Climate Change and Policy¶

Some science¶

What we know:

Accumulation of $CO_2$ and other so called greenhouse gases (GHG) reduce the earth's ability to reflect energy outwards
High levels of GHG concentrations in atmosphere

In [3]:

from IPython.display import Image
display(Image('http://www.forestcarbonasia.org/wp-content/uploads/2010/09/Sciencefig41.jpg'))

Some science, continued¶

What we don't know:

Full carbon budget
- All GHG inputs
- Full functioning of GHG sinks (we know about 75%)
How GHG output from human choices will change in future

Predicted Outcomes¶

Our best estimate is that warming will continue and accelerate into the next century.
A number of estimated side effects
- Sea Level Rise
- Migration of Tropical Disease
- Desertification
- Increase in strength and severity of storms

Sea Level Rise in Bangladesh and India¶

In [4]:

display(Image('http://www.grida.no/images/series/vg-climate/large/33.jpg'))

Sea Level Rise here in the US:¶

In [5]:

display(Image('http://i.kinja-img.com/gawker-media/image/upload/s--UQ4oZZnu--/c_fit,fl_progressive,q_80,w_636/fvdlozrtgd52iidtjimy.png'))

In [6]:

display(Image('http://www.easterbrook.ca/steve/wp-content/IPCC-AR5-Fig-12.5.png'))

Cost Benefit Analysis with large, nearly existential, threats far into the future¶

Most probabilistic estimates put sea level rise at approximately 1 meter for our region over the next century. There is evidence that in the past very large sea level changes have occured in relatively short periods of time:

To see what may happen scientists of CEREGE laboratory and the Universities of Tokyo and Oxford have studied the largest known ocean level rise: Melt-Water Pulse 1A. They found that during a relatively warm period called the Bølling Oscillation roughly 14,650 years ago sea levels rose an average of 14 meters in just 350 years.

Cost Benefit Analysis: Probabilities¶

To consider how cost benefit analysis works under uncertainty, consider the following simplicifications of the choice problem facing society:

Let the uncertainty as to the severity of climate change impacts be
- $\pi_{N}$ = the probability of no impacts
- $\pi_{H}$ = the probability of a high impact event
- $\pi_{L}$ = the probablity of a low impact event

Cost Benefit Analysis: Payoffs and Costs¶

We need to characterize the payoffs of the various states of the world that might happen in the future:

Policy Outcome	Impacts	GDP	Costs (% GDP)	Damages (%GDP)
No Abatement	None	$B$	0	0
No Abatement	High	$B$	0	$D_H$
No Abatement	Low	$B$	0	$D_L$
Abatement	None	$B$	C	0
Abatement	High	$B$	C	$D_H^A$
Abatement	Low	$B$	C	$D_L^A$

In [8]:

display(Image('climate_payoff_tree.png'))

The Cost Benefit Analysis:¶

For each node on the payoff tree, calculate the Net Present Value of GDP minus costs of abatement and damages due to climate change through time. For the abatement, high impact node the net present value of all future costs and benefits would be:
$$ B -D^A_H - C =\sum_{t=2015}^{2515}\frac{(B_{t} - D^A_{Ht} - C_t)}{(1+r)^{t-2015}} $$

For the No Abatement portion of the tree calculate the expected payoffs:
$$ E(P_{NA}) = \pi_N B + \pi_H (B - D_H) + \pi_L (B - D_L) $$

Do the same for the abatement portion of the tree:
$$ \begin{align} E(P_{A}) = &\pi_N (B - C) + \pi_H (B - D^A_H - C) + \\ &\pi_L (B-D^A_L - C) \end{align} $$

The Cost Benefit Analysis, cont.¶

We should undertake abatement if $$ E(P_A) > E(P_{NA}) $$

Since all variation across scenarios occurs via the abatement and damage costs, we can simplify this to $$ \pi_H D^A_H + \pi_L D^A_L + C < \pi_H D_H + \pi_L D_L $$
or if
$$ C < \pi_H (D_H - D^A_H) + \pi_L (D_L - D^A_L) $$ which says that if the expected costs of doing nothing exceed the abatement costs we should abate. Notice in our model, abatement doesn't affect the probability of impact types, which is probably unrealistic.

