Assignment: Economics of Global Warming

Econ2216 (2012): Assignment 4
Cap and Trade

Ruth Forsdyke

Due Date: Monday April 8th
This assignment is optional as your assignment grade is the best 3 out of 4 assignments. However, even if you do not hand in
the assignment, I recommend doing it, to 1) learn and 2) to help you to study for the final exam.

Problem 1: Dire Predictions
a) We can see from the graphs on pg. 41 and 84 that both atmospheric CO2 concentrations and
temperatures have oscillated greatly throughout Earth’s history. Given this, some people argue that
anthropogenic climate change is not a great threat to Earth’s ecosystems and human civilizations as the
ecosystems have proven to be able to withstand such large changes. Provide two basic reasons why this
argument is wrong (see pg. 142 – 143).

b) Why can conserving and repairing ecosystems like forests help us to both mitigate and adapt to
climate change? Is adaptation a sufficient response to climate change or is mitigation also necessary?
(pg. 142) (pg. 195)

c)The social cost of carbon (SCC) is another name for the marginal damage. What are the ranges of
estimates for the SCC for first decade of the 21st century? (pg. 146).

d) Mann and Kump list some limitations of Nordhaus’s model. Please list. (Pg. 146)

e) Provide three ways to adapt to rising sea levels. Which nations will have more difficulty adapting?
(pg. 148-149)
* you may also want to read through the water management and agricultural adaptation strategies. Also,
note that conserving and re-establishing wetlands is important for minimizing damages from storm

f) Based on the IPCC estimates graphed on pg. 156 of DP (which seem low to me), at a carbon tax of 30
$/ tonne CO2e, how many emissions would be abated in each sector and in aggregate?

g) Did global aggregate emissions go down in any sector in 2004 relative to 1990? (pg. 159)

h) Which region has the highest energy consumption per capita? (pg. 161 map)

i) Which type of transport emissions, road, air or sea is responsible for most of transport emissions? Out
of this sector, rank the emissions from each type of transport.

j) Biofuels have the potential to be carbon neutral because once you combust the carbon in the plants,
you can recapture the carbon by photosynthesis as the plants grow. Although these technologies have
potential and need to continue to be heavily researched, there are problems. List two (pg. 172).
– note that more recent research indicates that ethanol biofuels can cause more emissions than diesel.

k) 2004 net emissions from deforestation were estimated at 6 Gt/y (pg. 174). Which two regions were
the biggest net sources in 1995? Which two regions were net sinks? We can now see why Al Gore
wanted to include forest offsets in the Kyoto Protocol. Canada did too but this might not have worked in
our favour! Also, notice the rate at which African deforestation emissions is growing over time period
depicted in graph. We discussed how this is the biggest share of Ghana’s emissions.

l) What is geoengineering? Give an example. (pg. 178 – 179)

m) List three things you can do to reduce GHGs. (pg. 180 – 181)

n ) Based on pg. 195 to 197, would you describe Mann and Kump as having given up on solving the
problem of climate change or are they hopeful?

Problem 3: Cap and Trade Markets and Monetary Cost Effectiveness

In this question, we will assume a mini world with 2 firms with the following MACs.

MAC1 (E1) = 13 – E1
MAC2 (E2) = 7 – E2

– MAC units are in $/ tonne CO2e and emissions units are in megatonnes/year.
– 1 megatonne = 1 million tonnes.
– Prices are unrealistically low to keep math simple.
– assume perfectly competitive cap and trade markets (although this would not be realistic with 2
firms—we use two firms for simplicity).

Firm 1 is a coal fired electricity company in Canada while firm 2 represents Ecuadorian farmers
who are planning to cut down rain forest under BAU in order to grow crops. For the farmers, if E2 = 0
Mt/y, all of the land is a healthy natural rainforest which sequesters carbon in the soil, plants and other
organisms while if E2 = 7 Mt/y, all of the forest has been converted to farmland causing the release of 7
megatonnes of GHG emissions in CO2e. If E2 = 3.5 Mt/y, half the forest has been converted to farmland
and so on. Recall that farmland sequesters far less carbon than natural forests and there are also
emissions due to running farm machines, transporting food to markets and for refrigeration.

In Assignment 3, we illustrated that carbon taxes provide a higher incentive to invent or adopt low
GHG technology than emissions standards although the latter may have the advantage in that the
firm has a greater ability to finance the invention and adoption of the technologies given that it does
not have to pay to pollute as long as it remains below the standard. A perfectly competitive cap and
trade model theoretically provides identical incentives to invent and adopt low GHG technology as
marginal carbon taxes except that we replace the tax line with the permit price and the area
representing the total tax represents the total opportunity cost of holding permits.

Cap and Trade with perfectly competitive auctions raises government revenue which can potentially
be rebated in lump sums to consumers (to make policy equitable) and to firms (to enable them to
finance low GHG technology adoption). Both enable for reduction of efficiency distorting taxes (ex.
income taxes particularly on low and middle income groups). If permits are instead given away, no
such revenue will be generated similar to a standard. Mixtures are possible and used.

Another important policy criteria is monetary cost effectiveness, that is that the policy achieves a
given emissions reduction target as cheaply (money-wise) as possible. For example, if a given
emission costs $10 to abate via saving a forest but $250 to abate via CCS from a coal fired plant and
these are the only two options, then the former is cost effective.

