Assignment 5a and answers

Assignment 5a 28/05/2014 Question 1 Consider an urban pollution problem caused by car transportation, which emits 12 tons of pollution, and factories, which emit another 18 tons. The costs of reducing car and factory pollution are Cc  yc2  20 and C f  0.5 y 2f  10 , respectively, where yc and y f denote the reductions in car and factory pollution [hints: the marginal cost functions are therefore MCc  2 yc and MC f  y f ]. The social benefit of reducing pollution are B  0.25 y 2  2 y  30 , where y  yc  y f . [hint: the marginal benefit is therefore MB  0.5 y  2 ] Suppose that the government uses tradable pollution permits to achieve the socially efficient reduction and issues k tons of permits. Answer the following questions: (a) Calibrate the socially optimal k. (b) At the socially optimal level of k, calibrate optimal yc and y f . (Answers omitted) Question 2 (This question continues from the example employed in Lecture 6) There are two firms S and F, producing steel (s) and does fishing (f) respectively. By producing a unit of steel, S generates pollution x and dumps it into a river, increasing the cost of fishing. Assuming S and F’s cost functions are: c
cs ( s, x )  s 2  ax  bx 2 , and where s  0
x
c

f
c f ( f , x )  f 2  cx  dx 2 , where
0

x
Further assuming that S has the property rights of x units of clean water, and can sell ( x  x ) to F. Show that the optimal level of pollution is the same as the socially optimal level. Answer: The profit maximisation problems for S and F are: max ps s  r ( x  x )  ( s 2  ax  bx 2 )
s,x
max p f f  r ( x  x )  ( f 2  cx  dx 2 )
f
The two f.o.c.s for S are: 1
c ( s  , x  )
c ( s  , x  )
ps  s
and  r  s
s
x
The two f.o.c.s for F are: c f ( f  , x  )
c f ( f  , x  )
p

and
r

f
f
x
The two FOC wrt x form a supply function and a demand function. Two together will solve for: ac
x 
 x†  x '
2(b  d )
Question 3 The Pristine River‐ has two polluting firms on its banks. Acme Industrial and Creative Chemicals each dump 100 tonnes of glop into the river each year. The cost of reducing glop emissions per tonne equals $10 for Acme and $100 for Creative. The local government wants to reduce overall pollution from 200 tonnes to 50 tonnes. a. If the government knew the cost of reduction for each firm, what reductions would it impose in order to reach its overall goal? What would be the cost to each firm and the total cost to the firms together? b. In a more typical situation, the government would not know the cost of pollution reduction at each firm. If the government decided to reach its overall goal by imposing uniform reductions on the firms, calculate the reduction made by each firm, the cost to each firm, and the total cost to the firms together. c. Compare the total cost of pollution reduction in parts (a) and (b). If the government does not know the cost of reduction for each firm, is there still some way for it to reduce pollution lo 50 tonnes at the total cost you calculated in part (a)? Explain. Answers: a. If the government knew the cost of reduction at each firm, it would have Acme eliminate all its pollution (at a cost of $10 per tonne times 100 tonnes = $1,000) and have Creative eliminate half of its pollution (at a cost of $100 per tonne times 50 tonnes = $5,000). This minimises the total cost ($6,000) of reducing the remaining pollution to 50 tonnes. 2
b. If each firm had to reduce pollution to 25 tonnes (so each had to reduce pollution by 75 tonnes), the cost to Acme would be 75 x $10 = $750 and the cost to Creative would be 75 x $100 = $7,500. The total cost would be $8,250. c. In part a, it costs $6,000 to reduce total pollution to 50 tonnes, but in part b it costs $8,250. So it’s definitely less costly to have Acme reduce all its pollution and have Creative cut its pollution in half. Even without knowing the costs of pollution reduction, the government could achieve the same result by auctioning off pollution permits that would allow only 50 tonnes of pollution. This would ensure that Acme reduced its pollution to zero (since Creative would outbid it for the permits) and Creative would then reduce its pollution to 50 tonnes. Question 4 Assume that in California the Family Law requires mutual agreements from both husband and wife to divorce. But the state government is contemplating a change to abolish the mutual‐agreement requirement and thus allow for a partner to divorce without another partner’s consent. Use the Coase Theorem to predict the effect of the change on the divorce rate in California. Answer: At the absence of transactions costs, the law change did not make any difference in the divorce rate. See the following table. Case mutual consent Unilateral system 1. both want to divorce Divorce
Divorce
2. both want to stay Stay
Stay
3. A’s willingness to pay Divorce (A “pays” B to Divorce to divorce is higher than divorce) the B’s willingness to pay to stay 4. A’s willingness to pay Stay to divorce is lower than B’s willingness to pay to stay Stay (B pays A to say) 3

Download Report