1. Energy Economics and Policy
Spring 2012
Instructors: Chu Xiaodong , Zhang Wen
Office Tel.:

2. Energy Supply
Economics of energy supply study the manner in which energy resources are allocated through time and space
Energy resources can be classified as either depletable or non-depletable
Depletable: The stock of the resources is not replaceable over a limiting time horizon, e.g., fossil fuels
Non-depletable: The stock of the resources can be replenished within a reasonable timeframe
The emphasis is on the allocation of depletable energy resources

3. Characteristics of Depletable Resources
Stock declines over time
Costly process of discovery
Costly process of extraction
Technical change decreases costs of exploration and extraction over time
Key results
Physical Stocks Decline over time
Price eventually increases with time
Technical change may cause prices to decrease initially

4. Example 3.1: Decision to Sell Oil
Because of limited supply, depletable resources command a scarcity value
If you own a barrel of oil which can sell today for 30, should you sell today, or wait for next year? (assuming rate of interest r = 0.05)

5. Example 3.1: Decision to Sell Oil
What is a reasonable decision?
If p1 > 31.5, wait
If p1 < 31.5, sell today
In equilibrium: p1 = p0(1+r)

6. Model of Extraction of a Depletable Resource
Starting from the framework by Hotelling, the models aim to maximize the present value of profits from extraction of a depletable resource
The basic model: A perfectly competitive market
qt: quantity supplied
pt: price
c(qt): cost of supplying
Rt: resource remaining at the beginning of each period
βt: rate at which future profits are discounted

7. Model of Extraction of a Depletable Resource
With the basic model, assume there is a finite stock of resource at the beginning, , and the time period in account is T, then
and
i.e., the constraint can be replaced by the above equation, so

8. Model of Extraction of a Depletable Resource
Using the Lagrange multiplier method, the former problem can be solved as
where λ is the Lagrange multiplier
The first-order condition for a maximum is given as
which is true for all time periods

9. Model of Extraction of a Depletable Resource
The term λ can be interpreted as the shadow price of the resource, i.e., the incremental value to the resource owner of adding an additional unit of resource
From the first-order condition of the maxima that
one can deduce that
Extraction will occur so that the present value of the marginal profit is the same in all periods

10. *Writing Skill
The paragraph of “The intuition behind the result is rather elegant…” below equation (3.3) on page 53 of [Evans & Hunt, 2009]) is a good example of interpreting the logic of a mathematic expression

11. Model of Extraction of a Depletable Resource
From the first-order condition, the price can be expressed as
The first term on the right-hand side is the marginal user cost (MUC), which reflects the opportunity cost of extraction
The second term is the marginal extraction cost (MEC), which is the cost of incremental production

12. Model of Extraction of a Depletable Resource
The optimal price path of a depletable resource with constant MEC

13. Model of Extraction of a Depletable Resource
Backstop technology
A perfect substitute for depletable resource that can be produced in any amount at constant (usually high) price
When price of the depletable resource is equal to price of backstop, we should switch to the backstop

14. Model of Extraction of a Depletable Resource
Price
Price path with
backstop
Time

15. Model of Extraction of a Depletable Resource
The resource is no longer used when its price reaches that of the backstop
A new resource will be extracted instead of the older one since it is much more economical
Backstop establishes the long-run price at which demand for the depletable resource goes to zero
If the backstop price is lowered, then the price in all periods falls
The nature of MEC is vital in characterizing resource depletion
The MUC falls if MEC is rising through time

16. Model of Extraction of a Depletable Resource
Price path with
high backstop price
Price path with
low backstop price
Time

17. Monopoly of Energy Supply
In a market characterized by imperfect competition, the resource owner’s extraction decision influence price, e.g., the production decisions of OPEC influence the global crude oil price
The resource owner will raise price in the current period by constraining the level of production provided that demand elasticity is not constant
If demand elasticity is constant, the optimal price and extraction paths are the same with the competitive case

18. Monopoly of Energy Supply
Price
Quantity
Monopoly
Time
Time

19. Generalization of the Basic Model
US domestic first purchase crude oil price and that from the basic model

20. Generalization of the Basic Model
In many cases, the basic model fails to adequately explain reality since many assumptions for the model is not realistic
Extraction costs are function only of current extraction
The total initial quantity of resource is known
There is no uncertainty
Extraction, marketing, and exploration investment occur in an incremental manner

21. Generalization of the Basic Model
Extraction costs
Factors such as reserve dependency and technological change should be included
Costs increase as the resource is depleted
Costs reduce as the technological innovation is applied

22. Generalization of the Basic Model
Exploration
Reserves can be expanded through exploration of new resources
Extraction costs fall with reserves expanded
Exploration itself becomes increasingly costly as depletion occurs

23. Generalization of the Basic Model
Uncertainty
Considering various sources of uncertainty (e.g., future demand, price, the cost of exploration, the backstop price, and technological innovations), the resource owner’s decision must be based on expected conditions, and the problem becomes one of investment under uncertainty

24. Generalization of the Basic Model
Capital investment
The production and exploration process is very capital intensive, and the capital investments generally occur in large discrete lumps
The investments are typically not reversible, which results in a short-run supply curve relatively inelastic
Short-run supply is constrained by current productive capacity, and short-run current productive capacity is constrained by the level of investment

25. Generalization of the Basic Model
Optimal price paths under different model assumptions

26. Firm Behavior
What does a firm actually do when determining whether or not to explore, develop and market a depletable resource deposit?
The exploration and development phase is typically the most capital-intensive phase of a project
The firm has multiple such investment opportunities at any given time
The firm must decide how to allocate a limited amount of capital to a suite of potential projects to which it has access

27. Peak in Production
Rising prices do not necessarily mean that the world is running out of crude oil, which may be caused by that demand is currently accelerating faster than supply
The Hubbert curve is widely used in the analysis of peaking production of petroleum and other fuels on a nation scale or on a global scale

28. Peak in Production
The Hubbert curve and peak oil

29. Peak in Production
The Hubbert curve is a physical description of the production life of a depletable resource
: recoverable resource
Qt: cumulative production to date
a, b: fitted parameters

30. Peak in Production
The implication of the Hubbert curve is that once half of the resource is consumed, a peak in production will occur and decline will commence
Diminishing production capacity and well productivity
Constraints on equipment and personnel for exploration and development, which comes about from having to drill an increased number of wells to sustain a given level of production
Declining exploration success

31. Next Lecture The main topic will be Models of Competitive Markets
Chapters 8 and 9 of [McConnell, Brue & Flynn, 2012] are within the scope