EconS 582, Fall 2011 Midterm #1: Due November 9th, 8.45am
EconS 582, Fall 2011 Midterm #1: Due November 9th, 8.45am
EconS 582, Fall 2011 Midterm #1: Due November 9th, 8.45am
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<strong>EconS</strong> <strong>582</strong>, <strong>Fall</strong> <strong>2011</strong><br />
<strong>Midterm</strong> <strong>#1</strong>: <strong>Due</strong> <strong>November</strong> <strong>9th</strong>, <strong>8.45am</strong><br />
Ana Espinola-Arredondo, anaespinola@wsu.edu<br />
O¢ ce: 111C Hulbert Hall<br />
1 Question <strong>#1</strong> - 15 Points<br />
The Coase Theorem is often applied in court cases where the parties seek to clarify who has the right to<br />
do what in the presence of externalities. Consider the case of the addition to my house that will then cast<br />
a shadow on your swimming pool. Suppose that my bene…t from the addition is b, and the cost you incur<br />
from my shadow is c. Suppose throughout this exercise that transaction costs are zero.<br />
First: assume that you and I both know what b and c are.<br />
a. If we both know b and c, why don’t we just get together and try to settle the matter over co¤ee rather<br />
than ending up in court<br />
b. If the judge (who has to decide whether I have a right to build my addition) also knows b and c, propose<br />
a sensible and e¢ cient rule for him to use to adjudicate the case.<br />
c. Judges rarely have as much information as plainti¤s and defendants. It is therefore reasonable for the<br />
judge to assume that he cannot easily ascertain b and c. Suppose he rules in my favor. What does<br />
Coase predict will happen<br />
d. What if he instead rules in your favor<br />
e. In what sense will the outcome always be the same as it was in part (b), and in what sense it will it<br />
not<br />
Next, assume that I know b and you know c, but I do not know c and you do not know b.<br />
f. Suppose the judge rules in your favor, and I now attempt to convince you to let me build the addition<br />
anyhow. I will come to your house and make an o¤er based on my belief that your cost is less than c<br />
with probability (c) = c <br />
. What o¤er will I make<br />
g. For what combinations of b and c will the outcome be ine¢ cient<br />
h. Suppose instead that the judge rule in my favor. You therefore come to my house to convince me not<br />
to build the addition even though I now have the right to do so. You will make me an o¤er based on<br />
your belief that my bene…t from the addition is less than or equal to b with probability delta (b) = b .<br />
What o¤er will you make<br />
i. Explain how the cost of obtaining information might be considered a transactions cost, and the results<br />
you derived here are therefore consistent with the Coase theorem.<br />
2 Question #2 - 15 Points<br />
Consider the "two-part instrument" developed by Fullerton and Wolverton (2000). Identify a particular<br />
functional form for the utility u(c; d; h; G; D) de…ned over per capita consumption of a clean good c, dirty<br />
good d, homeproduced good h, the total amount of a government-provided public good G, and total waste<br />
D (where D = nd), and show that the two-part instrument is equivalent to the pigouvian tax on the dirty<br />
activity. Provide some intuitions about your results and discuss each variable of your model. [Assume that<br />
n = 2]<br />
1
3 Question #3 - 20 Points<br />
Suppose there are two polluters that have a hidden characteristic, . Note that does not have to be the<br />
same for both …rms. Assume that can take on one of two values: 1 or 2. These two …rms emit pollution,<br />
with marginal saving functions equal to MS(e; ) = 1 e. Total savings from pollution for each …rm are<br />
(1 e)<br />
S(e; ) = 1<br />
2<br />
2<br />
. Damage from pollution is D(e 1 + e 2 ) = (e1+e2)2<br />
2<br />
with a marginal damage of (e 1 + e 2 ).<br />
a. Suppose the regulator knew the value of for each of the …rms, 1 and 2 . For all possible combinations<br />
of 1 and 2 , what would be the optimal amount of pollution for each …rm: e 1( 1 ; 2 ), e 2( 1 ; 2 )<br />
b. Now, assume the regulator does not know but asks each …rm its true . After receiving those reports<br />
from each …rm, each …rm i will be charged an amount, T i (e i ; i ), based on the reported i , the report<br />
