Energy Economics and Policy Spring 2012 Instructors: Chu Xiaodong , Zhang Wen Email：chuxd@sdu.edu.cn, zhangwen@sdu.edu.cn Office Tel.: 81696127

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

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

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)

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)

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

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

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

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

*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

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

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

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

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

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

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

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

Monopoly of Energy Supply Price Quantity Monopoly Time Time

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

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

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

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

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

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

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

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

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

Peak in Production The Hubbert curve and peak oil

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

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

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