In [9]:

t=arange(500)
GDP_0 = 1 
r = .02
gdp_growth = 1.02
cost_abatement = .03

# the low scenario will take 3% of gdp per year beginning in year 20
# the high scenario will take 3% for year 10-50, 6% for year 51-100, 10% for year 100-150, and 15% thereafter

# this procedure simulates data for 500 year time horizon
def simulate(GDP_current,GDP_growth,COST_abatement,T):
    GDP =  zeros(T.shape[0])
    damage_low =  zeros(T.shape[0])
    damage_high = zeros(T.shape[0])
    cost_abatement = zeros(T.shape[0])
   
    damage_rate_low = 0
    damage_rate_high = 0
    for t in T:
        # defines current year   
        GDP[t] = GDP_current * GDP_growth
        GDP_current=GDP[t] 
        cost_abatement[t] = COST_abatement*GDP_current
        #print COST_abatement,GDP_current,cost_abatement
        # damage for low impact event
        damage_low[t] = (t>10)*.03*GDP_current + (1-(t>10))*0
        # damage for high impact event
        damage_high[t] = 0
        if t>10 and t<50:
            damage_high[t] = .03 * GDP_current
        elif t>=50 and t<100:
            damage_high[t] = .06 * GDP_current
        elif t>=100 and t<150:
            damage_high[t] = .1 * GDP_current
        elif t>=150:
            damage_high[t] = .15 * GDP_current
    return [GDP,damage_low,damage_high,cost_abatement]

def npv(val,t,r):
    npv_val = val/(1+r)**t
    return npv_val

GDP,damage_low,damage_high,C = simulate(GDP_0,gdp_growth,cost_abatement,t)

damage_a_low = .5 * damage_low
damage_a_high = .5 * damage_high

plt.figure(figsize=(7, 4.5), dpi=300)
plt.subplot(111)
lw = 1
plt.xlim(0,200)
plt.ylim(0,2)
plt.title("Costs and Damages Throught Time",fontsize=20)
plt.plot(t,damage_high,color='y', label='Damage High')
plt.plot(t,damage_a_high,color='b',label='Damage High w/Abatement')
plt.plot(t,damage_low,color='r', label='Damage Low')
plt.plot(t,damage_a_low,color='k', label='Damage Low w/Abatement ')
plt.plot(t,C,color='c', label = 'Costs of Abatement')
plt.legend(loc='upper left')
plt.savefig('costs_damages.png', dpi=120)

In [13]:

display(Image('costs_damages.png'))

In [14]:

display(Image('costs_damages_discounted.png'))

In [15]:

display(Image('abate_or_not.png'))

The Stern Review¶

The Stern Review conducted an in-depth Cost Benefit Analysis for climate change mitigation and adaptation for the British Government. They conclude:

From all of these perspectives, the evidence gathered by the Review leads to a simple conclusion: the benefits of strong, early action considerably outweigh the costs.

Policy Approach: The Kyoto Protocol

In [16]:

display(Image('timeline.png'))

In [17]:

display(Image('annex1.png'))

Focus of the Kyoto Protocol¶

Adaptation: seek technical solutions for lessening severity of climate impacts
- Build sea walls
- Develop drought resistant/resilient crops
- Move populations inland
Mitigation
- Abate carbon emissions
- Enhance carbon sinks
- Geo-engineering

Focus on Mitigation: What are the sources of GHG?¶

In [18]:

display(Image('emissions_sources.png'))

Mitigation: How do we assign cuts to countries?¶

Energy Intensity
Historical Accountability
Per Capita Intensity

In [19]:

display(Image('emissions_sources2.png'))

In [20]:

display(Image('historical_account.png'))

In [21]:

display(Image('per_cap_emissions.png'))

The Market Failure¶

GHG free (or low GHG) atmosphere is a common-property open access resource
- Rival
- Non-excludable
One country's emissions affects everyone else's climate
Location of GHG emissions irrelevant: it uniformly affects everyone

Policies¶

Country-level GHG limits (standards)
International Market-based Policies
- Carbon tax
- Tradable Pollution Permits- fully tradable firm to firm across country boundaries
- Technology transfer programs (Clean Development Mechanism)

Carbon Taxes¶

Most of the reductions in carbon emissions over the next twenty years will occur because of a shift away from high intensity (high carbon content) fossil fuels.

