Assignment: The Economics of Global Warming

L6_ Practice Problems Direct Regulation Externalities in Markets for goods, services or Inputs

Ruth Forsdyke Regulating Negative Externalities: 1) This problem continues on from the L5 and L6 Practice Problem: Note: Demand and Supply Curves are hypothetical but roughly intersect world demand and price point.

QD(P) = 190 – P QS (P) = 3P/2 – 60

The marginal external cost is: MCExternal = 25$/bbl (assumed low carbon tax of $50/tonne CO2e) The quantity units are in millions bbl oil/day while the price units are in $US/bbl. a) Find the marginal Pigouvian tax to regulate this market and plot on your graph. Illustrate how this shifts the producer’s marginal cost curve. b) Starting at the point in time immediately after the tax is imposed, explain the process by which the market moves to the new equilibrium. c) Use areas under curves to illustrate the following under the tax and indicate whether they rose or fell:

i) total consumer surplus ii) total producer surplus iii) total external costs iv) total social surplus v) total tax revenue

d) Find the monetarily socially efficient crude oil quota and label on your graph. e) Starting at the point in time immediately after the quota is imposed, explain the process by which the market moves to the new equilibrium. f) Use areas under curves to illustrate the changes in the following due to the quota:

i) total consumer surplus ii) total producer surplus iii) total external costs iv) total social surplus v) total quota rent (goes to firms if given away, goes to government if auctioned in perfectly competitive market with no corruption, i.e. regulatory capture).

Variable vs Fixed External Costs: 2) Suppose that you take a return trip by Air from Halifax to Vancouver and back. The GHGs due to combustion of the fuel used to power your trip are approximately 1 tonne of CO2e. Suppose the price of carbon dioxide is $200/tonne CO2e. This is only part of your carbon footprint—by taking the trip, you are also responsible for some very small fraction of the emission used during the air plane’s product life cycle and also that of the air port. These get diluted out over many people and so your airplane trip still has a carbon footprint of about 1 tonne. Like private costs, external costs can be either fixed or variable. Identify some variable and fixed external costs of your trip. Positive Externalities from Forests: 3) Consider the town of Thneedville. Their monetary marginal willingness to pay for a truffala forest is: MWTP = 10 – Q/2 (in millions of $/hectare) Suppose that the monetary marginal opportunity cost of the forest is cutting down the forest to make thneeds is MCPrivate = 10Q (in millions of $/hectare)

Suppose that the forest stores 2000 tonnes of CO2e/ hectare and that it is estimated that the price of carbon dioxide is $20,000/ tonne. This problem is complicated in reality because it takes time to grow a forest during which carbon dioxide is sequestered in the soil, plants and other organisms. When the forest comes into equilibrium, there will be no net exchange of carbon dioxide with the atmosphere. For simplicity, assume the forest grows immediately and all of the above benefits and costs are in terms of hectares per century.

a) Find the perfectly competitive market equilibrium quantity and price of forest and plot on a graph and label curves and equilibrium.

b) Find the marginal external benefit of forest and plot and label on your graph. c) Find the marginal social benefit of the forest and find the socially efficient price and

quantity. Plot and label on your graph. d) Label the total external benefit from the forest at the SE level and calculate it. e) Label the deadweight loss (i.e. total social surplus loss from the market). f) Suggest a quantity and price mechanism by which to regulate the forest. g) Which of the quantity and price mechanisms is more likely to hit the quantity target? h) Which policy would be easier for government to finance?

4) Suppose that you are considering 3 policies to regulate GHG emissions from buses. These are 1) a tax on buses, 2) a tax on gasoline and 3) a tax on tailpipe CO2 emissions from buses. Compare pros and cons of these policies. 5) List some thneeds that produce positive GHG externalities. Answers: a) The marginal tax is equal to the marginal external cost of $25 at the socially efficient quantity. The producers now pays $25/ barrel to the government increasing their private costs by $25/ barell. The supply curve shifts up by $25/ thneed (red to dashed green). The equation of the new MC private curve is 65 + 2Q/3 (the same as the social marginal cost curve).

