ENVIRONMENTALAND NATURAL RESOURCES ECONOMICS

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1 6/02/2015 Master in Human Development & Food Security 1 ENVIRONMENTALAND NATURAL RESOURCES ECONOMICS Luca Salvatici (Department of Economics Roma Tre University

2 6/02/2015 Master in Human Development & Food Security 2 Renewable, Nonrenewable, and Enviromental Resources Economics might be defined as the study of how society allocates scarce resources. The field of resource economics would then be the study of how society allocates scarce natural resources. QUESTION 1: What is the central subject in the field of resource economics? A distinction between resources and environmental economics is necessary to continuous our analysis.

3 6/02/2015 Master in Human Development & Food Security 3 RENEWABLE, NONRENEWABLE, AND ENVIROMENTAL RESOURCES Environmental Economics is concerned with the conservation of natural environments and biodiversity. But our focus is about Natural Resources Renewable resource Nonrenewable resource Must display a significant rate of growth or renewal on a relevant economic time scale. An economic time scale is a time interval for which planning and management are meaningful. A critical question in the allocation of natural resources is How much of the resource should be harvest today, and in each period? Dynamic optimization problem

4 6/02/2015 Master in Human Development & Food Security 4 Question QUESTION 2: What is the economic distinction between renewable and non renewable resources? A renewable resource must display a significant rate of grown or renewal on a relevant economic time scale. An economic time scale is a time interval for which planning and management are meaningfuly.

5 6/02/2015 Master in Human Development & Food Security 5 Natural resources: definitions Limited availability (stock) at a given time and: Nonrenewable resources: given stock on a relevant economic time scale => Nonrenewable resources are incapable of significant growth, e.g., fossil fuels, ores, diamonds Renewable resources: renewable resources are capable of growth (on some meaningful timescale), e.g., fish, (young growth) forests => rate of growth is determined by biological factors that can be influenced by human activity but the maximum rate cannot be changed

6 6/02/2015 Master in Human Development & Food Security 6 Natural resources: basic concepts Natural resources are natural assets from which we derive value (utility) Broad definition includes amenity value, provision of ecosystem services, etc. We focus here on natural resources that must be extracted or harvested In general, efficient and optimal use of natural resources involves intertemporal allocation Distinguish between renewable and non-renewable resources

7 6/02/2015 Master in Human Development & Food Security 7 Definitions and key features of natural resources Natural resources are stocks of materials that exist in the natural environment that are both scarce and economically useful in production or consumption, either in their raw state or after a minimal amount of processing. Imperfections in some natural resource markets raise questions about the efficiency of extraction and optimal extraction rates: the impact of trade on resource management in these circumstances is difficult to assess (open access may reverse some of the predictions of standard trade theory). Technical change and capital accumulation can partially offset the exhaustibility of non-renewable resources. Trade can contribute to this process.

8 6/02/2015 Master in Human Development & Food Security 8 RENEWABLE, NONRENEWABLE, AND ENVIROMENTAL RESOURCES Maximize some measure of net economic value Dynamic Optimization Problem Solution: schedule or time path indicating optimal amount to be harvested in each period. The optimal rate of harvest in a particular period may be zero Example If a fish stock has been historically mismanaged, and the current stock is below what is deemed optimal, then zero harvest may be best until the stock recovers.

9 6/02/2015 Master in Human Development & Food Security 9 Dynamics Finding the best allocation over time is a dynamic (not static) optimization problem What makes a problem dynamic? The critical variable in a dynamic optimization problem is a stock or «state» variable that requires a difference or differential equation to describe its evolution The key feature is that a decision taken today will change the state variable in the next period Robinson Crusoe example

10 6/02/2015 Master in Human Development & Food Security 10 Nonrenewable resources dynamics R(t): remaining reserves in period t q(t): rate of extraction R(t+1) R(t) = q(t)

11 6/02/2015 Master in Human Development & Food Security 11 Renewable resources dynamics y(t) = harvest in period t X(t) = stock at the beginning of period t F(Xt) = net growth function X t+1 X t = F ( X ) y t t Escapement: 0 < >0

12 6/02/2015 Master in Human Development & Food Security 12 Discounting In general, individuals have positive time preferences over consumption (money) This gives the social discount rate or time preference δ pure social rate of High discount rates heavily discount future benefi ts and costs The discount rate and the interest rate measure essentially the same thing Hence, the discount rate re flects the opportunity cost of investment (saving) Market interest rates also re flect risk, in flation, taxation, etc.

