Assignment 5

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PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE 
FA C U L T A D D E C I E N C I A S E C O N ÓM I C A S Y A D M I N I S T RA T I V A S 
 
 
Environmental and Natural Resource Economics EAE 295C 
Professor Guillermo Donoso (gdonosoh@uc.cl) 
 
Homework Assignment 5 
General instructions 
1. The assignments must be solved individually. The answers to each question must be 
presented in a single Word file. It is not allowed to scan handwritten tasks to send a 
PDF file to the Buzón de Tareas. 
2. In the development of the answers it is mandatory the use of the Microsoft Equation 
Editor of Microsoft Word (or, alternatively, some other equation editor) in order to 
express mathematically what is requested in each question. 
3. If an attempt of academic fraud is detected, the assignment will be rated with a grade 
of 1.0 both for the student who copied and the one who let them copy their work. 
4. The assignments that do not comply with the indicated instructions will be penalized 
with a cumulative reduction of 30% of the final grade obtained. 
5. An electronic copy of the resolution of the assignment must be sent to the Buzón de 
Tareas on Thursday, November 2 before 10:00 and another printed copy must be 
handed in by 10:00 on the same date. 
 
Show all your calculations 
 
 
Pollution Control 
1) Under which circumstances will the economically optimal level of pollution be zero? Under 
which circumstances will it be optimal to undertake zero pollution abatement? Use graphs. 
 
Economic efficiency requires a balancing of benefits and costs. The optimal level of pollution is 
zero in the case where, 
1. Either abatement or prevention cost is always zero, or the damages of pollution are 
infinitely large. 
2. If the marginal cost of abatement is everywhere less than the marginal benefits of pollution 
abatement 
 
 
 
 
PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE 
FA C U L T A D D E C I E N C I A S E C O N ÓM I C A S Y A D M I N I S T RA T I V A S 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
It is optimal to undertake zero pollution abatement in the case where the marginal cost of 
abatement is everywhere greater than the marginal benefit of abatement. 
 
 
 
2) You are given the following information: 
a) A programme of air pollution control would reduce deaths from cancer from 1 in 8000 to 1 
in 10 000 of the population. 
b) The cost of the programme is expected to lie in the interval £2 billion (£2000 million) to £3 
billion annually. 
c) The size of the relevant population is 50 million persons. 
d) The ‘statistical value’ of a human life is agreed to lie in the interval £300 000 to £5 million. 
MC (Pollution control) 
MB(Pollution ) 
$ 
Q abatement 
 
 
PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE 
FA C U L T A D D E C I E N C I A S E C O N ÓM I C A S Y A D M I N I S T RA T I V A S 
 
 
If the only benefit from the programme is the reduced risk of death from cancer, can the 
adoption of the programme be justified using an economic efficiency criterion? 
 
The program’s benefit is a reduction in the Δ𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑒𝑎𝑡ℎ𝑠 = 1.250. Since the ‘statistical 
value’ of a human life is agreed to lie in the interval £300 000 to £5 million, the program’s benefits 
lie in the interval £375 million to £6.250 billion annually. The expected yearly cost of the program 
lies between £2 billion to £3 billion annually: 
 
As long as the expected benefits are greater than the expected costs it will be convenient. Thus, it 
dependes on the probability distribution of benefits and costs. 
 
3) Consider a good whose production generates pollution damage. Would the effects of a tax on 
the output of the good differ from that of a tax on the pollutant emissions themselves? Which of 
the two is likely to be economically efficient? (Hint: think about substitution effects on the 
demand side and on the supply side.) 
 
In the case that the emissions to output ratio is fixed a tax on the units of output will be the 
same as a tax on the units of emission. When this ratio is not constant, a tax on emissions will 
have a greater proportional impact on emissions. A tax on the emission encourages the proper 
substitution effect. The profit maximizing change induced by the tax will be driven by 
substitution effects, for example towards cleaner energy resources. 
 
4) Use graphs to compare pollution tax instruments with tradable emission permit systems, pay 
attention to the distributional consequences of the two forms of the instrument. (Assume a 
given, target level of pollution abatement, and that permits are initially distributed through sale 
in a competitive market.) 
 
 
 
PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE 
FA C U L T A D D E C I E N C I A S E C O N ÓM I C A S Y A D M I N I S T RA T I V A S 
 
 
P 
 
 
 
 
 
 
 
Imposing a tax can be as effective as tradable permits, when there are no transaction costs. The 
tax should internalize the marginal damage cost at the efficient level of pollution. The tax 
reduces the marginal benefit of abatement (Figure 1). 
 
Under tradable permits, there is a negotiation between companies until they reach the socially 
optimal pollution level. Given an initial allocation they reallocate the permits in order to, given 
the well- defined property rights, reach the optimum. (Figure 2). The trades between firms 
represents a wealth distribution. 
 
 
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𝑀𝐵1 𝑀𝐵1 
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