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: –fixed supply of depletable resource –demand is constant –MWTP: P = 8-0.4Q –MC = $2 (constant)

Period 1Period 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? 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?

Period 1Period units in period 1 / 5 units period 2

Period 1Period units in period 1 / 10 units 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

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.

Period 1Period units in period 1 / units period

check and what is PVNB? pd. 1 = $45 – ½ * $ *4.762 = $ pd. 2 = $45 – ½ *$2.0952*5.238 = $ –(then discount) –assume r=10% –$ /(1+r) = $ –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, 1 st period gets more than 2 nd 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 1 st 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 1Period 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 1Period efficient allocation units in period 1 / units period 2: $40.46 period 1 / $39.51 period 2 (now current value!)

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 $ $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!