale The optimal quantity under perfect competition occurs where MPCrMSB.
120—2Q= 20+Q Qpc = M— — 33. 3 P116 2 ﬁ— _ 53 3 100 TECpc ==f0rMECdQ f032QdQ—Q20_030:%:1111,1 CSpc :f0(1’c (—MPB Ppc) dQ: f0(1"° 1(20—2Q—1—g°)dQ c 2 _
_0Qp (3_60_2Q_1_60)d=Q (2_00Q_ Q2)0—003 _m.m_ (100) = w = w = 1111.1 Pspc :f0 PC( (Ppc — MPC)dQ= f0(1c(1—g0 (—20 + Q))dQ 00
=(f0 pc (@___ ))dQ_ (1—30Q_%3)0—3 szgz5555 5ch : cspc + Pspc — TECPC : 1—0300 + w — —1Og°°: T115110 : 555.5 DWLPC : SW* — 5ch : 444.4 Now assume that this industry is operate by a middleman who buys up all the rambutans
from local farmers and packages them, and she is the only source of rambutans to
consumers. What is the quantity produced (Qmm)? Calculate the total external cost
(TECm), consumer surplus (CSm), producer surplus (PSm), total social welfare (SWm)
and deadweight loss (DWLm) under a middleman. Figure not drawn to scale The optimal quantity under a middleman occurs where M OzMR.
120—4Q220+2Q Qmm = 1—30_ — 16 6 Pmmseu— _ 612—0 2 *—1—g° :36°;1°° : 86.6 Pmmbuy— _ 20 + 1_00_ _6120—é—100 : 36.6 100 TECPC :fOQmm MECdQ= foe 2QdQ: Q20—3° : w 2277:; cspc :f0 mm (MPB— Pmmseu) dQ: f0 mm1(20— 2Q— 2—g°)dQ 3 :fg mm (3—60 _2Q_2g—O)dQ: (1_00Q_ Q2)0—006 : 100 _1_gO (120)2 : 1010800_ 1%%0()_ _ 1030600_ _ 277 7 PSpc =f0 mm( Pmmbuy _ MP0) )ZdQ foQ mm (L20 _(20 + Q))dQ (1_00 =5 W <— — — — c2» d=c2 <1—2°c2— %)l 6 = = — = 1388 :PQmm( mmsell _ Pmmbuy) : 1_g0 ' 50 2 8333 SWmm = 05mm + PSmm + 7rmm — TECmm = 277.7 + 138.8 + 833.3 — 277.7 2 972.2 DWme 2 SW* — SWmm = 1000 — 972.2 2 27.7 Now suppose that the government wants to ﬁx the externality problem using a price
mechanism (tax or subsidy). Calculate the optimal tax or subsidy under a competitive
market (part b) and under a middleman (part c). Graphically, show how this tax or
subsidy (choose one) is chosen under both cases. Perfect competition: From the graph we see that we need to push MPC up to the point
where it crosses MPB at 62*. Therefore, we need to institute a tax equal to MPB(Q*) — MPC(Q*) = (120 — 2  20) — (20 + 20) = 80 — 40 = 40 Middleman: Uner the middleman, we see that we need to institute a subsidy to lower MO
so that it crosses MR at 62*. Therefore, the subsidy is equal to MO(Q*) — MR(Q*) = (20 + 2  20) — (120 — 420) 2 60 — 40 = 20 Note: you were given full credit if you noted that we would not want to subsidize the
middleman, since it is a negative externality and he is producing less externality. It might
be more optimal to introduce competition of some sort. Assume that the market is perfectly competitive, and the government imposes the
appropriate tax or subsidy (calculated in part d). Be sure that you clearly indicate which
one you are using! Compared to (part b), how do the government’s ﬁnances change? What
is the change in consumer surplus, producer surplus, total external costs, and social
welfare? What is the level of dead—weight loss? Government revenue: G = t  Q* = 40  20 = 800 A08 2 08mm — C'S'pC = 08* — CS“ 2 400 — 1111.1 2 —711.1 A2PS= Pam—PS“: fOQ"( —(MPC+t)dQ— 555 5— _ 020(80— (20+Q+40)dQ—555.5 =
020(20 + Q)dQ — 555 5— _ (20Q + %)30 — 555. 5— _ 400—200—555 5— _ —355. 5 ATEC : TECm — TECZ,c : TEC* — TECpc : 400 — 111.1 : 711.1 ASW = SVVW, — SW1,C 2 05th + PStam + G — TECtaw — 555.5 2
400 + 200 + 800 — 400 — 555.5 2 444.4 DWL = SW* — SW,” = 1000 — 1000 = 0 2. (30 Points) Suppose the Oakland School of Art and Music (OSAM) is run with
private funds and it has net costs of schooling, MPC=100+4Q since schooling is
costly and the monetary returns are low. (Q represents a unit of schooling.) On the
other hand, many people argue that art and music enrich the public culture and
therefore provide an external beneﬁt associated with schooling given by MEB=400—Q. (a) What is the optimal amount of schooling provided by OSAM? What is the
optimal amount of schooling from the public point of View (those experiencing
the external beneﬁts)? What 1s the optimal amount of schooling from the
societal point of view? Explain your answers. Since OSAM is always running with positive net costs, this means that for any
unit they provide, the costs outweight the beneﬁts. Thus, their optimal amount
would be to provide Qomm : 0 units of schooling. For those experiencing the external beneﬁts, they do not face any costs. This
means they would want schooling to be provided until their external beneﬁts were
no longer positive. This occurs where qublic = 400. Many people found this
confusing. Think, for instance, that you get paid 100 dollars for every year that
your friend goes to school. You would want your friend to get inﬁnite schooling
if possible. This is the same situation that the people experiencing the external
beneﬁts are in { except their marginal beneﬁt is decreasing). The societal point of view cares about both the private costs (faced by the school)
and the external beneﬁts. Thus, the optimal occurs where MPCzMEB, Q* = 60. (b) What is the dead—weight loss under the OSAM’s optimal choice? What is the
dead—weight loss under the public’s optimal choice? Recall that DWL is the difference between the social welfare in the current
situation and the social welfare under the optimal situation. So, we ﬁrst
calculate social welfare in each situation. Social welfare is usually given by
consumer plus producer surplus, subtracting off any additional costs. It is
equivalent to taking the integral below the MSB and above the MSC' from 0 to Q.