Money cost effectiveness is also important across all GHGs, not just CO2. For example, suppose it
costs $10/ tonne CO2e to reduce methane from cows by eating tofu instead and it costs $250/tonne to
capture CO2 emission from a coal plant and trap it in an oil well. If these were the only two abatement
options, the “eat tofu” option is the money cost effective one.

a) On graph 1, plot both MACs side by side making sure that the y axis units are the same for both
graphs. Label BAU emissions for each firm.

b) Suppose that the United Nations imposes an aggregate emissions cap of EAgg = 10
megatonnes/y on both firms and gives each firm 5 million permits, each of which gives the
holder the right to emit 1 tonne CO2e/year. Draw the initial permit allocation on your graph and
label the MAC of each firm at this initial allocation.

c) Suppose that the permits are tradable. Which firm is expected to buy permits from the other?
Explain with reference to the different MACs at the initial permit allocation and the
equimarginal principle.

Hint: The MAC is the marginal willingness to pay (MWTP) to pollute and is also the marginal
willingness to accept (MWTA) as compensation for not polluting.
d) Now suppose that the two parties trade permits and assume that the market is perfectly

competitive. How many permits will be traded? What is the final permit allocation after
permits have been traded? What is the market equilibrium price of permits? Show work and
illustrate on your graph.

Assume all permits trade at the equilibrium price in the following:
e) On your graph, for the seller, label and calculate the following:

i) total permit revenue
ii) change total abatement costs (TAC)
iii) change total private surplus (TPS) due to selling the permits.

– These will be areas between the initial permit allocation and the final permit allocation.

f) On your graph, for the buyer, label and calculate the following:
i) total cost of buying permits

ii) change TAC
iii) change TPS due to buying permits

g) Substitute each party’s emissions after the permits have been traded into the respective MAC and

calculate the MACs. Does the equimarginal principle hold? Why can there no longer be any
more gains from trade?

h) On graph 2, aggregate the two MACs horizontally to plot the aggregate MAC. It will have a
kink. This is your aggregate demand for permits. Your aggregate supply of permits is 10
megatonnes, the amount that were given out by the United Nations. Plot this as a vertical line at
10 Mt/y. Find the price of permits based on the aggregate graph and compare it to the
equilibrium permit price calculated earlier.

Next, we compare 3 policies based on monetary cost effective abatement (see def’n in question

i) Using graph 1, relative to BAU emissions, calculate the TAC for each firm at the final permit
allocation and add together to find the aggregate TAC. Fill in the cap and trade policy row in
the following chart.

Policy TAC1 TAC2 TACAggregate Does EM principle

Is abatement money cost

Cap and Trade

Carbon Tax

j) Notice that if the permits are given out and firms are NOT allowed to trade, then the policy is
equivalent to an emissions standard. Calculate the TAC of each firm and in aggregate given
the emissions standard and fill in chart 1.

k) Now assume that instead of the emissions standard or cap and trade policy, the government
instead uses a marginal carbon tax. What carbon tax will get the firms to abate to 10 megatonnes
in total. Calculate the TAC of each firm and in aggregate given the emissions standard and fill in
chart 1.

l) Under which of the 3 policies is the equimarginal principle satisfied? Which of the three
policies are monetarily cost effective?
m) Which of the following 4 policies generates revenue for the government and which leaves firms
with more money to finance invention and adoption of low GHG technologies?
i) a) cap and trade (permit give away)
b) cap and trade (permit auction)
c) marginal carbon tax
d) emissions standard

ii) On graph 2 label, the total permit revenue government generates by auctioning the
permits instead of giving them away (assume all permits sell at equilibrium permit price).

n) In our forest offset example above, explain how carbon leakage could occur due to incorrect
estimation of BAU emissions levels.1
o) While the cap and trade may be monetarily cost effective (assuming no carbon leakage) it may
not be “utility cost effective”. Provide a hypothetical example to illustrate. Hint: once money is
being paid to save the forest, there will be large incentives for people to get the money. Are these
necessarily the same people as those who will experience the costs of not being able to use the forest
for agriculture?

1 Another reason for carbon leakage is the difficulty of accounting for carbon sequestration by forests & other ecosystems.
The methods are imprecise but are improving. For example, early methods weighed wood and branches with later methods
measuring carbon captured in the soil. Sink capacity will vary according to location.

Note: A drawback of the tax is that the government will need to know the MAC in order to set the
correct marginal tax to hit the target. Hence, the tax runs the risk of not hitting the aggregate target, a
potentially significant drawback. It may however learn the MAC based on its observations of how
firms behave under the tax. It can then adjust the tax—however, there may be a regulatory lag.
Firms may also have incentives to change their abatement strategy to avoid revealing their true MAC
to the government (similar to offset subsidy example).

Note: While cap and trade looks great based on criteria of monetary cost effectiveness, high
incentives to adopt and invent low GHG technology, potential to generate government
revenue, and hitting the aggregate cap (if full compliance is enforced), a big drawback is
that it is complicated! A new market in permits is created and this will require regulation to
ensure that it operates competitively (ex. big firms might collude at bid rigging in permit
auctions), firms might hoard permits to prevent market entry, and associated derivatives
markets (ex. forward options in permits) can potentially be gamed (another means by which to
deprive pensioners of their life savings). Loopholes like the Harper Safety Clause (remove
cap if price exceeds some limit) might encourage speculation to drive the price up above the
threshold safety level, thereby bringing about removal of the cap. Cap and trade may also be
inequitable in the case of forest offsets, if offsetting money does not go to those who bear the
actual costs of abatement. However, powerful forces for saving forest and wetland
ecosystems might be put into action (if designed carefully) preventing species extinctions and
improving the health of ecosystems helping humans both mitigate and adapt to climate change.

Assn 4:

Graph 1: ___________________________________________________________

Electricity Emissions (E1)
(Mt CO2e/y)





Deforestation Emissions (E2)
(Mt CO2e/y)




Graph 2: ___________________________________________________________

Electricity Emissions (E1)
(Mt CO2e/y)

Deforestation Emissions (E2)
(Mt CO2e/y)

Aggregate Emissions (E1)
(Mt CO2e/y)

0 0 0


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