Idea: Charge per unit tax based on carbon content of fossil fuel

Taxes based on Carbon Intensity¶

	Coal (ton)	Gas (Gallon)	Natural Gas (1000 cf)
Tons of Carbon per Unit	.605	.0098	.06
Average price (2015)	\$55.00	\$2.50	\$12.00
Carbon Tax:
Absolute Tax:	\$/ton	\$/Gallon	\$/1000 cf
\$20/ton Carbon	\$12.10	\$0.198	\$1.20
Tax as % of price:	22.0%	7.84%	10.0%

Currently, in the European Permit Trading System, the carbon price is around \$5/ton.

In [23]:

# plot direct effect of tax (ignoring shifts due to price changes in related markets):
p_oil_equil_t = p_ngas_equil*1.25
p_ngas_equil_t = p_ngas_equil*1.1

#solve for q_oil_equilibrium at own price above, holding substitute
#prince at pretax levels: partial equilibrium
q_oil_equilibrium_tp = q_oil(p_oil_equil_t,p_ngas_equil)
q_ngas_equilibrium_tp = q_ngas(p_oil_equil,p_ngas_equil_t)

plt.figure(figsize=(12,5),dpi=100)
plt.tight_layout
plt.subplot(1, 2, 1)
plt.plot(graph_q_oil_0,poil,c='r')
plt.plot((0,q_oil_equilibrium_tp),(p_oil_equil_t,p_oil_equil_t),'k--')
plt.plot((q_oil_equilibrium_tp,q_oil_equilibrium_tp),(0,p_oil_equil_t),'k--')
plt.plot((0,q_oil_equilibrium),(p_oil_equil,p_oil_equil),'k--')
plt.plot((q_oil_equilibrium,q_oil_equilibrium),(0,p_oil_equil),'k--')
plt.arrow(q_oil_equilibrium-.2, 7, -.8*(q_oil_equilibrium - q_oil_equilibrium_tp),0, head_width=3, head_length=.7, fc='k', ec='k')
plt.arrow(7,p_oil_equil+.2, 0,.7*(p_oil_equil_t-p_oil_equil), head_width=1.3, head_length=.8, fc='k', ec='k')
plt.annotate('new price = $40 x (1.25)', xy=(0,50.5), xytext=(10, 70),arrowprops=dict(facecolor='black', shrink=0.05,
                      width=2,headwidth=9))


plt.xlim(0,55)
plt.title('More Carbon Intensive (t=25%)')
plt.ylabel('Price')
plt.xlabel('Quantity of Coal')

plt.subplot(1, 2, 2)
plt.plot(graph_q_ngas_0,pngas,c='g')
plt.plot((0,q_ngas_equilibrium_tp),(p_ngas_equil_t,p_ngas_equil_t),'k--')
plt.plot((q_ngas_equilibrium_tp,q_ngas_equilibrium_tp),(0,p_ngas_equil_t),'k--')
plt.plot((0,q_ngas_equilibrium),(p_ngas_equil,p_ngas_equil),'k--')
plt.plot((q_ngas_equilibrium,q_ngas_equilibrium),(0,p_ngas_equil),'k--')
plt.arrow(q_ngas_equilibrium-.2, 7, -.5*(q_ngas_equilibrium - q_ngas_equilibrium_tp),0, head_width=5, head_length=.7, fc='k', ec='k')
plt.arrow(7,p_ngas_equil+.2, 0,.8*(p_ngas_equil_t-p_ngas_equil), head_width=1.3, head_length=.8, fc='k', ec='k')
plt.annotate('new price = $40 x (1.1)', xy=(0,44.5), xytext=(10, 70),arrowprops=dict(facecolor='black', shrink=0.05,
                      width=2,headwidth=9))


plt.xlim(0,55)
plt.title('Less Carbon Intensive (t=10%)')
plt.xlabel('Quantity of Natural Gas')
plt.savefig('tax2.png', dpi=150)

In [24]:

# now model impact of substitute prices:
#solve for q_oil_equilibrium at own price above, holding substitute
q_oil_equilibrium_t = q_oil(p_oil_equil_t,p_ngas_equil_t)
q_ngas_equilibrium_t = q_ngas(p_oil_equil_t,p_ngas_equil_t)