by the other …rm, j , and actual emissions e i :<br />
T i (e i ; i ) = D[e i + e j ( 1 ; 2 )] S j [e j (( 1 ; 2 ); j )]<br />
Where i and j are the two …rms. The …rms know this before they report their values of . Show that it<br />
is in the best interest of each …rm to tell the true about and also to emit the right amount of emissions, e .<br />
4 Question #4 - 20 Points<br />
Let us analyze a Voluntary Contribution Mechanism (VCM) to …nance a green electricity program. Two<br />
households have the opportunity to make a voluntary contribution to …nance the creation of new generation<br />
capacity. Total capacity, measured in …nancing expenditures, is determined by the aggregate level of<br />
2X<br />
contributions such that G = g i , where g i 2 R + is household i’s contribution. An important feature<br />
i=1<br />
of this program structure, is that contribution levels are not a function of electricity consumption. While<br />
contributions are used to …nance green electricity, households continue to purchase conventional electricity<br />
at the price p c . Each household is endowed with exogenous income w and seeks to maximize a continuous<br />
and strictly quasi-concave utility function of the form:<br />
U i (g i ; g j ) = [w g i ] 0:5 + [m(g i + g j ) + (g i g j )] 0:5<br />
where w g i denotes the remaining units of money which have not been contributed and that can be<br />
used for consumption of private goods. In addition, let m 2 R + be the (constant) return from the total<br />
contributions to the public good, g i +g j . Assume that players increase their perception of social status when<br />
their contribution to the public good is above that of the other donor, i.e., when g i > g j . For simplicity, let<br />
us construct a linear distance function D i i (g i g j ), where player i’s comparison point is g i , and her<br />
reference point is g j . That is, player i compares her own contribution with that of the other donor.<br />
a. Identify player i’s best response function.<br />
b. Obtain the optimal contributions of this simultaneous public good game. Provide some intuition for<br />
your results.<br />
5 Question #5 - 20 Points<br />
Assume there are two identical countries X and Y , each producing a polluting homogeneous good L. Production<br />
in each country occurs within a monopolistic industry. The entry of new …rms is prevented by some<br />
sunk cost already incurred by the established …rm. These two …rms, i (located in X) and j (located in Y ),<br />
x<br />
compete in a third market Z. Marginal production cost for …rm i and j are 2<br />
i 4 and j x2<br />
2<br />
, respectively. In<br />
1<br />
addition, the cost of acquiring technology is<br />
K<br />
, where k = i; j. The abatement cost for both …rms is identical<br />
and equal to a2<br />
2<br />
, where a represents the abatement level. Finally, assume that there is transboundary<br />
pollution, that is, a proportion 2 (0; 1) of the local emissions also a¤ect the other country. Note that the<br />
total damage is d and depends on the total amount of emissions, e.<br />
2
a. Solve the two stage game, where …rst each government independently selects the optimal emission level<br />
and, second, each …rm chooses its optimal output level.<br />
b. Develop a comparative static. Please discuss your results.<br />
c. Assume that both …rms decide to sign a bilateral agreement, identify the optimal emission fee.<br />
d. Compare the emission fee, e , obtained in part (c) with e i and e j obtained in part (a). Why are they<br />
di¤erent<br />
6 Question #6 - 10 Points<br />
Weitzman (1974) de…nes the comparative advantage of prices over quantities as<br />
E[(B(eq(); ) c(eq(); )) (B(^q; ) c(^q; ))]<br />
Develop Weitzman’s model using speci…c functional forms. Make sure your functions satisfy the following<br />
assumptions: B 00 (q) < 0, C 00 (q) > 0, B 0 (0) > C 0 (0), and B 0 (q) < C 0 (q) for q su¢ ciently large. In addition,<br />
assume that there is a disturbance term or random variable, unobserved and unknown at the present time, .<br />
Show that using a price control policy could have detrimental consequences. Provide intuitions and discuss<br />
your results.<br />
GOOD LUCK!<br />
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