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Section 3/6/2009

- VSL
- Static vs. Dynamic Efficiency
(Example: optimal extraction of a non-renewable resource)

- Defining/ measuring scarcity
- Definitions of sustainability
- These concepts are all important for the part of the course we are now covering: natural resource economics

VSL

- How to value reductions in risk of mortality?
- Empirical Methods include those we have already seen- hedonic wage studies, averted behavior studies, and contingent valuation
- VSL is also a concept used
- VSL is people’s stated or revealed marginal valuation for a small change in risk, standardized (extrapolated) for a risk change of 1.0 (one life).

VSL Continued

- VSL= MWTP or MWTA/ small risk change
- MWTP or MWTA estimated from hedonic wage or contingent valuation
- Important remember: this is not a value of a life
- Not in ethical terms
- Not in technical terms
- Not in economic terms (due to non-linearity)

- Government uses VSL estimates in decision making
- Remember: calculations on per life saved basis, ignore scale of policies

Static vs. Dynamic Efficiency

- Review: static efficiency?
- maximizing welfare (net benefits) at a point in time
- Assumes that time is not a crucial part of the decision (what you do now does not affect future)
- i.e. one period model
- O.k. for pollutant that dissipates rapidly or reproducible capital, etc.

MB

MC

Demand = 8 – 0.4(Q)

MC = 2

What is the quantity consumed that satisfies static efficiency?

Net MB = 6 – 0.4 (Q)

Another way to see the same thing. . .

All these graphs point to the same thing:

Static efficiency would be achieved by consuming 15 units of the resource.

BUT

- Today’s use of a non-renewable resource affects our ability to use it tomorrow
- So we must consider dynamics
- Dynamic efficiency:
- Maximizing total welfare over a set of time periods
- Equivalent to maximizing the sum of the net present values of all benefits
- We need to use it when time imposes significant constraints on a problem
- E.g. in our example, we have two periods and total availability of resource is less than 30 units

Choosing the dynamically efficient allocation of a non-renewable resource

Understanding the tradeoff:

In standard consumption framework, we are trading off the consumption of two goods.

We maximize utility (as a function of both goods) subject to budget constraint.

Now: trading off the consumption in different time periods, subject to budget constraint (total stock of resource)

U

Period 2 consumption

Period 1 consumption

Choosing dynamically efficient allocation, cont. non-renewable resource

- First, we must convert value of benefits from different time periods into present value terms (why?)
- Recall:
- Compounding:
Future Valuet = Present Value · (1 + r)t

- Discounting:
Present Value = Future Valuet / (1 + r)t

Choosing dynamically efficient allocation, cont. non-renewable resource

- In our example the discount rate was 10%
- So: divide net marginal benefits in current value terms by 1.10 to get the net marginal benefits in present value terms
- Now our benefits are expressed in the same units (dollars today) and can be compared

PERIOD TWO (now in present value terms) non-renewable resource

PERIOD ONE

Net MB = 6 – 0.4 (Q)

Net MB = 5.45 – 0.36 (Q)

Choosing dynamically efficient allocation, cont. non-renewable resource

- Now we must find the solution that maximizes total (present value) net benefits from both periods.
- How do we find this?
- Solution will be where the present values of marginal net benefits are equal
- (same idea as consumption of goods—where ratio of marginal benefits equals price ratio)

Graphically. . . non-renewable resource

PERIOD ONE non-renewable resource

PERIOD TWO (now in present value terms)

Net MB = 6 – 0.4 (Q1)

Net MB = 5.45 – 0.36 (Q2)

Algebraically: set present values of net MB equal to each other

1) 6 – 0.4(Q1) = 5.45 - .36(Q2)

2) Q1 + Q2 = 20 (Budget constraint)

Two equations, two unknowns: solve for Q1, Q2: Q1=10.238; Q2=9.762

Use Q to find prices in each period.

Warning: non-renewable resource

- Please note: static and dynamic optimization are different models. They will usually NOT lead to the same solution!!
- E.g. in our example: static efficiency would call for us to consume Q1=15 in the first period. But dynamic efficiency calls for Q1=10.2.

Measuring economic scarcity. . . non-renewable resource

- Economic scarcity is NOT a measure of how many physical units of a good exist: is is NOT a measure of physical abundance
- It IS marginal user cost: let’s see what that means . . .

Marginal User Cost = the additional marginal value of a resource above marginal cost due to its scarcity.

MUC = P - MC

If we had 30 units of the non-renewable resource, we know we would just have used 15 in each period.

Price = MC.

Marginal user cost = 0

The resource would not be economically scarce.

The opportunity cost of using the resource today would have been zero, because it wouldn’t affect our use of the resource tomorrow.

BUT: SCARCITY? resource above marginal cost due to its scarcity.

If we only have 20 units.

Marginal User Cost = the additional marginal value of a resource due to its scarcity.

MUC = P- MC

Now, the resource is economically scarce: the efficient price will be higher than the marginal cost of extraction

Our decisions about use today affects our use of the resource tomorrow.

Efficient pricing takes into account the opportunity cost: today’s price is higher than it would be if the resource were unlimited.

Hotelling rule for non-renewable resource prices resource above marginal cost due to its scarcity.

- Assumes a model with constant marginal extraction costs; assumes efficient rates of extraction
- States that the marginal user cost (MUC) will rise at the rate of interest.
- MUC1*1.10 = MUC2
- 1.095*1.10 = 2.095

But economic scarcity is a dynamic concept; it may change over time. Why?

- You tell me. . .
- What might affect marginal user cost over time?
- Changing marginal extraction costs
- Cheaper extraction technologies

- Development of backstop technologies (substitutes)
- Discovery of new reserves
- Changing tastes for a resource
- Discount rate

- Changing marginal extraction costs
- Try to makes sense of how each one might affect marginal user cost (see Tietenberg text for help)

How would a higher discount rate affect the efficient allocation of a non-renewable resource?

- Suppose we had a higher discount rate: 40% instead of 10%
- What would this do to the allocation between periods?
- Would consume more in period one, less in period two; more weighting on period one
- Marginal user cost for period one would decrease: also indicates smaller opportunity cost from using more of the resource today

Defining economic sustainability allocation of a non-renewable resource?

- Several definitions of economic sustainability proposed: still a controversial subject
- Economists tend to define sustainability in terms of intergenerational equity.
- E.g. Tietenberg (p.94): “The sustainability criterion suggests that at a minimum, future generations should be left no worse off than current generations. . . .earlier generations are at liberty to use resources that would thereby be denied to future generations as long as the well-being of future generations remains just as high as that of all previous generations.”
- Tietenberg also distinguishes between
- “weak sustainability” which implies that the value of the total capital stock (natural capital plus physical capital) should not decline
- “strong sustainability” which implies that the value of the stock of natural capital itself should be preserved

Sustainability, cont. allocation of a non-renewable resource?

- Dynamically efficient allocations have the potential for producing intergenerational equity but will not automatically fulfill this criterion (and vice versa).
- Note that economists define sustainability in terms of economic well-being. This may be different from the way that natural scientists tend to think of it: as maintaining specific levels of ecosystem capability in a physical sense. (Just like economic scarcity, economic sustainability is not defined in physical terms.)
- For another definition of sustainability, see the paper by Wagner, Wagner and Stavins: “Interpreting sustainability in economic terms: dynamic efficiency plus intergenerational equity.” Economic Letters, 2002 (see www.stavins.com)

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