#Need to calculate shifted demand curve (since subs price increased):
# generate data to plot demand curve
graph_q_oil_1 = q_oil(poil,p_ngas_equil_t)
graph_q_ngas_1 = q_ngas(p_oil_equil_t,pngas)


plt.figure(figsize=(12,5),dpi=100)
plt.tight_layout
plt.subplot(1, 2, 1)
plt.plot(graph_q_oil_0,poil,c='r')
plt.plot(graph_q_oil_1,poil,'r--',label='Demand After Substitutes')
plt.plot((0,q_oil_equilibrium_t),(p_oil_equil_t,p_oil_equil_t),'r--')
plt.plot((q_oil_equilibrium_tp,q_oil_equilibrium_tp),(0,p_oil_equil_t),'k--')
plt.plot((0,q_oil_equilibrium),(p_oil_equil,p_oil_equil),'k--')
plt.plot((q_oil_equilibrium,q_oil_equilibrium),(0,p_oil_equil),'k--')
plt.arrow(q_oil_equilibrium-.2, 7, -.8*(q_oil_equilibrium - q_oil_equilibrium_tp),0, head_width=3, head_length=.7, fc='k', ec='k')
plt.arrow(7,p_oil_equil+.2, 0,.7*(p_oil_equil_t-p_oil_equil), head_width=1.3, head_length=.8, fc='k', ec='k')
plt.annotate('new price = $40 x (1.25)', xy=(0,50.5), xytext=(10, 70),arrowprops=dict(facecolor='black', shrink=0.05,
                      width=2,headwidth=9))
plt.plot((q_oil_equilibrium_t,q_oil_equilibrium_t),(0,p_oil_equil_t),'r--')

plt.legend()
plt.xlim(0,55)
plt.title('More Carbon Intensive (t=25%)')
plt.ylabel('Price')
plt.xlabel('Quantity of Coal')

plt.subplot(1, 2, 2)
plt.plot(graph_q_ngas_0,pngas,c='g')
plt.plot(graph_q_ngas_1,pngas,'g--',label='Demand After Substitutes')
plt.plot((0,q_ngas_equilibrium_t),(p_ngas_equil_t,p_ngas_equil_t),'g--')
plt.plot((q_ngas_equilibrium_tp,q_ngas_equilibrium_tp),(0,p_ngas_equil_t),'k--')
plt.plot((0,q_ngas_equilibrium),(p_ngas_equil,p_ngas_equil),'k--')
plt.plot((q_ngas_equilibrium,q_ngas_equilibrium),(0,p_ngas_equil),'k--')
plt.arrow(q_ngas_equilibrium-.2, 7, -.5*(q_ngas_equilibrium - q_ngas_equilibrium_tp),0, head_width=5, head_length=.7, fc='k', ec='k')
plt.arrow(7,p_ngas_equil+.2, 0,.8*(p_ngas_equil_t-p_ngas_equil), head_width=1.3, head_length=.8, fc='k', ec='k')
plt.annotate('new price = $40 x (1.1)', xy=(0,44.5), xytext=(10, 70),arrowprops=dict(facecolor='black', shrink=0.05,
                      width=2,headwidth=9))
plt.plot((q_ngas_equilibrium_t,q_ngas_equilibrium_t),(0,p_ngas_equil_t),'g--')
plt.legend()
plt.xlim(0,55)
plt.title('Less Carbon Intensive (t=10%)')
plt.xlabel('Quantity of Natural Gas')
plt.savefig('tax3.png', dpi=150)

Tradable Carbon Permits¶

Each nation allocated a set amount of carbon emissions
- Emissions allocated to firms
- Nations might trade
- Firms might trade (inter and intranationally)
Leads to global least cost solution for set amount of carbon emissions
Developed countries could transform these Carbon Permits into an export commodity by choosing a non-carbon technology.

In [29]:

display(Image('cdm.png'))

In [31]:

display(Image('http://cdn.static-economist.com/sites/default/files/imagecache/full-width/images/2013/02/blogs/schumpeter/20130216_woc070_0_0.png'))

In [32]:

display(Image('design1.png'))

In [33]:

display(Image('design2.png'))

In [34]:

display(Image('design3.png'))

Taxes versus Standards (or Permits)¶

Advantage depends on the shape of the MCC curve
The MCC for carbon (for current levels) is extremely elatistic
The benefits of pollution reductions depend on stocks, and these are unaffected by current period pollution
The MCC depends on flows (emissions this year)

In [35]:

display(Image('nyt.png'))

In [36]:

display(Image('forbes.png'))

Market	Original Demand	Own Price Demand	Demand After Substitutes
Coal	40	35	36
Gas	40	38	40.5