13 6/02/2015 Master in Human Development & Food Security 13 Discounting Two explanations for discounting: money could be invested for a greater future return (the opportunity cost of capital), and people are impatient (time preference). If we think in terms of the market for investment funds, the opportunity cost rationale says what firms are willing to pay for new funds, while the impatience rationale identifies the amount that individuals require as compensation for delaying consumption by investing their funds. In the economists ideal world fully competitive markets, no distortionary taxes, perfect information, and complete rationality these rates would be identical. In point of fact, most economists agree that the discount rate suggested by the impatience explanation the social discount rate is substantially lower than the rate indicated by the opportunity cost of alternative investments.

14 6/02/2015 Master in Human Development & Food Security 14 Intergenerational equity If the weight attached to the welfare of the next generation is small, investments to protect the environment are unattractive and inventories of natural resources tend to be low What are we doing for the next generation? But what have they done for us? I do not have to spend time worrying about my neighbor s children because my neighbor can take care of them just fine, and I apply the same thinking, absent exceptional circumstances, to distant future generations. I am not willing to spend a lot of money to help very remote future generations, because I think they will be just fine without my concern and resources indeed, there is every reason to think that their lives will be far more pleasant than those of the current generation. (John J. Donohue III, Why We Should Discount the Views of Those Who Discount Discounting, 108 Yale L.J. 1901, 1905,

15 6/02/2015 Master in Human Development & Food Security 15 What is (or ought ot be) the right discount rate? The present value of a payment 10 years from now would be 7441 if δ =0.03, but if the time horizon is 100 years it drops to 520, and with δ =0.1 to 0.72 Exponential discount: a human life today would be worth less than a slice of cake in the Roman period!

16 6/02/2015 Master in Human Development & Food Security 16 The economic measure of scarcity Economia delle risorse naturali (a.a.2006/07)

17 6/02/2015 Master in Human Development & Food Security 17 Economic valuation P = C + A P - C = A - Resource market price (P) - Average extraction cost (C): constant dependent on the flow (control) variable (e.g., proportional to the extraction rate) dependent on the stock (state) variable (e.g., inversely related to the stock level) - Rental value (A): present value of the benefits to be obtained postponing the exploitation of one resource unit (resource rent)

18 6/02/2015 Master in Human Development & Food Security 18 What is a rent? In economics, the concept of economic rent is equivalent to that of (positive) economic profit that is a return in excess of normal profit, where the latter is the return that an entrepreneur should earn to cover the opportunity cost of undertaking a certain activity rather than its best alternative. In other words, any revenue exceeding total costs including the opportunity cost (or normal profit) is economic rent. Two types of rents: 1. Differential (Ricardian) rent: The classical notion of differential rent is related to land. The idea is that greater rent accrues to land of higher productivity and better quality (e.g. greater fertility), with marginal land receiving no rent. 2. Scarcity rent: Scarcity rents arise when there are restrictions on the supply of a natural resource, so thatdemand exceeds supply. These restrictions can be natural or legal. In general, the resource rent is the total of the differential rent and the scarcity rent.

19 6/02/2015 Master in Human Development & Food Security 19 Scarcity assessment Real world: Natural resource commodity prices may rise or fall over time because: Marginal production cost might decrease (technology improves) or increase (exploit cheapest sources first). Demand may grow over time unless a new technology displaces this demand (e.g., coal replaced firewood, natural gas replaced coal, alt. energy replaces natural gas?), Future demand and marginal cost cannot be known with certainty.

