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Chapter 5

Efficiency and Sustainability

We bring together MWTP and MC

1. Static Efficiency

• Static: from the perspective of a single time period, in particular the present one

• The rate of output q* is socially efficient; it yields the maximum net benefits to society– Total social benefits = a + b– Total social costs = b– Net social benefits = (a + b) – b = a; also CS + PS

• At other output levels, net benefits are not maximized

2Page 71: Figure 5-1

2. Dynamic (Intertemporal) Efficiency

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• To choose one time series of quantities that gives the maximum present value of net benefits

• Present value of net benefits = Net benefits in year 0 + (Net benefits in year 1) [1/(1+r)] + (Net benefits in year 2) {1/[(1+r)2]} +…

• The sum should be as large as possible, which means that decisions that increase the net benefits of using a natural resource in the present period often have the effect of decreasing net benefits from the resource in the future

Present value of net benefits = Net benefits in year 0 + Sum of all discounted future net benefits

Present value of net benefits = benefits in year 0 – costs in year 0 + Sum of all discounted future net benefits

If there is a one-unit change (let’s say, increase) in today’s rate of resource use, we have:Change in the present value of net benefits = Change in benefits in year 0 – Change in costs in year 0 + Change in sum of all discounted future net benefits, or

MNB = MCB – MCC + UC– MNB: marginal net benefits– MCB: marginal current benefits– MCC: marginal current costs 4

• UC: user costs; the change (decrease) in the discounted value of future net benefits; the lost present value of future net benefits due to the use of the resource at present; negative

• If the choices of today’s output actually have no future consequences, then user costs would be zero– How much water to take out of a passing river to

irrigate some crops: increasing the amount withdrawn is not likely to have an impact on future water availabilities in the river

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User Costs

• If user costs are not zero, intertemporal efficiency requires that today’s rate of output be set so that MCB is equal to the sum of MCC and the absolute value of UC, i.e., MCC + UC , or ___________

• For a static problem: the intersection of MCC with MCB gives q0

1 as the social efficient rate of output

• For an intertemporal problem: the intersection of MTC (= MCC + UC ) with MCB gives q0

* as the social efficient rate of output in the current period

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User Costs

Page 74: Figure 5-3

3. Natural Resource Rents

• The in situ price of a natural resource is its price as situated in the natural world– The stumpage price for wood, what it sells for on the

stump– The price of a ton of copper in the ground– The price of land to be used for farming

• The in situ price of a natural resource is called its resource rent: it is the value of something that the workings of nature itself have made available

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• The lobster market in New England– The intertemporally efficient quantity is 1.8 million pounds,

and the efficient price is $3.50 per pound– The marginal harvesting cost at this level of catch is $2.80

per pound– The marginal rent = the market price – marginal harvesting

costs = $3.50 – $2.80 = $0.70– Total rent = $0.70/pound * 1.8 million pounds = $1.26

million – Marginal rent is called the stumpage price in timber

economics; it is called the royalty rate in mineral economics

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Page 75: Figure 5-4

• Resource rent and user cost are the same! But they emphasize different perspectives

• A price is a market phenomenon. If there is no market, there can be no rent. If resources produce services that do not pass through markets, then the rent for these resources will not reflect these services

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4. Is it Appropriate to Discount?

• Discounting appears to put a lesser value on future net benefits that on net benefits occurring closer in time

• Whether people actually discount in practice, in their everyday lives? Yes! There are positive interest rates

• Water development projects in the 1960s: up-front construction costs; low discount rates led to high aggregate benefits and greater dam building

10Page 78: Exhibit 5-1

• At the macroeconomic level: low discount rates spur investment, which enhances economic growth rate. By leading to higher rates of production and consumption in the future, higher growth rates cause a greater future demand for natural resources

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5. Efficiency and Intergenerational Equity: The Issue of Sustainability

• Sustainable development: “development that meets the needs of the present without compromising the ability of future generations to meet their own needs”

• Sustainability implies that future generations are to be no worse off than today’s generation

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• In the sense of the physical supplies and availabilities of natural resources, future generations should have no smaller supplies than currently exist

• For renewable resources: ok• For nonrenewable resources: any extraction rate today

must lead to reduced availabilities at some time in the future– We may interpret it as nondiminution of the total of natural

resources– Drawing down a nonrenewable natural resource could be

compensated for by augmenting supplies of a renewable resource

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• Need to recognize that human welfare is based on natural resource capital and other forms of productive capital (human capital and physical capital/produced capital)

• A broader sustainability: Use of a nonrenewable natural resource is sustainable if the value of the resource used up is matched by capital investments of equal value in other natural resource or in productive nonresource capital

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Sustainability, Broadly Considered

• Remember that user cost is a measure of the present value of future net benefits sacrificed as a result of today’s extraction

• If compensating investments can be made sufficient to offset the user costs of a nonrenewable resource extraction, sustainability will be attained

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Sustainability – feasible?Sustainability is a constant level of consumption/utility indefinitely

Production functions with capital and natural resource inputs

Is sustainability feasible when production uses a non-renewable resource input?

tttβRαKQ

1βαwithRKQ β

t

α

tt

For α>β, YES (Cobb Douglas CRS)

YES, perfect substitutability

Qt = min(αKt, βRt) NO, non-substitutability (Leontief)

Perman’s book3rd edition, Ch4

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Weak and strong sustainability

Are not different kinds of sustainability—both refer to constant consumption/utility.

The distinction is between assumptions about substitution possibilities.

For weak sustainability the assumption is that these possibilities are as for the Cobb Douglas production function so that sustainability is feasible via the substitution of K for R.

For strong sustainability the assumption is that these possibilities are as for the Leontief production function.

More generally

Q = Q(L, KN, KH)

where KN is natural capital, and KH is human-made, or reproducible, capital and the weak/strong sustainability distinction is in terms of the substitution possibilities between KN and KH. Perman’s book

3rd edition, Ch4 17

Ecologists on sustainability

Sustainability is a relationship between human economic systems and larger dynamic, but normally slower changing, ecological systems in which (1) human life can continue indefinitely, (2) human individuals can flourish, and (3) human cultures can develop, but in which effects of human activities remain within bounds, so as not to destroy the diversity, complexity and function of the ecological life support system (Costanza et al., 1991).

In effect, ecologists judge the possibilities for substituting KH for KN to be limited, especially in regard to the ‘ecological life support system’.

Sustainability requires resilience—the maintenance of the ecosystem’s functional integrity in the face of exogenous disturbance. Resilience is not guaranteed by following standard economic criteria.

Ecologists, and strong sustainability proponents, argue for explicit protection for ‘critical’ natural capital.

Perman’s book3rd edition, Ch4

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