ENVIRONMENTALAND NATURAL RESOURCES ECONOMICS · Renewable, Nonrenewable, and Enviromental Resources...

ENVIRONMENTALAND NATURAL RESOURCESECONOMICSLuca Salvatici

(Department of Economics –Roma Tre University

6/02/2015 Master in Human Development & Food Security 1

Renewable, Nonrenewable, and EnviromentalResources

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.

A distinction between resources and environmental economics is necessary to continuous our analysis.

economics?QUESTION 1: What is the central subject in the field of resource

economics?


RENEWABLE, NONRENEWABLE, AND ENVIROMENTAL RESOURCES

Environmental Economics is concerned with the conservation of natural environments and biodiversity.

Natural Resources

But our focus is about 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


QUESTION 2: What is the economic distinction between renewable and non renewable resources?

Question

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.


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

Master in Human Development & Food Security6/02/2015 5

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


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.


RENEWABLE, NONRENEWABLE, AND ENVIROMENTAL RESOURCES

Dynamic Optimization

Problem

Maximize some measure of net economic value

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

If a fish stock has been historically

may be best until the stock recovers.

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.

Example


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 optimizationproblem is a stock or «state» variable that requiresa difference or differential equation to describe itsevolution

• The key feature is that a decision taken today willchange the state variable in the next period

Robinson Crusoe example


Nonrenewable resources dynamics

R(t): remaining reserves in period t

q(t): rate of extraction

R(t+1) – R(t) = – q(t)


Renewable resources dynamics

y(t) = harvest in period t

X(t) = stock at the beginning of period t

F(Xt) = net growth function

Escapement: �� − �� ≥ 0

�� < � �� ⇒�� − �� > 0

( )tttt yXFXX −=−+1


Discounting

• In general, individuals have positive time preferences over consumption (money)

• This gives the social discount rate or pure social rate of time preference δ

• 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.


Discounting

Two explanations for discounting:•money could be invested for a greater future return (theopportunity cost of capital), and•people are impatient (time preference).If we think in terms of the market for investment funds, theopportunity cost rationale says what firms are willing to payfor new funds, while the impatience rationale identifies theamount that individuals require as compensation fordelaying consumption by investing their funds.In the economists’ ideal world – fully competitive markets,no distortionary taxes, perfect information, and completerationality – these rates would be identical. In point of fact,most economists agree that the discount rate suggested bythe impatience explanation – the “social” discount rate – issubstantially lower than the rate indicated by the opportunitycost of alternative investments.


14

Intergenerational equity• If the weight attached to the

welfare of the next generation is small, investments to protect the environment are unattractive and inventoriesof 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, 1999.


What is (or ought ot be) the ‘right’ discount rate?

• The present value of a €10000 payment 10 years from now would be €7441 if δ =0.03, but if the time horizon is100 years it drops to €520, and with δ =0.1 to €0.72

• Exponential discount: a human life today would be worthless than a slice of cake in the Roman period!


Economia delle risorse naturali (a.a.2006/07)

The economic measure of scarcity


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 beobtained postponing the exploitation of one resourceunit (resource rent)


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 theopportunity cost of undertaking a certain activity rather than its bestalternative. In other words, any revenue exceeding total costs including theopportunity 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.


Scarcity assessment

Real world: Natural resource commodity prices may riseor fall over time because:

• Marginal production cost might decrease (technologyimproves) or increase (exploit cheapest sources first).

• Demand may grow over time unless a new technologydisplaces this demand (e.g., coal replaced firewood,natural gas replaced coal, alt. energy replaces naturalgas?),

• Future demand and marginal cost cannot be knownwith certainty.


20

Hotelling rule: intuitionIn the absence of extraction costs, the firm isindifferent between maintaining or extracting theresource only if the resource price increases at rateδ:

• for a lower increase rate, it would be convenientto extract at the most rapid rate;

• for a higher increase rate, it would never beoptimal to extract the resource.


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)


Two-periods example: data

Demand: P = 200 – Q

Supply: P = 10

Discount rate “δ” = 10 percent (0.1)

Total resource stock Qtot = 100


Case 1: Ignore period 1 while in period 0 (“live for today”)

Competitive market equilibrium:

200-Q0 = 10 � Q0 = 190

Problem! Qtot = 100 < 190.

Scarcity-constrained market equilibriumQ0 = 100;

P = 200 – 100 = $100.


Case 1: Consume All in Period 0

0

50

100

150

200

250

0 20 40 60 80 100 120 140 160 180 200

Quantity

Pri

ce

DemandSupply


Case 1: Consume All in Period 0

0

50

100

150

200

250

0 20 40 60 80 100 120 140 160 180 200

Quantity

Pri

ce

DemandSupply

CS = $5000

PS = $9000

PV of total gains from trade = $14,000


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

Case 2: Consume Half in Period 0 and Half in Period 1

0

50

100

150

200

250

0 20 40 60 80 100 120 140 160 180 200

Quantity

Pri

ce

DemandSupply

CS = $1,250

PS = $7,000


Case 2: Divide Qtot equally over periods 0 and 1:

Sum of the PV of total gains from trade overperiods 0 and 1:

$8,250 + $7500 = $15,750

Note that $15,750 in PV of total gains from trade fromdividing the resource equally over periods 0 and 1EXCEEDS the $14,000 in total gains from trade whenwe consumed all of the resource in period 0. Thusequal division is closer to being dynamically efficient.


