178.307 markets, firms and consumers lecture 7- natural resource economics

178.307 Markets, Firms and Consumers

Lecture 7- Natural Resource Economics

Introduction

Many firms employ natural resources– Non-renewable resources

Coal Iron ore Oil

– Renewable resources Fish Forests

Distinction between exhaustible and non-exhaustible is not preferred.

What makes Natural Resources different?

Time– The efficient use of

natural resources depends on time.

– This dynamic nature makes these inputs different from other inputs (like capital).

Public Ownership– Many natural resources

are not privately owned.– Forests, fisheries and

mineral deposits are often owned by the state.

Elementary Capital Theory We consider natural

resources as a form of capital.

– We then derive the arbitrage equation.

– Let pt be the price, vt be the rent of a durable asset.

– Firm is indifferent between a numeraire asset and the durable asset.

)()()()(

)(

1

111

111

tptptrtv

ppprv

rp

pv

ttttt

tt

tt

The last equation is expressed in continuous time.

Hotelling’s Rule

Assume that– The stock is sterile. No

benefit derives from holding the stock.

– This implies rental value is 0.

– For convenience, suppose extraction is costless.

)(

)()(

tp

tptr

This defines the optimal extraction of a non-renewable resource (Hotelling, 1931).

Hotelling’s Rule Expanded

The rule implies that the rate of price increase must equal r to maximise profits.

This fundamental rule is difficult to put into practice.

Some empirical studies provide some support for Hotelling’s Rule.

– In strong form it assumes perfect foresight by firms.

– Technological change must also be accounted for.

Are natural resources getting depleted?

Economists used to be pessimistic. Jevons stockpiled paper.

Post-war studies came up with surprising results.

Prices (fundamental measure of scarcity) for natural resources have tended to fall.

A price increase indicated in late 70s.

Prices have since fallen again

– Simon’s Bet

Simon’s Bet

Mineral Qty (lbs) 1980 price 1990 price

Copper 196.56 $200 $163

Chrome 51.28 $200 $120

Nickel 65.32 $200 $193

Tin 229.1 $200 $56

Tungsten 13.64 $200 $86

How does the Market Economy solve scarcity?

Economise on resources that become more expensive.

– OECD oil-consumption peaked in 1978.

Increase supply– exploration

Innovate– Horizontal bores in oil-

wells

Reward Innovation– Patents– Fibre-optics,

communication satellites- less copper.

Winner’s Curse

Derived from auctions of drilling rights (1971).

Auctions are common value auctions.

Even if estimates of value are unbiased, they are dispersed.

Even if risk averse, a firm may overbid based on a high provided estimate.

Effect increases with increase in number of bidders.

Winner’s Curse

Curse 1– The bid exceeds the

value of the tract and the firm loses money.

Curse 2– The value of the tract is

less than expert’s estimate.

– The firm is disappointed.

Solving for optimal bid is not trivial.

– More bidders implies you must bid aggressively to win.

– More aggressive bidding means you are more likely to overestimate value.

Winner’s Curse has been applied to other problems (IPOs).

Renewable Resources

The problem here is the resource can reproduce.

Solution concepts depend on tools of dynamic optimisation (and sometimes stochastic calculus).

Hamiltonians beyond scope of this paper…it’s rocket science.

Forestry Rotation

The fundamental rule for optimal exploitation of forests is the Faustmann solution.

“Kaingaroa Timberlands aim to increase target rotation age from 25-26 years to 29-30 years over the next 10 years. CHH is moving towards target rotations of 28-32 years”.

– Bruce Manley, NZ Journal of Forestry, November 2004.

Single Rotation

)()(

)()(

0)()(

)(

TpfTfp

r

TfpeTpfre

TfpeTpfreT

cTpfe

rTrT

rTrT

rT

Multiple Rotation

ccTpfeJ

ctpfectpfecJ

i

Tr

rtrt

i

)(

)()(

1

11

This occurs because the producer faces the same problem in every rotation, hence becomes a convergent geometric progression.

This simplifies to…

ce

cTpfJ

ccTpfe

J

rT

rT

1)(

)(1

1

Differentiate with respect to T (quotient rule), set equal to 0.

21

))((1)(

0

rT

rt

rTTe

recTpfeTfp

J

1))((

)( rT

rT

erecTpf

Tfp

Solution

rT

rTrt

er

cTpfTfp

eer

cTpfTfp

1)()(

)1()()(

Discussion

Faustmann formula is difficult to employ because

– Age of trees differ– Forests have multiple

values, not just timber production

Many natural resources however are extracted at rates above profit maximising levels.

Public Ownership

Government’s may have different objectives than maximising long term profits.– NZ over-harvested native trees in 50s-70s.– Policy was to lower timber costs (flood market).– This would lower housing prices.

State Ownership can be source of inefficiency.

Fundamental problem is the “Tragedy of the Commons”.

An open access resource will be over-harvested with multiple users.

Tragedy of the Commons solved by:

Private Property Rights– Access limited by prices, – Freedom of contract– Torts to recover damage

from trespass. Used to have right to

trespass when hunting game.

Communal Property Rights

– Access limited to members of a community.

– Extraction rates determined by customs.

Public Property

Access limited by– Regulations– Bureaucratic controls.

But…– Property rights that are

either unenforced or unenforceable lead to open access problems.

Many fisheries managed as public property.

– Incentives to over-harvest weakly influenced by regulations.

– Enforcement costly and imperfect

– Fishers subsidised!

References

Thaler (1997) Anomalies: The Winner’s Curse.

http://links.jstor.org/sici?sici=0895-3309%28198824%292%3A1%3C191%3AATWC%3E2.0.CO%3B2-Y