EconS 582, Fall 2011 Midterm #1: Due November 9th, 8.45am

EconS 582, Fall 2011 

Midterm #1: Due November 9th, 8.45am 

Ana Espinola-Arredondo, anaespinola@wsu.edu 

O¢ ce: 111C Hulbert Hall 

1 Question #1 - 15 Points 

The Coase Theorem is often applied in court cases where the parties seek to clarify who has the right to 

do what in the presence of externalities. Consider the case of the addition to my house that will then cast 

a shadow on your swimming pool. Suppose that my bene…t from the addition is b, and the cost you incur 

from my shadow is c. Suppose throughout this exercise that transaction costs are zero. 

First: assume that you and I both know what b and c are. 

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 

than ending up in court 

b. If the judge (who has to decide whether I have a right to build my addition) also knows b and c, propose 

a sensible and e¢ cient rule for him to use to adjudicate the case. 

c. Judges rarely have as much information as plainti¤s and defendants. It is therefore reasonable for the 

judge to assume that he cannot easily ascertain b and c. Suppose he rules in my favor. What does 

Coase predict will happen 

d. What if he instead rules in your favor 

e. In what sense will the outcome always be the same as it was in part (b), and in what sense it will it 

not 

Next, assume that I know b and you know c, but I do not know c and you do not know b. 

f. Suppose the judge rules in your favor, and I now attempt to convince you to let me build the addition 

anyhow. I will come to your house and make an o¤er based on my belief that your cost is less than c 

with probability (c) = c 

. What o¤er will I make 

g. For what combinations of b and c will the outcome be ine¢ cient 

h. Suppose instead that the judge rule in my favor. You therefore come to my house to convince me not 

to build the addition even though I now have the right to do so. You will make me an o¤er based on 

your belief that my bene…t from the addition is less than or equal to b with probability delta (b) = b . 

What o¤er will you make 

i. Explain how the cost of obtaining information might be considered a transactions cost, and the results 

you derived here are therefore consistent with the Coase theorem. 

2 Question #2 - 15 Points 

Consider the "two-part instrument" developed by Fullerton and Wolverton (2000). Identify a particular 

functional form for the utility u(c; d; h; G; D) de…ned over per capita consumption of a clean good c, dirty 

good d, homeproduced good h, the total amount of a government-provided public good G, and total waste 

D (where D = nd), and show that the two-part instrument is equivalent to the pigouvian tax on the dirty 

activity. Provide some intuitions about your results and discuss each variable of your model. [Assume that 

n = 2] 

1


Suppose there are two polluters that have a hidden characteristic, . Note that does not have to be the 

same for both …rms. Assume that can take on one of two values: 1 or 2. These two …rms emit pollution, 

with marginal saving functions equal to MS(e; ) = 1 e. Total savings from pollution for each …rm are 

(1 e) 

S(e; ) = 1 

2 

2 

. Damage from pollution is D(e 1 + e 2 ) = (e1+e2)2 

2 

with a marginal damage of (e 1 + e 2 ). 

a. Suppose the regulator knew the value of for each of the …rms, 1 and 2 . For all possible combinations 

of 1 and 2 , what would be the optimal amount of pollution for each …rm: e 1( 1 ; 2 ), e 2( 1 ; 2 ) 

b. Now, assume the regulator does not know but asks each …rm its true . After receiving those reports 

from each …rm, each …rm i will be charged an amount, T i (e i ; i ), based on the reported i , the report 

by the other …rm, j , and actual emissions e i : 

T i (e i ; i ) = D[e i + e j ( 1 ; 2 )] S j [e j (( 1 ; 2 ); j )] 

Where i and j are the two …rms. The …rms know this before they report their values of . Show that it 

is in the best interest of each …rm to tell the true about and also to emit the right amount of emissions, e . 


Let us analyze a Voluntary Contribution Mechanism (VCM) to …nance a green electricity program. Two 

households have the opportunity to make a voluntary contribution to …nance the creation of new generation 

capacity. Total capacity, measured in …nancing expenditures, is determined by the aggregate level of 

2X 

contributions such that G = g i , where g i 2 R + is household i’s contribution. An important feature 

i=1 

of this program structure, is that contribution levels are not a function of electricity consumption. While 

contributions are used to …nance green electricity, households continue to purchase conventional electricity 

at the price p c . Each household is endowed with exogenous income w and seeks to maximize a continuous 

and strictly quasi-concave utility function of the form: 

U i (g i ; g j ) = [w g i ] 0:5 + [m(g i + g j ) + (g i g j )] 0:5 

where w g i denotes the remaining units of money which have not been contributed and that can be 

used for consumption of private goods. In addition, let m 2 R + be the (constant) return from the total 

contributions to the public good, g i +g j . Assume that players increase their perception of social status when 

their contribution to the public good is above that of the other donor, i.e., when g i > g j . For simplicity, let 

us construct a linear distance function D i i (g i g j ), where player i’s comparison point is g i , and her 

reference point is g j . That is, player i compares her own contribution with that of the other donor. 

a. Identify player i’s best response function. 

b. Obtain the optimal contributions of this simultaneous public good game. Provide some intuition for 

your results. 


Assume there are two identical countries X and Y , each producing a polluting homogeneous good L. Production 

in each country occurs within a monopolistic industry. The entry of new …rms is prevented by some 

sunk cost already incurred by the established …rm. These two …rms, i (located in X) and j (located in Y ), 

x 

compete in a third market Z. Marginal production cost for …rm i and j are 2 

i 4 and j x2 

2 

, respectively. In 

1 

addition, the cost of acquiring technology is 

K 

, where k = i; j. The abatement cost for both …rms is identical 

and equal to a2 

2 

, where a represents the abatement level. Finally, assume that there is transboundary 

pollution, that is, a proportion 2 (0; 1) of the local emissions also a¤ect the other country. Note that the 

total damage is d and depends on the total amount of emissions, e. 

2

a. Solve the two stage game, where …rst each government independently selects the optimal emission level 

and, second, each …rm chooses its optimal output level. 

b. Develop a comparative static. Please discuss your results. 

c. Assume that both …rms decide to sign a bilateral agreement, identify the optimal emission fee. 

d. Compare the emission fee, e , obtained in part (c) with e i and e j obtained in part (a). Why are they 

di¤erent 


Weitzman (1974) de…nes the comparative advantage of prices over quantities as 

E[(B(eq(); ) c(eq(); )) (B(^q; ) c(^q; ))] 

Develop Weitzman’s model using speci…c functional forms. Make sure your functions satisfy the following 

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, 

assume that there is a disturbance term or random variable, unobserved and unknown at the present time, . 

Show that using a price control policy could have detrimental consequences. Provide intuitions and discuss 

your results. 

GOOD LUCK! 

3

EconS 582, Fall 2011 Midterm #1: Due November 9th, 8.45am

Create successful ePaper yourself

Delete template?

Save as template?