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Econ2216 (2013): Assignment #2
MAC MD Framework
Ruth Forsdyke
Due: Wed. Feb. 20th in class.
For algebraic questions, please show all work and use short sentences to guide reader through your
work. Please use graph paper provided for Problem 2.
Problem 1: Dire Predictions (use DP to answer questions/ please be brief)
a) About 12,000 ago, at the end of the warming period after the large ice age, evidence from
paleoclimate studies suggests that a large pool of melted ice from the great Laurentide Ice Sheet (that
covered much of North America) was suddenly released into the North Atlantic. This made the
water less salty so that it did not sink as fast causing a slow down of the North Atlantic Ocean
current conveyer belt which pumps water via the Gulf Stream Current from the equator to Greenland
and back. This caused Northern Europe to temporarily returned to glacial climate conditions. Do
scientists think that melting of the Greenland Ice Sheet will have a similar effect? (pg. 60 to 61 DP)
b) What do climate models suggest will happen to the intensity of tropical cyclones and hurricanes
due to climate change? What about the frequency? (Pg. 56 – 57).
c) How many people died due to an unprecedented heatwave in Europe in 2003? Multiply by the
value of a statistical life ($2.5 million) to get an estimate of the damages due to the heatwave. Can
we with certainly attribute these damages to global warming? Why or why not? Are these damages
consistent with predictions of climate models? Hint: consider smoking example in course outline
description. (pg. 52 – 54).1
d) Globally, based on the Palmer Drought Severity Index, what has happened to the number of
regions experiencing more intense droughts since the end of the 1980s? List some damages due to
droughts.
e) How do scientists explain the shrinking of the glaciers on Mount Kilimanjaro? (pg. 59)
f) Temperatures eventually come into equilibrium for a given concentration of greenhouse gases.
The temperature rise that occurs for a doubling of carbon dioxide to 560 ppms from the 280 ppm is
referred to as climate sensitivity. When was the CO2 concentration expected to double based on DP
1 Note: Other damages included crop loss.
which is based on UN IPPC FAR (2007)? When if the full effect on warming due to this doubling
expected to be experienced? What is the range of estimated climate sensitities? (pg.
g) Scientists have developed future scenarios, which include parameters affecting Kaya equation
variables. They include changes in income inequality, the rate of industrialization in low income
countries, technological growth rates, population growth, the degree to which people adopt “post-
materialist attitudes” and how quickly we reduce the “material intensity of consumption” to service
based economies, and lastly, the degree to which we globally cooperate on climate change
abatement. Four representative CO2 emissions scenarios, A1, A2, B1 and B2 are represented on pg.
86-87. On the following page (89), the graph illustrates expected temperature rises under the three
scenarios.
i) Of the scenarios illustrated, which one do scientists estimate can prevent the 20C
temperature rise that countries agreed to cooperate to prevent under the Copenhagen
Agreement?
ii) Return to pgs 86-87. For your chosen scenario in i), list the 5 key components of this
scenario.
h) Based on the predicted changes in the Hadley Circulation patterns, which regions will get dryer
and which wetter due to global warming?
i) Based on the IPCC FAR results reported in DP, when does fossil fuel use need to peak by to
enable atmospheric CO2 levels to remain below 450 ppms? Out of the 4 possible scenarios, which
one is predicted to make it just possible to achieve this objective.
Note: The 450 ppm target is 100 ppms higher than the Hansen recommended target of 350 ppms and
possibly lower. Recall that the GHG concentration changed by about 100 ppm from about 180 ppm
to 280 ppms during the transition from the last ice age to the current interglacial (17,000 to 12,000
years ago).
Problem 2:
This question continues on from Problem 3 in Assn 1. Here, we will derive the MAC and MD for
emissions from combusting coal.
Recall that in 2010, coal combustion was estimated to cause the release of about 13.029 gigatonnes
(Gt) of CO2 into the atmosphere. As before, we assume one type of coal and one global coal price.