20 6/02/2015 Master in Human Development & Food Security 20 Hotelling rule: intuition In the absence of extraction costs, the firm is indifferent between maintaining or extracting the resource only if the resource price increases at rate δ: for a lower increase rate, it would be convenient to extract at the most rapid rate; for a higher increase rate, it would never be optimal to extract the resource. 20

21 6/02/2015 Master in Human Development & Food Security 21 Two-periods example: assumptions 1. There is a well-functioning competitive market for the nonrenewable resource in question (no monopolies or cartels) 2. Market participants are fully informed of current and future demand, marginal production cost, market discount rate, available supplies, and market price 3. We will look at the most basic dynamic case: two time periods: today (period 0) and next year (period 1) 4. Marginal cost is constant 5. Market demand is steady state, meaning that demand in period 1 is the same as in period 0 (no growing or shrinking demand)

22 6/02/2015 Master in Human Development & Food Security 22 Two-periods example: data Demand: P = 200 Q Supply: P = 10 Discount rate δ = 10 percent (0.1) Total resource stock Q tot = 100

23 6/02/2015 Master in Human Development & Food Security 23 Case 1: Ignore period 1 while in period 0 ( live for today ) Competitive market equilibrium: 200-Q 0 = 10 Q 0 = 190 Problem! Q tot = 100 < 190. Scarcity-constrained market equilibrium Q 0 = 100; P = = $100.

24 6/02/2015 Master in Human Development & Food Security 24 Case 1: Consume All in Period Price Demand Supply Quantity

25 6/02/2015 Master in Human Development & Food Security 25 Case 1: Consume All in Period Price CS = $5000 PS = $9000 Demand Supply Quantity PV of total gains from trade = $14,000

26 6/02/2015 Master in Human Development & Food Security 26 Case 2: Consume Half in Period 0 and Half in Period Price CS = $1,250 PS = $7,000 Demand Supply Quantity PV of total gains from trade, period 0, = $8,250 PV of total gains from trade, period 1, = $8,250/(1+0.1) 1 = $7,500

27 6/02/2015 Master in Human Development & Food Security 27 Case 2: Divide Q tot equally over periods 0 and 1: Sum of the PV of total gains from trade over periods 0 and 1: $8,250 + $7500 = $15,750 Note that $15,750 in PV of total gains from trade from dividing the resource equally over periods 0 and 1 EXCEEDS the $14,000 in total gains from trade when we consumed all of the resource in period 0. Thus equal division is closer to being dynamically efficient.

28 6/02/2015 Master in Human Development & Food Security 28 Hotelling s rule Methods for solving for the dynamically efficient allocation of the fixed stock of resource over time: the dynamically efficient allocation occurs when the PV of marginal profit (also known as marginal scarcity rent or marginal Hotelling rent) for the last unit consumed is equal across the various time periods. (P 0 -MC)/(1+δ) 0 = (P 1 MC)/(1+δ) 1 Marginal profit, period 0 Marginal profit, period 1

29 6/02/2015 Master in Human Development & Food Security 29 Hotelling s rule: example Let demand be given by P = a bq i. The integral of demand is total benefits, aq i bq i2 /2. Likewise total cost is cq i (c is constant MC). If the available resource stock is Q tot, then the dynamically efficient allocation of a resource over n years is the solution to the following maximization problem:

30 6/02/2015 Master in Human Development & Food Security 30 Example: FOCs i (aq i bq i2 /2 cq i )/(1+δ) t + λ[q tot - i q i ], where t = 0, 1, 2,, n. If Q tot is constraining, then the dynamically efficient solution satisfies: (a bq i c)/(1+r) t - λ = 0, i = 0, 1,, n. [Q tot - i q i ] = 0

31 6/02/2015 Master in Human Development & Food Security 31 2 periods problem: FOCs Now let s apply the parameters from our problem (a = 200, b = 1, c = 10, δ = 0.1, 2 periods). The dynamically efficient solution satisfies: (200 q 0 10)/(1+0.1) 0 = λ (200 q 1 10)/(1+0.1) 1 = λ 100 = q 0 + q 1

32 6/02/2015 Master in Human Development & Food Security 32 2 periods problem: Hotelling s rule (200 q 0 10)/(1+0.1) 0 = (200 q 1 10)/(1+0.1) 1 Since q 1 = q 0, substitute (100 - q 0 ) for q 1 and simplify: q 0 = (190 - (100 - q 0 ))/(1.1) *90 = q 0 ( ) = q 0 = / = q 1 = =

33 6/02/2015 Master in Human Development & Food Security 33 Hotelling s rule: test P 0 = = (P 0 MC)/(1+0.1) 0 = $ P 1 = = (P 1 MC)/(1+0.1) 1 = $ Therefore, Hotelling s rule is satisfied.