$/ barrel

Crude oil (millions barrels /day

PMarket = 100

QMarket = 90

$MCPrivate_Old

$ MBSocial

A

B C

190

40

0 0 190

$ MBPrivate&Social

$ MCSocial = MCPrivate_New = $ MCPrivate_Old + $t

PSE = 115

QSE = 75

D E

F

H G

I

J

65 t = $25/barrel {Marg. tax shifts supply curve up} by)

b) Now, immediately after the tax is imposed, at the old market price of $100/barrel, firms are willing to supply 52.5 million barrels which is less than the demand of 90 million barrels so there is excess demand. The price rises causing demand to fall (move along demand curve). The new regulated market equilibrium occurs when new supply = demand with the new price being $115 and the new quantity being 75 million barrels. This is monetarily socially efficient. c) Use areas under curves to illustrate the following under the tax: i) The new consumer surplus is equal to A = (190 – 115) * 75 million/2 = Total willingness to pay for 75 barrels – total expenditure on 75 barrels = [A+B+C+D+ E+F] – [B+C+D+E+F] = A = $ 2812.5 million. The Tot. Cons. Surplus fell relative to the unregulated market allocation at which it was (190 – 100)*90/2 = $4050 million. ii) The new total producer surplus is equal to B+D which is equal to the producers’ total revenue (their variable benefits) – their total production costs = [B+C+D+E+F] – [ F + E + C] = (115 – 65) * 75/2 = $1875 million. The old tot. prod. surplus was equal to (100 – 40)*90/2 = $2700 which is bigger than under the tax regulation. Hence tot. prod. surplus fell. Note that tot. prod. surplus is also called “variable profits” or “economic rent”. Producers profits fall & hence they may lobby against the tax policy. iii) tot. external costs = C + E = $1875 (green area) iv) tot. social surplus = ABD (note deadweight loss at market allocation is G) = $ 4687.5 million. v) The tot. tax revenue is equal to $25/barrel * 75 million barells = $1875 million = E + C d. Set the Quota at the SE quantity of Oil as illustrated below.

$/ barrel

Crude oil (millions barrels /day

PMarket = 100

QMarket = 90

$ Marginal Private Cost

$ Marginal Social Benefit

A

B C

190

40

0

0 190

65

$ Marginal Private Benefit

$ Marginal Social Cost

PSE = 115

QSE = 75

D

E

F

H

Quota = 75 million barrels/ day

G

I

J

90

e) The money socially efficient quota is applied at the socially efficient level of output. The new supply curve is the same as the old supply curve for quantities lower than the quota after which it becomes vertical at the quota (dashed crimson line). At the old market price of $100/ barrel, the demand is 90 million barrels while the supply is 75 million barrels such that there is excess demand. This drives the price up PSE = $100/thneed until the demand equals new supply at QSE = $ 100 mill barrels per day. f)

i) $ Total Consumer Surplus = $Total Willingness to Pay (Benefits) - $ Total Expenditure (Costs)

= [A+B+C+D+E+F] – [B+C+D+E+F] = A = (190 – 115) * 75/2 = $ 2812.5 million

The total consumer surplus in the unregulated market is (190 – 100)*90/2 = $4050 million/ year. Hence, consumer surplus has fallen. ii) $ Total Producer Surplus = $Total Revenue (Benefits) – $Total Producer Costs = [B+C+D+E+F] – F = B+C+D+E = [$115/thneed * 75 million thneeds] – [40*75 million thneeds + (90 – 40)*75/2] = $ 8625 mill - $ 4825 = $ 3750 million/year.

This is less than the producer surplus under the unregulated market ($ 90 * 90 mill/2 = $4050 million/ year). Hence, in our example, the total producers surplus went down –however, it is possible that it could rise because the price they receive rises (which all else equal increases revenue) while the amount sold falls (which all else equal reduces revenue). In our example, the latter effect dominates the former so our total producer surplus fell.

iii) total external costs = C+E iv) total social surplus = ABD v) total quota rent = E+C (this is how much quotas would sell for in a perfectly competitive auction)

Under quota giveaway, the government collects no revenue. If instead, we auctioned off the quotas, and each quota sold for a price of 25$/bbl, the government would collect a revenue equal to area C+E = 25 $/barrel * 75 million barrels = $1875 million. The total consumer surplus is the same as under the quota give way while the producer surplus is equal to area B+D = (115 – 65) * 75 million/2 = $1875 million. We can see from the small numbers I am getting for total producer surplus and so on that my demand curve intercept is far too low (however, my x-axis is based on the data). Also, the linear curves were employed for heuristic purposes. Also, the demand is by oil refineries and hence, the consumer surplus is the surplus to the refineries. There will be more surplus higher up the supply chain. 2) Fixed external costs include GHGs produced when the airplane was made and when the airport was constructed. These do not vary with the number of flights. Variable GHG costs is 1 tonne/flight* 200 $/tonne = $200. We can see that this carbon tax will provide some deterrent to flying.