Let P represent the price of coal in $/ tonne and let Q represent the quantity in Gt/year.
Recall that the monetary marginal costs of producers and monetary marginal benefits (as measured
based on marginal $WTP of consumers) were assumed respectively to be2:
MCPrivate (Q) = 10
Q
MBPrivate (Q) = 400 – 40Q
Assuming a carbon price of $100/tonne CO2e (similar to the Stern Review estimate for the first
decade of the 21st century), and using the LCA estimate of 1.70 tonnes CO2e/tonne coal combusted,
we got an external cost of coal of $170/tonne. Again, we will assume that these are the only
externalities from coal combustion for simplicity.
2 Recall, these were based on rough estimations of current prices and quantities of coal but all slopes were made up. To
get better estimates, we need to estimate demand and supply elasticities using statistical methods. This is complex due to
demand and supply curves shifting about over time. Take econometrics to learn how to do this.
a) The marginal private surplus of coal is equal to the net private benefits of coal combustion such
that: MPS (Q) = MBPrivate(Q) – MCPrivate(Q)3. Find the marginal private surplus for world coal
based on the equations in the preamble. Plot on figure 1.
b) Plot the marginal external cost on figure 1. Set MCExternal = MPS(Q) and solve for the monetary
socially efficient ($SE) level of coal output. Label the market “BAU” level of coal output and the
$S
E
output on your graph.4
c) Suppose that we impose a Pigouvian tax on coal of $170/tonne OR a quota on coal extraction set
at the $SE level. This leads to a reduction in coal combustion from the BAU level to the $SE level.5
i) What is the net benefit to the third parties of the policy? (This will be their reduction in
total external costs). Calculate and label area on your graph.
ii) What is the net cost to the private parties of the policy (their loss in total private
surplus). Calculate and label area on your graph.
iii) How much total coal tax will the government collect in the case of the tax. Label on your
graph.
d) Now, we will shift our focus to emissions. Recall that each tonne of coal causes 1.7 tonnes of
residual byproducts. This means that E = 1.7 Q. Rearranging, we get:
Q (E) = E/1.7 [eq’n 1]
i) Substitute eq’n [1] in your MPS equation to get the MAC (marginal cost of abatement)
equation. This tells you the amount of private surplus that must be given up in order to
reduce emissions by one unit (here a tonne).
ii) Plot the MAC on figure 2.
iii) Label the BAU level of emissions (it won’t be quite the same as the estimate in the
preamble but it should be in the ballpark).6
e) We know that given our carbon shadow price estimate of $100/tonne, the marginal damages from
1 tonne of CO2e are estimated to be $100/tonne.
i) Plot and label the MD curve on figure 2.
ii) Set MAC = MD to find the monetarily socially efficient level of GHG emissions from
coal combustion.
Price Mechanisms:
f) Suppose that Nations agree under the UN FCCC convention to regulate GHGs by imposing a
price mechanism of a marginal carbon tax (t) of $100/tonne CO2e. Illustrate t on graph 2.
Recall that private parties will abate GHGs if the cost of reducing emissions by an additional unit
(the MAC) is less than the marginal tax saved. They will hence abate until MAC = t at which the
SE level of abatement is achieved. Calculate and label the following on your graph.
i) Total Damages (TD) 3rd parties save under regulation relative to BAU.
3 Note that more accurately the MBPrivate is equal to the MBConsumers + MBProducers while the MCPrivate = MCConsumers +
MCProducers. Since, using the money measure, MCConsumers = MBProducers = Price (i.e. consumer expenditures equal
producer revenues), we ignore the consumer costs and producer benefits in our analysis. This will only hold using the
money measure.
4 Recall that BAU stands for “Business as Usual”, which refers to the level of output in an unregulated market.
5 Recall that totals always correspond to areas under corresponding marginals curves. This is a key idea in economics so
make sure you understand it.
