1. Environmental Economics 2
Lecture 6
Non-Renewable Resources

2. Overview of this part… Natural Resources theory:
Non-renewables
Renewables
Applied studies of theory – is it true?
Fisheries
Forestry
Energy security – valuation issues
Climate Change

3. Health warning This lecture contains a lot of maths.
Later lectures won’t be quite so bad (promise!!!)
Key: understanding the concepts, not necessarily the maths
Though if you can handle the maths this would be great.

4. Readings This lecture largely based on chapters 7,8,9 of HSW
More advanced – see Conrad and Clark chapter 3
Other sources (go to if don’t follow above): Perman et al

5. Definitions Non-renewables – eg coal
Renewables – eg fish stocks or flows (eg wind)

6. Concepts you will need to have an idea of…
Hamiltonian – specialised form of Lagrangian – see Perman or Pemberton and Rau if you don’t understand this in this lecture.
Market structures – monopoly, oligopoly, perfect competition – see basic micro text book to refresh if you’ve forgotten!
Discounting – intertemporal issues. See Perman.

7. Hamiltonian
Hamiltonian helps to solve the control problem. Similar to Lagrangian. ) , ( ] [ t q x g H l p + = ð
profit plus change in stock valued by shadow price.
To maximise => = q H l - = x H
and
These conditions and equation of motion (change in x) give a set of differential
equations which define an optimal solution. (it also has to satisfy travers
ality
conditions
but we won
’t go into this –
see
HSW 186 -
188)

8. Discounting
Social rate of time preference => reduce future values to reflect this.
Usual notation: discount rate is r (occasionally i).
1/((1+r)^t) gives you the multiplier to reduce any value in time t to the current time.
Eg 1/1.08 may give you the multiplier for t=1 and r=8% => £1 = £
Note r=8% does not lead to 0.92 in period t=1, because 1.08 in t=1 would be equal to 1 in t=0 (0.92 in t=0 does not equate to £1 in t=1 => try it!)

9. The basics If LHS is greater than RHS it pays to reduce extraction
If LHS is less than RHS it pays to increase extraction
But note, adjustment is inherently unstable!

10. The basics (2): No Substitute for the ER
Resource is progressively exhausted on the price path.
Eventually resource may be exhausted but this can take infinitely long!

11. The Basics (3): Backstop exists
Resource is progressively exhausted on the price path.
But now when price reaches Backstop Price the producer must have nothing left.
For this to work initial price must be ‘correct’
Lower is r, higher is initial price and lower is extraction initially

12. Extensions to model: Effect of Extraction Costs
Now net income (price minus extraction cost) must rise at rate of interest.
But if extraction costs fall, then initially extraction increases.
Price
time

13. Extensions to the Model (3)
New Discoveries
Effect is similar to an decrease in the price of the substitute – you extract faster. With unanticipated discoveries we see the following pattern:

14. Extensions to Basic Model (2)
Capital Costs
These are part of extraction costs and are sensitive to interest rates. If ‘r’ rises then extraction costs rise, resulting in slower extraction. But higher is ‘r’ faster is extraction on Hotelling grounds.
Technology Changes
If backstop price falls, extraction must increase.
If technology lowers extraction costs, extraction also increases initially.

15. Economic Approach to Resource Use: Theoretical Background
Capital Theory Approach
In equilibrium the returns from buying machines = the total return from holding the numeraire asset =>
(vt+1 + μt+1)/ μt=1+ rt+1
If out of equilibrium then there is the chance of pure profits from arbitrage.
The own rate of return = rental income/price
If rate of return of using machines and numeraire good is different this can only be accounted for by a change in the price =>
vt+1= rt+1 μt-(μt+1 - μt )
So the difference in interest rates must be accounted for by a change in the price of the asset.

16. Capital Theory In the continuous form:
where is the time derivative (increase or fall in the price of capital).
This is the short-run equation of yield or the arbitrage equation.

17. Non-Renewables

18. Renewables

19. Growth function

20. Equilibrium

21. Equilibrium

22. Market Structure
The market structure of an industry may be important in determining the rate of extraction of a resource. Here we will take the earlier analysis further, building on mathematical techniques of comparative dynamics.

23. Competitive Industry

24. Competition

25. Consumer Surplus

26. Hamiltonian

27. Monopoly

28. Hamiltonian

29. Hotelling Rule for Monopoly

31. Perfect Competition

32. Monopoly

33. Comparison

34. Comparative dynamics
Figure 9.1 in Hanley, Shogren and White

35. Conclusions
Initially competitive industry extracts more rapidly than monopoly but then less rapidly as the price increases towards the backstop price. Initial price for monopoly is higher than that for competitive industry. Then increases more gradually towards the backstop price,
Rate of price increase for monopolist is less than discount rate, otherwise resource can be purchased by speculators, stored and sold at later date, so reducing monopoly profits.

36. Heroic Assumptions
Non-linear extraction costs => solving for extraction path for competitive industry formidable problem
Exploration issues
Resource scarcity
Uncertainty

37. Does it work?
Will examine this in later lecture on empirical validation.