NR Econ Lecture 13 Module V. Nonrenewable Natural Resources and Alternative Energy Futures Today's outline: Introduction to topic: economics of nonrenewable resources Hotelling Model: intertemporal depletion of a nonrenewable resource Introduction: Economics of Nonrenewable Resources Hotelling Model: intertemporal depletion of a nonrenewable resource "Time" as central to the analysis Intertemporal tradeoffs Use today or use in the future Choices today constrain choices in the future Nonrenewable Resource Definition: A natural resource whose stock does not increase over time. Use of the resource reduces its stock. Also known as "exhaustible resource" Examples Fossil fuels (petroleum, natural gas, coal, tar sands) Non-energy minerals (copper, bauxite, tin, etc.) Groundwater (deep aquifers) Nonrenewable Resource (cont.) Economic issues Dynamic efficiency: how should the economy deplete a nonrenewable resource through time? Market equilibrium: will a competitive market in a nonrenewable resource be dynamically efficient? What happens to an economy when the stock of the resource is exhausted? Dynamic efficiency (definition): the intertemporal depletion path that maximizes the present value of the surplus from use of the nonrenewable resource stock. Nonrenewable Resource (cont.) Intertemporal models Put structure on tradeoffs Generate predictions about patterns of use through time Graphs stocks and flows Interest rates and discount rates Discounting and Compounding Motivation Nonrenewable resource use involves consumption over time -- benefits and costs in different time periods Discounting creates a common monetary metric to compare these intertemporal benefits or costs Metric: present-value dollars Definitions Discounting: an algebraic method to convert future occurrences of benefits or costs in to present-value dollars Discount rate: the rate used to convert futurevalue dollars into present-value dollars Compounding: an algebraic method to convert present-value dollars to future-value dollars Interest rate: the rate used to convert present-value dollars into future-value dollars PV = present value FV = future value r = interest rate, discount rate t = time (a specific point in time) Interest rates as market prices We observe interest rates in financial markets Today's outline: Introduction to topic: economics of nonrenewable resources Lecture tomorrow afternoon: China's Environmental Challenges Hotelling Model: intertemporal depletion of a nonrenewable resource We will be developing the basic model and extensions of the model over the next two weeks Hotelling Model What is the dynamically efficient time path of depletion of a nonrenewable resource? Choose the resource quantities through time that maximize surplus Surplus = net benefit = benefits of resource use minus resource extraction costs Market perspective we apply the resource quantities to find the efficient intertemporal price path for the resource Four elements of the model Aggregate demand function Assume: the function is the same year after year ("stationary" demand) Marginal extraction cost function Assume: the marginal extraction cost function is constant Stock of the resource Assume: the stock is fixed and known at time t Interest rate Assume: the interest rate is constant year after year Perspectives on the model Extends the supply/demand framework to an intertemporal case with supply fixed intertemporally Industry-level analysis of resource market not analyzing individual firms at this point Geographic scope of the model global in many cases Perspectives on the model (cont.) Simplifying assumptions in the model Choice variables in the model Benefit function = area underneath demand function Setting up the model Notation: qt = quantity depleted (used, consumed) in time t B(qt) = benefit function c = marginal extraction cost cqt = total extraction cost at time t pt = resource price in time t r = interest rate S0 = stock available at time 0 T = exhaustion date Two-period example Discrete time (not "continuous" time) Constrained maximization problem Form the Lagrangean function ... and then you know how to proceed! Key results General findings: qo* > q1* po* < p1* (p1 c) = (p0 c)(1+r) [Hotelling's rule] Hotelling rent. Price marginal cost Hotelling's rule: net price (pt c) increases over time at the interest rate Numerical example B(qt) = 700qt 0.125qt2 c = 200 [dollars/ton] S0 = 2500 [tons] r = 5% [dollars] Inverse demand function = B'(qt): pt = 700 0.25qt