Hotelling’s rule

Methods for solving for the dynamically efficient allocation of the fixed stock of resource over time:

Master in Human Development & Food Security

the dynamically efficient allocation occurswhen the PV of marginal profit (also known asmarginal scarcity rent or marginal Hotellingrent) for the last unit consumed is equalacross the various time periods.

(P0-MC)/(1+δ)0 = (P1–MC)/(1+δ)1

Marginal profit, period 0 Marginal profit, period 1

6/02/2015 28

Hotelling’s rule: example

Let demand be given by P = a –bqi. Theintegral of demand is total benefits, aqi –bqi

2/2. Likewise total cost is cqi (c is constantMC). If the available resource stock is Qtot,then the dynamically efficient allocation of aresource over “n” years is the solution to thefollowing maximization problem:


Example: FOCsMaster in Human Development & Food Security

∑i (aqi – bqi2/2 – cqi)/(1+δ)t + λ[Qtot - ∑i

qi],

where t = 0, 1, 2, …, n. If Qtot isconstraining, then the dynamicallyefficient solution satisfies:

•(a – bqi – c)/(1+r)t - λ = 0, i = 0, 1, …, n.

•[Qtot - ∑i qi] = 0

6/02/2015 30

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 – q0 – 10)/(1+0.1)0 = λ

(200 – q1 – 10)/(1+0.1)1 = λ

100 = q0 + q1

6/02/2015 31

2 periods problem: Hotelling’s rule

(200 – q0 – 10)/(1+0.1)0 = (200 – q1 – 10)/(1+0.1)1

Since q1 = 100 - q0, substitute (100 - q0) for q1 and simplify:

190 - q0 = (190 - (100 - q0))/(1.1) �

190 – 0.9091*90 = q0(1+0.9091) = �

q0 = 108.182/1.9091 = 56.667 �

q1 = 100 – 56.667 = 43.333


Hotelling’s rule: test

P0 = 200 – 56.667 = 143.333

(P0 – MC)/(1+0.1)0 = $133.33

P1 = 200 – 43.333 = 156.667

(P1 – MC)/(1+0.1)1 = $133.33

Therefore, Hotelling’s rule issatisfied.



Dynamically Efficient Market Allocation I

Period 0 gains from trade:

CS = (200 - 143.333)*56.667/2 =$1,605.55

PS = (143.333-10)*56.667 =$7,555.56

PV(TS) = $9,161.11


Dynamically Efficient Market Allocation II

Period 1 gains from trade:

CS = (200-156.667)*43.333/2 = $938.87

PS = (156.667-10)*43.333 = $6,355.48

PV(TS) = $7,294.35/1.1 = $6,631.23

Sum of PV of total gains from trade, periods 0and 1: $9,161.11 + $6,631.23 = $15,792.34.

This is $42.34 larger than a 50/50 split in Case2.


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.


Economia delle risorse naturali a.a.2007/08 38

Non-competitive markets: Solow paradox

• Solow, Robert M. 1974. “Intergenerational Equity and Exhaustible Resources”, Review of Economic Studies, pp. 29-45.

• The optimal extaction period is longer in the case of monopoly than in perfect competition


39

p

P

pc

pm

Tc Tmt

x

x*c

x*m

Tc Tmt

0

0


What is the ‘paradox’ about?

Should we prefer monopoly overcompetion?It could be a «second-best» option,but we need to show that the perfectcompetion extraction path is notoptimal:• Different δ?• Externalities?

Economia delle risorse naturali a.a.2007/08 40


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


6/02/2015 41

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.


Renewable resources

Wildlife Populations: groups of animals, all of the samespecies, that live together and reproduce

Issues:

• Sustanability• AccessBiomass: the aggregate mass of the biological material (suchas the total weight of fish of particular age classes or the cubicmetres of standing timber), or in terms of population numbers


43

6/02/2015 43

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).







Economia delle risorse naturali (a.a.2006/07)

Stability


Economia delle risorse naturali (a.a.2006/07) 51

Critical depensation: graphMaster in Human Development & Food Security6/02/2015 51

Gordon-Schaefer model: graph


6/02/2015 52

Gordon-Schaefer model: rentdissipation

Rent: TR - TC

Free access ==> TR - TC = 0

• E > E* ==> TC > TR

• E < E* ==> TC < TR


6/02/2015 53

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 XMSY 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 XMAX 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 XMSY so that the fishery is capable of producing some more under increased fishing pressure.

• When X is in the (close) neighbourhood of XMSY the fishery is ‘fully exploited’ (and the fishery is producing close to its MSY).

• When X is less than XMSY we might choose to apply one of three labels depending on how much lower is X than XMSY and in which direction the fishery is moving:

• The fishery is ‘overfished’: stocks at lower level than XMSY; 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 XMSY.

• 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 XMSY.


Master in Human Development & Food

Security

Single owner: economic and biological over-exploitation

6/02/2015 55Master in Human Development & Food Security

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.



Dynamics

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

Date post:	16-May-2020
Category:	Documents
Upload:	others
View:	6 times
Download:	0 times

ENVIRONMENTALAND NATURAL RESOURCES ECONOMICS · Renewable, Nonrenewable, and Enviromental Resources...

Documents