Assignment: Economics of Global Warming

Please see the attachment.

Econ2216 (2013): Assignment #1
Market Failure Due to Externalities

Ruth Forsdyke

Due: Monday, Jan. 28th in class.
For algebraic questions, please show all work and use short sentences to guide reader through your
work. Please use graph paper on page 4 for Problem 2.

Problem 1: Dire Predictions (use DP to answer questions/ please be brief)
a) Look at the picture of the Florida Keys on page 62 of DP. During the last interglacial period
between 130,000 and 114,000 years ago, these were coral reefs. How much higher was the sea level
estimated to be based on DP? During the depth of the last ice age, how much lower were the sea
levels?
b) Look at the three types of Milankovitch orbital cycles pictures on page 63. Which orbital cycle
change is thought to have initiated the end of the last ice age?
c) List two feedbacks which amplified the effect in b.
d) How high were the ice caps which covered most of Canada and the Northern US during the last
ice age? (pg. 62)
e) Increasing GHGs increases the rate at which water evaporates to become water vapour which
forms clouds. Clouds reflect light back to space if they are low but trap heat if they are high.
Overall, models suggest that clouds cool the Earth. Is this an example of a negative or positive
feedback effect? (pg. 25).
f) When GHGs rise, it gets hotter in summer and in equatorial countries. People then use their air
conditioners more. Is this an example of a negative or positive feedback loop? Draw a “systems
diagram” to illustrate. See lecture note 2.
g) We discussed ice core proxy measures which allow scientists to estimate temperatures and GHG
concentrations going back 800,000 years. Fossils are another type of proxy measure, which allow
estimates to be made even further back in time. Briefly explain how scientists use fossil ferns to get
proxies of past temperatures going back tens of millions of years. Based on such proxies, i) how
high might the atmosphere’s carbon dioxide concentration rise to if we burn the estimated remaining
fossil fuel reserves? How far back in time do we need to go to get estimates of CO2 that are this
high? (pg. 42 – 43)
h) Currently, the atmosphere’s concentration of carbon dioxide is 392 ppm. Based on the graph
on page 41, how far back in time do we need to go to get CO2 concentrations that are this high.
Based on the temperature graph immediately above the CO2 graph, how much higher were the polar
temperatures relative to today?
i) Based on pg 27, identify human caused sources of nitrous oxide (N2O). How long is the average
N2O molecule expected to remain in the atmosphere?

Problem 2: Kaya Equation
a) Please go to the following World Bank website to get the population for China in 2002.
http://data.worldbank.org/indicator/SP.POP.TOTL?page=2

b) Consider the following numbers for China in 2002:

Average GDP/capita = $ 4379/person
CO2 emissions from energy use = 0.26483 tonnes CO2/megaWatthour.
Average Energy Used to Produce each unit of GDP = 2548 megaWatthour/million $.

Find per capita GDP for China in 2002.

c) Find aggregate energy CO2 emissions for China in 2002.

Problem 3:
Coal is the single largest source of GHG emissions in the world. In 2010, the combustion of coal to
produce electricity, to provide heat, and to make steel caused 13.029 gigatonnes (Gt) of CO2 to be
released into the atmosphere. In this question, we will assume there is one type of coal and that
there is one global coal price. 1

Let P represent the price of coal in $ tonne and let Q represent the quantity in Gt/year.

Suppose that the world supply and world demand for coal are respectively represented by the
equations:
QS(P) = P/

10

QD(P) = 10 – P/40

Note that I have assumed linear demand and supply curves for heuristic purposes while in reality, we
would expect demand to get steeper and steeper at low quantities and supply to become steeper and
steeper at high quantities. The market equilibrium point is roughly calibrated to data with quantity
being accurate and price not being accurate. Assume competitive markets although this may be a
poor assumption given oligopolistic markets.

a) Find the inverse demand and inverse supply for coal and use these to get the marginal private
cost and marginal private benefit (marginal WTP) equations.
b) Plot the marginal $ private benefit ($MBPrivate) and marginal $ private cost (MCPrivate) curves on
the graph paper provided (figure 1). Label axis including units and give your graph a title.
b) Equate MBPrivate with MCPrivate to find the market equilibrium quantity and price of coal and
label on your graph.
c) At the market equilibrium quantity, find the following and label on your graph. Please show
work.

i) Total $WTP to pay for coal (total consumer benefits)
ii) Total $ Consumer Expenditure on coal (total consumer costs)
iii) Total $ Producer Revenue from coal (total producer benefits)
iv) Total $ Producer Variable Costs
v) Total $ Producer Surplus
vi) Total Private Surplus

d) Each tonne of coal combusted created an average of 1.7 tonnes CO2 in 2010. Suppose that the
2011 carbon price is $100/tonne CO2, that is each tonne of CO2 causes $100 of damages to society.
Multiplying, we get an estimate of the marginal external cost of coal (MCExternal) of $170/ tonne. We
will ignore other coal damages like local air pollutants such as SO2, NOx, Mercury (Hg), ground
level ozone, and ecosystem damages due to mining. Add the MCExternal to the MCPrivate to get the
MCSocial as a function of the quantity of coal.
e) Re-plot the marginal private cost and marginal private benefit curves on figure 2 along with the
marginal external cost, marginal social cost and marginal social benefit curves. Re-label the market
quantity and price.
f) Solve for the socially efficient quantity and price and label on your graph.
g) At the socially efficient quantity and price, label the following:

i) total external costs

1 In reality, there are a variety of different types of coal and these are used for a variety of purposes including electricity
and heat production and coking coal to make steel. Also, coal prices are differ between regions. To do this properly, we
would need to weight different coal prices by the quantity of each type.

ii) total private costs
iii) total social costs
iv) total social benefits
v) total social surplus
vi) loss of total social surplus (deadweight loss at the market quantity)

h) What world coal quota could you impose to attain monetary social efficiency? Illustrate on your
graph.
i) Calculate the marginal tax on coal producers that could be used to attain monetary social
efficiency and illustrate how this shifts the coal supply curve. Label the marginal tax.
j) Label the total tax collected and calculate.
k) Both the quota or the tax policy will theoretically increase coal prices by the same amount causing
increases in the price of electricity, heating and steel. These price increases will hurt poor and
middle-income people. Which of the above two policies would provide the government with the
ability to compensate the poor and to finance low GHG energy adoption? Briefly explain.
l) Would these policies provide incentives for firms to develop carbon capture and storage
technology (CCS)?

Note: I have ignored positive externalities from coal. Coal is used to provide the energy to make
many goods (ex. education, immunization), many of which confer positive externalities.

Figure 1: _____________________________________________________________

Figure 2:______________________________________________________

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