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35 6/02/2015 Master in Human Development & Food Security 35 Dynamically Efficient Market Allocation I Period 0 gains from trade: CS = ( )*56.667/2 = $1, PS = ( )* = $7, PV(TS) = $9,161.11

36 6/02/2015 Master in Human Development & Food Security 36 Dynamically Efficient Market Allocation II Period 1 gains from trade: CS = ( )*43.333/2 = $ PS = ( )* = $6, PV(TS) = $7,294.35/1.1 = $6, Sum of PV of total gains from trade, periods 0 and 1: $9, $6, = $15, This is $42.34 larger than a 50/50 split in Case 2.

37 6/02/2015 Master in Human Development & Food Security 37 Dynamically efficient equilibrium: intuition When a resource is abundant then consumption today does not involve an opportunity cost of foregone marginal profit in the future, since there is plenty available for both today and the future. Thus, when resources traded in a competitive market are abundant, P = MC and thus marginal profit is zero. As the resource becomes increasingly scarce, however, consumption today involves an increasingly high opportunity cost of foregone marginal profit in the future. Thus as resources become increasingly scarce relative to demand, marginal profit (P-MC) grows The profit created by resource scarcity in competitive markets is called Hotelling rent (also known as resource rent or by the Ricardian term scarcity rent). Hotelling rent is economic profit that can be earned in certain natural resource cases due to the fixed supply of the resource. Due to fixed supply, consumption of a resource unit today has an opportunity cost equal to the present value of the marginal profit from selling the resource in the future.

38 6/02/2015 Master in Human Development & Food Security 38 Non-competitive markets: Solow paradox Solow, Robert M Intergenerational Equity and Exhaustible Resources, Review of Economic Studies, pp The optimal extaction period is longer in the case of monopoly than in perfect competition Economia delle risorse naturali a.a.2007/08 38

39 p 6/02/2015 Master in Human Development & Food Security 39 P pm pc x 0 Tc Tm t x*c x*m 0 Tc Tm t 39

40 6/02/2015 Master in Human Development & Food Security 40 What is the paradox about? Should we prefer monopoly over competion? It could be a «second-best» option, but we need to show that the perfect competion extraction path is not optimal: Different δ? Externalities? Economia delle risorse naturali a.a.2007/08 40

41 6/02/ Why are natural resources prone to cartelization? A producer cartel is about monopolistic coordination aimed at jointly cutting supply or raising price, thus leading to increased revenue for the group. There are 3 major problems that a cartel must overcome if it is to be successful. 1. There is the problem of determining the optimal level of output and the rules governing the allocation of that output among cartel members 2. Once output decisions have been taken, cartel members have an incentive to renege on the agreement and sell additional output, thus reaping additional profits. 3. A cartel has to be able to prevent entry by new firms. The case of natural resources: 1. natural resources tend to be concentrated in few countries, hence few producers generally account for a large proportion of world supply. 2. natural resources tend to exhibit high fixed costs of extraction. These costs reduce the risk of dissolution of a cartel due to entry by new firms, as they make it difficult for outside producers to equip themselves with the production capacity necessary to enter the market. 3. natural resources tend to be relatively homogeneous. This increases the incentive for firms to defect, as a higher responsiveness to price changes is associated with less differentiated goods. However, deviations from a cartel agreement are easier to detect when products are similar than when they are differentiated Master in Human Development & Food Security

42 6/02/2015 Master in Human Development & Food Security 42 Sustainability Solow shows that constant consumption can be sustained by a suitable path of capital accumulation, despite declining resource flows. This is possible only if there is a certain degree of substitutability between capital and a natural resource, and if the latter is a non-essential input. This intuition was translated into a policy rule by Hartwick, who argued that the rent derived from resource extraction should be invested in building the capital stock (broadly defined to include infrastructure, physical capital, education) needed to guarantee constant consumption over time.

