Transcript sustainability and population

sustainability
chapter 5
what else besides efficiency?
• fairness or justice should accompany efficiency
concern
• this chapter considers one particular concern:
the treatment of future generations
• how to allocate a depletable resource over time?
• using a numerical example, trace out temporal
allocation and show how it is affected by
changes in the discount rate
two-period model
• dynamic efficiency: balances present and
future uses of a depletable resource by
maximizing PVNB
• simplest of models: 2 periods
• assume:
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fixed supply of depletable resource
demand is constant
MWTP: P = 8-0.4Q
MC = $2 (constant)
Period 1
Period 2
two-period model
• notice if total supply 30 or greater
– efficient allocation would just be to produce 15 in
each period, regardless of discount rate
– supply is sufficient to cover demand in both periods
what happens if supply < 30?
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suppose only have 20 units
try 15 units period 1 / 5 units period 2
what is PVNB?
period 1 = ½ *6*15 = $45
period 2 = $45 – ½ *4*10 = $25
– (then discount)
– assume r=10%
– $25/(1+r) = $22.73
• total PVNB = $67.73
• is this the best?
15 units in period 1 / 5 units period 2
Period 1
Period 2
6
10 units in period 1 / 10 units period 2
Period 1
4
Period 2
4
check 10 and 10
• what is PVNB?
• period 1 = $45 – ½ *2*5 = $40
• period 2 = $45 – ½ *2*5 = $40
– (then discount)
– assume r=10%
– $40/(1+r) = $36.36
• total PVNB = $76.36
• better, but is it the best? how do we
know?
how to find the best (optimal) allocation?
• dynamically efficient allocation rule =
present value of marginal net benefit from
the last unit in period 1 equals the PVNB
in period 2.
(MB = P-MC)
Period 1: left to right. Why intersects at $6 and Q = 15?
Period 2: right to left (and discounted, 6 / 1.10 = 5.45)
Draw it this way so that any allocation between periods equals 20
how to solve for efficient allocation?
Efficient allocation (10.238, 9.762) is where two curves intersect.
highest PVNB (compare to others we tried)
Total PVNB is area under NB curves.
Try to allocate another way, and total area will decline.
10.238 units in period 1 / 9.762 units period 2
Period 1
Period 2
4.0952
3.9048
10.238
9.762
check 10.238 and 9.762
• what is PVNB?
• pd. 1 = $45 – ½ * $1.9048 *4.762 = $40.4646
• pd. 2 = $45 – ½ *$2.0952*5.238 = $39.5127
– (then discount)
– assume r=10%
– $39.5127/(1+r) = $35.921
– total PVNB = $76.39
• highest PVNB
marginal user cost
• when resources are scarce, greater current use
diminishes future opportunities
• MUC = present value of those forgone
opportunities at the margin
• uses of resources that would have been
appropriate in the absence of scarcity may no
longer be appropriate once scarcity is present
marginal user cost
• with 30 or more units, no MUC
• with only 20 units, what is MUC?
• PV of MUC? Height btw quantity axis
and intersection (approx. $1.90)
• if 15 each period, would not be any
intersection. So height represents
opportunity cost / MUC due to scarcity
efficient price
• no scarcity:
P = marginal extraction cost
• with scarcity:
P = marginal extraction cost + MUC
solve for efficient prices
under scarcity
• plug efficient quantities into price
equation, P = 8– 0.4Q
• P1 = $3.90
• P2 = $4.09
• supply and demand given by…
MUC is the difference btw price
and MC (extraction cost)
$3.90-$2.00 = $1.90
$4.09-$2.00 = $2.09
(1.90)*(1+r)
discount rate
• affects size of the MUC and the allocation
between periods
• because of discounting, 1st period gets
more than 2nd period
• higher discount rates skew resource
extraction towards the present because
gives future less weight
defining intertemporal fairness
• what do we “owe” the future?
• one starting point: A Theory of Justice, by
John Rawls
– “veil of ignorance,” born not knowing
eventual position (generation) in society –
make up rules they would later have to live by
– what kind of rule might come out of this?
sustainability criterion
• at a minimum, future generations should be left
no worse off than current generations
• are efficient allocations fair?
– in the 2 period model, more is allocated to current
than future
– but 1st period can save net benefits for the future
– if an allocation is dynamically efficient, always
possible to make next generation at least as well off
as any other allocation scheme
is being “fair” optimal?
10 units in period 1 / 10 units period 2:
$40 period 1 / $40 period 2 (now current value!)
Period 1
4
Period 2
4
efficient allocation
10.238 units in period 1 / 9.762 units period 2:
$40.46 period 1 / $39.51 period 2 (now current value!)
Period 1
Period 2
4.0952
3.9048
10.238
9.762
sharing the efficient allocation
better than the equal allocation
• suppose first generation spends $40 and
saves $0.46 for future
• at 10% interest, this would grow to $0.513
• $39.51 + $0.51 > $40
• future better off accepting the
dynamically efficient allocation than the
equal allocation
applying the sustainability
criterion
• how to make this operational?
• Hartwick rule (“weak sustainability”)
– constant consumption can be maintained
perpetually if all scarcity rent / profit
invested in capital
– value of total capital stock will not decline
example
• receive inheritance of $10,000
• put it in bank w/ 10% interest
• if you spend exactly $1,000 per year,
always be $10,000 and the income will last
forever
• spending $1,000 (from interest) is
sustainable
applied to the environment
• current generation has been given an
endowment (total capital)
– total capital = natural + physical
– sustainable use implies we keep the principle
(endowment) and live off of the flow of
services provided
– ensure that the value of the total capital stock
is maintained
substitutability
• can physical capital readily substitute for
natural capital?
• other definitions of sustainability?
strong sustainability
• maintain value of stock of natural capital
environmental sustainability
• certain physical flows of certain individual
resources should be maintained
• not sufficient to maintain the value of an
aggregate
sustainability vs. efficiency
• not all efficient allocations are sustainable
• not all sustainable allocations are efficient
• choose the sustainable allocation that
satisfies dynamic efficiency!