sustainability chapter 5. what else besides efficiency? fairness or justice should accompany...
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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:
– fixed supply of depletable resource– demand is constant– MWTP: P = 8-0.4Q– MC = $2 (constant)
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?• 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?
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
Efficient allocation (10.238, 9.762) is where two curves intersect.
how to solve for efficient allocation?
highest PVNB (compare to others
we tried)
Total PVNB is area under NB curves.Try to allocate another way, and total area will decline.
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
Period 1 Period 2
4
is being “fair” optimal?10 units in period 1 / 10 units period 2:$40 period 1 / $40 period 2 (now current value!)
4
Period 1 Period 2
4.0952
efficient allocation 10.238 units in period 1 / 9.762 units period 2:$40.46 period 1 / $39.51 period 2 (now current value!)
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?
environmental sustainability• certain physical flows of certain
individual resources should be maintained
• not sufficient to maintain the value of an aggregate
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