43 6/02/2015 Master in Human Development & Food Security 43 Renewable resources Wildlife Populations: groups of animals, all of the same species, that live together and reproduce Issues: Sustanability Access Biomass: the aggregate mass of the biological material (such as the total weight of fish of particular age classes or the cubic metres of standing timber), or in terms of population numbers 43

44 6/02/2015 Master in Human Development & Food Security 44 Biological growth processes In order to investigate the economics of a renewable resource, it is first necessary to describe the pattern of biological (or other) growth of the resource. To fix ideas, we consider the growth function for a population of some species of fish. This is conventionally called a fishery. We suppose that the population in this fishery has an intrinsic (or potential) growth rate denoted by γ. This is the proportional rate at which the fish stock would grow when its size is small relative to the carrying capacity of the fishery, and so the fish face no significant environmental constraints on their reproduction and survival. The intrinsic growth rate γ may be thought of as the difference between the population s birth and natural mortality rate (again, where the population size is small relative to carrying capacity). Be careful not to confuse a rate of change with a rate of growth. A rate of change refers to how much extra is produced in some interval of time. A rate of growth is that rate of change divided by its current size (to measure the change in proportionate terms).

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50 6/02/2015 Master in Human Development & Food Security 50 Stability Economia delle risorse naturali (a.a.2006/07)

51 6/02/2015 Master in Human Development & Food Security 51 Critical depensation: graph Economia delle risorse naturali (a.a.2006/07) 51

52 6/02/ Gordon-Schaefer model: graph Master in Human Development & Food Security

53 6/02/ Gordon-Schaefer model: rent dissipation Rent: TR - TC Free access ==> TR - TC = 0 E > E* ==> TC > TR E < E* ==> TC < TR Master in Human Development & Food Security

54 6/02/2015 Master in Human Development & Food Security 54 When is a fishery overfished? When stock is at X = K, the fishery is unexploited (and in effect has been for some considerable span of recent time). When stock is below X MSY the fishery could be described as being in a developmental phase. Specifically, we might say that the fishery is under exploited if stocks are close to X MAX so that the fishery is capable of producing a great deal more under increased fishing pressure, or as moderately exploited if X is closer to X MSY so that the fishery is capable of producing some more under increased fishing pressure. When X is in the (close) neighbourhood of X MSY the fishery is fully exploited (and the fishery is producing close to its MSY). When X is less than X MSY we might choose to apply one of three labels depending on how much lower is X than X MSY and in which direction the fishery is moving: The fishery is overfished : stocks at lower level than X MSY ; and the catches in recent years have been showing a downward trend (so current catches less than recent historical high). The fishery is depleted a more extreme version of overfished in which stocks are very far below X MSY. A recovering fishery is one in which stocks are very low relative to historical maximum levels, but in which harvest levels are trending upwards (the fishery is moving from left to right towards X MSY.

55 6/02/2015 Master in Human Development & Food Security 55 Single owner: economic and biological overexploitation Master in Human Development & Food Security

56 6/02/2015 Master in Human Development & Food Security 56 Maximizing the Present Value of Resource Rent in a Gordon-Schaefer Model The classical Gordon Schaefer model presents equilibrium revenue (TR) and cost (TC), including opportunity costs of labor and capital, in a fishery where the fish population growth follows a logistic function. Unit price of harvest and unit cost of fishing effort are assumed to be constants. In this case, the open access solution without restrictions (OA) is found when TR=TC and no rent (abnormal profit, P=TR-TC) is obtained. Abnormal profit (here resource rent) is maximized when TR'(X)=TC'(X) (maximum economic yield, MEY). Discounted future flow of equilibrium rent is maximized when P'(X)/d=p, where p is the unit rent of harvest and d is the discount rate. This situation is referred to as the optimal solution (OPT), maximizing the present value of all future resource rent. The open access solution and MEY equilibriums are found to be special cases of the optimal solution, when the discount rate is infinite or null, respectively.

57 6/02/2015 Master in Human Development & Food Security 57 Dynamics Master in Human Development & Food Security

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