In our case, MPB=0, and MEC=0, so MSBzMEB and MSCzMPC'. OSAM: Optimal quantity is zero, so there is nothing to integrate over. Public: f04°°(400 — Q— [100 + 4Q] )dQ= [040% 300— 5Q) dQ—
[300Q — gQ2]300 = 120000 — E 160000— — —280000 Alternatively, total beneﬁt is given by the triangle with area §400 >1: 400 = 80000
and total cost is given by the sum of the rectangle 100 * 400— — 40000 and the triangle $—(1600)(400) — 320000. Again, the social welfare is given by
80000— 40000— 320000— — —280, 000 Note: the negative social welfare indicates that the costs largely outweigh the
beneﬁts, which makes sense because we are very far past the social optimum in
this case. Society: 060(400—62— [100+4Q]) dQ— f0°( (300— 562) dc): [300Q— 362210":
18000 — g  3000 — 9 000 Thus, the deadweight loss in OSAM’S case is 9000 — 0 = 9, 000, and in the
public ’3 case it is 9000 — (—280000) 2 289, 000 (0) Suppose some people were interested in running a second school of art and
music with the same net costs as OSAM. Calculate the new optimum from the
societal point of View. Compare the total welfare under one school with that
under two schools. With a second school, the cost curves are changing but the beneﬁt curves are not.
This is because the external beneﬁts are only a function of the total schooling
provided and thus does not depend on whether or not it is provided by one or
many different schools. To ﬁnd the new cost curve, we add the MPO
horizontally. Intuitively, the two schools can now provide twice the units of
schooling at the same price as before. Rearranging, we have 100 + 462 = P => Q = 25 — g
Q2schools : 50 _ g 2} MPCZschools : 100 + 2Q Qaschools : 100 + 2Q : 400 _ Q => Qaschools : 100
SW* 2schools= “100(400 Q_ 3l100 + 2Q] )ZdQ f0(100 300— 3Q) ($le
[300Q— gQ2](1,°°— _ 30000 — — 10000_ — 15 000 Thus, under two schools, there is an additional 6,000 units of total surplus. (d) Return to the case of one school. Calculate the total amount of revenue that
would have to be raised for OSAM under the social optimal case for the school
to break—even. The break—even point is when the school exactly covers its costs. To cover its
costs, it must be given the total cost of providing the optimal quantity. The total
cost is f06°(100 + 4Q)dQ = (100Q + 2Q2)8° = 6000 + 23600 2 13200 Essay Question Write a brief typed essay (less than one page) on the topic described below. Be sure
to write your answer in the form of an essay; don’t just answer the questions listed below. Please relate your essay to what we have discussed in class and try to hit on
what you believe are the few relevant key points. (30 Points) Under the international agreement laid out by the Kyoto Protocol, the
participant countries committed to reach binding targets for green house gas
emissions. They also laid out three market based mechanisms to promote the
achievement of these targets: emissions trading, clean development mechanism, and
joint implementation. The emissions trading mechanism created a market for carbon
using the idea of tradable permits. The clean development mechanism allows
industrialized countries to earn credits toward their targets by implementing
emissionreduction projects in developing countries, while the joint implementation
mechanism allows the countries to earn credits with emission—reduction projects in
other paricipant countries. Discuss the beneﬁts and drawbacks of the emissions
trading mechanism and one of the two credit—earning mechanisms. Comment on the
likely advocates of each policy, and compare the mechanism with a carbon tax and
and an untransferrable carbon quota. (http: //unfccc.int/kyotopr0tocol/items/2830.php) Points were awarded for the following key points: 0 Tradable permits (10 points):
— Beneﬁts: No deadweight loss, economically preferred because producers
don’t suffer — Drawbacks: Diﬁicult to determine allocation. Outcome depends on market.
Dirty technologies may still exist as long as they are still proﬁtable. — Advocates: Freemarket economists who are against strong interventions
and companies which are not very clean but still efﬁcient enough to be able
to purchase permits and still make a proﬁt. 0 Creditearning mechanism (10 points): — Beneﬁts: Promotes clean—technology use in developing/ partner countries. — Drawbacks: Countries can get away with not reducing their own pollution
very much as long as they implement projects in other countries. — Advocates: Similar to advocates of tradable permits. Countries (developing
and partner) which get the project beneﬁts from the member countries.
Companies which do not want to overhaul their dirty technology and can
beneﬁt from the positive public relations from doing an external project. 0 Taxes (5 points) — Beneﬁts: Governments take in revenues. Outcome is certain.
— Drawbacks: Deadweight loss and producers suffer. o Quota (5 points) — Beneﬁts: outcome is certain, governments can tell each company exactly
what they can produce. — Drawbacks: Requires more monitoring and is therefore likely more
expensive. ...
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 Spring '11
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