3) Positive Externalities from forests a) $ MBPrivate = $ MWTP = 10 – Q/2

$ MC = 10Q To find market equilibrium, set MBPrivate = MCPrivate 10 – Q/2 = 10Q 10 = 10Q + Q/2 = 21Q/2 QMarket = 20/21= 0.9523 hectares PMarket = 10 – 0.9523/2 = $9.5 mill/ hectare ∴the unregulated competitive market will supply 0.9523 hectares at a price of $9.5 million each (the price here represents the net present value over the century).

b) MBExternal = PCO2 * CO2 sequestered / hectare = $ 20,000/tonne * 2000 tonnes/hectare = 40,000,000 $/hectare = 40 mill $/hectare

c) MBSocial = MBExternal+MBPrivate = 40 + 10 – Q/2 = 50 – Q/2 Set equal to MCSocial to get the efficient quantity of thneeds. We assumed no negative externalities, so MCSocial = MCPrivate MBSocial = MCSocial 50 – Q/2 = 10Q QSE = 4.76 & PSE = $47.62 mill $/hectare We can see that the market fails to provide enough of the forest due to the private parties being unable to capture the value of the externalities.

d) TBExternal = 4.76 hectares * 40 mill/hectare = $ 190.4 million. e) See graph. f) A quantity mechanism is a forest floor of 4.7 hectares while a price mechanism is a

marginal subsidy of $40 mill/hectare. Alternatively, if we start out with forest, we could charge a $40 mill/hectare for cutting it down.

g) The quantity mechanism (floor on amount of forest) is more likely to hit the target than the price mechanism (subsidy to conserve forest) because the government is unlikely to have accurate demand and supply curve estimates and hence will have trouble knowing how private parties will react to the tax. Quality mechanisms can also be employed. For example, all logging must sustainable practice standards.

h) The marginal subsidy is going to be expensive to finance. If the subsidy is relative to BAU (here the market quantity), the government is may mis-estimate this and end out paying too much subsidy. An alternative is to use nature as the baseline and to tax all alternative uses by $40 million/ hectare_century. The forest would generate revenue for the government and this could be used to reduce taxes elsewhere and to finance public goods.

4 a) A tax on buses only provides an incentive to reduce the number of buses. This will lower GHGs from buses but provides no incentive to develop low GHG buses. b) Since gasoline produces GHGs upon combustion and since a tax on gasoline will provide incentives to use less gasoline, this will provide an incentive for firms to produce buses that use less gasoline and potentially less GHGs. However, we also better make sure that there is a tax on liquefied coal because if the price of gasoline rises too much, liquefied coal may be used and this will also cause a lot of GHGs. c) A tax that is levied on the actual emissions from each bus would be difficult to implement due to needing to put emissions monitors on every bus (or car). Bus companies might tamper with the monitors to save money on the tax increasing government’s regulatory costs further. Although directly targeting transport GHGs would however provide incentives to reduce GHGs and might also provide incentives to invent ways to capture GHG emissions from transport vehicles, making a target on GHGs ideal in theory, in practice, scientists do not think that it is likely that we will be able to capture and store emissions from mobile sources such that the expected benefits of directly targeting transport GHG emissions are not expected to outweigh the additional regulatory costs of CO2 monitoring. The simplest policy on transport GHGs are levies on the final transport fuel that are proportional to the GHGs emitted when the gasoline is combusted. Taxes on GHG emissions can also be levied further up the supply chain at refining, transport, and processing and extraction stages. This will be an efficient way to tax gasoline and diesel as the tax will be proportionate to the GHG’s produced along the entire lifecycle. Transport fuels from high GHG sources like Tar Sands would be relatively expensive providing incentives to use the least dirty transport fuel during an oil phase-out. 5. An example of thneeds, which provide positive externalities are natural ecosystems like forests, wetlands and marine areas. A quantity mechanism to achieve socially efficient amounts of forests is a quantity floor (ex. National and Provincial Parks) or a subsidy. Households, firms and governments could be paid subsidies for the amount of natural ecosystems they conserve. Green subsidies can be financed by taxes on negative externalities. Another example is replacing high GHG energy source (ex coal) with wind turbines. The positive externality from the wind turbine equals the savings in external costs from not combusting coal minus wind power GHGs. Note that most of the externalities from wind are fixed external costs incurred when manufacturing the wind turbines as well as fixed costs on site such as roads to access turbines, costs of manufacturing computer equipment and so on.