6 Note that the number will not quite be BAU as there are already some, albeit far too lax, global warming regulations in
place.
ii) Total Abatement Costs (TAC) private parties.
iii) Total Tax Revenue.
iv) Total social surplus gained by society as a whole (i.e. benefits net costs to both private
and third parties).
Quantity Mechanism:
g) As an alternative to taxes, countries could instead impose National quotas on GHG emissions as
under the Kyoto Protocol and under the newer Copenhagen Agreement. Non-tradable quotas on
emissions are referred to as Emissions Standards. Emissions standards are also set at the level of
provinces, states, cities, firms, industries, and individuals.7 If the standard is not met, fines are
levied. For example, Nova Scotia Power is regulated by an emissions standards with a fine of
$500,000/day for violating the standard. Here, we will assume that emissions standards are
imposed upon the entire world coal industry. The standards are given away such that the
government receives no revenue. Calculate the following and label on figure 3.
i) The level of the emissions standard in gigatonnes of CO2e which would achieve $SE
abatement assuming full compliance to the policy.
ii) Total damages (TD) 3rd parties save under regulation relative to BAU. Find total
damages saved under the standard relative to BAU and label on your graph.
iii) Find the total abatement costs (TAC) incurred by private parties and label.
iv) Total Revenue collected by government.
v) Total Social Surplus gained.
h) Both policies raise the price of combusting coal and making steel making many goods more
expensive (at least in the short run while the low GHG energy sources are being invented and
adopted). Which of the above two policies provides governments with revenue to compensate low
income people? Discuss ways that low-income people might be compensated in theory.
i) Note that the above GHG targeted policies will not be targeted directly on coal companies but on
electricity producers, steel makers and heat providers. These firms will then reduce their demand for
coal as it becomes are relatively expensive energy source. For example, the CO2 tax is levied on
GHGS by measuring how many are released from a firm’s smoke stack, after which they are charged
$100 for each tonne. Which of the above policies will leave electricity companies with more money
to finance the adoption and invention of low GHG energy sources?8
Currently, under the UN Framework Convention on Climate Change (UN FCCC), countries have set
emissions standards with all countries being required to participate by 2015. Under the Copenhagen
Agreement signed in 2009, it was agreed to set up a climate fund, which by 2020 would contribute
$100 bill/year to help “developing countries” abate GHG emissions and adapt to climate changes as
they occur. To date, only $10 billion/year has materialized. In Doha, in 2012, countries agreed to a
Climate Damage Aid package, which commits Early Industrialized countries to compensating low
income countries for damages due to climate change. If this rule is enforced, continuation under
BAU will be very expensive for Annex 1 countries, providing them with strong incentives to reduce
7 An important example of the use of emissions standards occurs at the National level under which countries set
national abatement targets. The first set of National emissions standards was agreed to under the Kyoto Protocol but did
not include all nations. Last December at that COP 14 in Doha, Qatar, all of the United Nations of the Planet Earth,
agreed to set targets by 2015 for 2020. Given the national target, Nations are free to use a variety of policy tools to meet
targets. Given lack of action at the national level, targets are primarily being set at the Provincial level. The similar
situation holds in the USA.
8 An example is Nova Scotia Power, which is currently regulated via emissions standards and has incentives to develop
tidal electricity because if another firm develops tidal, it will be required to pay 65 cents per kWh under the feed in tariff
policy.
their emissions. This might provide us with a strong incentive to work together internationally to
reduce emissions. If the commitment is enforced, do you think that non-Annex I countries (the
“developing countries”) will have strong incentives to abate their emissions?
Check that you:
1) Labeled all graph axis.
2) Gave your graphs titles.
3) Used short sentences to guide reader through your work.
References:
Source: Pleistocene North Ice Map: http://en.wikipedia.org/wiki/Laurentide_ice_sheet
Marshall, Michael (Dec. 10th, 2012) Doha Summit Launches Climate Damage Aid, The New
Scientist. http://www.newscientist.com/article/dn22609-doha-summit-launches-climate-damage-
aid.html
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Figure 3:______________________________________________________
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