ORGANIZACIÓN Y RESPONSABILIDADES

For the study nation we assume that there is a fixed amount o f land that can either be used for agriculture (A, measured in hectares) or is covered by forest (L), and that deforestation is the process of conversion of some amount of forest land into agricultural land. The area deforested each year (i is initially covered with a forest stock of density S/L (in cubic metres per hectare), where S is the total stock of timber. On forested land the amount of harvest is given by R.

Standing forest grows according to a function g(S,L,X), with gs following the usual pattern of being positive, then zero, then negative (i.e., for a fixed L the growth curve is an inverted ‘U ’ which defines a maximum sustainable yield and a long run equilibrium growth rate of zero), while g i > 0. X is the global stock o f carbon dioxide (CO2). This CO2 fertilises forest growth, so that g% > 0. CO2 dissipates naturally as described by the function n(TjX), where rj is the share of the study country in the total global stock of CO2.

Slash and bum is the assumed forest clearance mechanism in the study country. It is assumed that each cubic metre of timber yields a tonnes of CO2 when burned, and symmetrically, that the growth of one cubic metre of timber absorbs a tonnes of CO2

(in other words, the only source o f carbon in trees is assumed to be atmospheric). The accounting identity for the stock of CO2, given deforestation, natural grov\rth and

dissipation is therefore,

X = a ^ d - c c g - n { i ] X ) , (A.l)

Deforestation is assumed to cost an amount f(d) of an aggregate good that can be consumed, invested or spent on deforestation. Standing forest is assumed to provide production externalities. The national accounting identity is therefore given by,

It is assumed that residents of the nation value consumption and standing forest, while the stock of CO2 causes harm. It is also assumed that the rest of the world derives benefits from the existence of the forested area in the study nation. Therefore, the utility function for the forestry model is (C ,Z ,X )+ [ / ’*'(/,), with U%< 0 and where

1/ and IJ^ refer to the utility of residents of the study nation and the rest of the world

respectively. Utility or welfare, U, to be maximised is defined as U = U ‘ { C ,L ,X ) + U'"{L).

The optimal growth model for this economy is specified as,

max W = rUe'^^dt subject to : C,R,d J) k = F - C - f À = d L = —d S = —R — — d + g V 7 X = a - d - a g - n L

For shadow prices yi the current value Hamiltonian for this problem is.

H ^ - y ^ { F - C - f ) + [ r ^ - y ^ ) d + y \ - R - ^ d + ^ + y l a ^ d - a g - n \ { A 3 )

The first order conditions for this accounting problem are:

— = 0 = î / c - n

(A4)

^ = o = n ^ / ? - r 4 = > n = ^ c ^ / ? (A5)

^ = o = ( r 2 - r , ) - r x f ' - r , j - 7 i C c j

I i (A.6)

^ ( / 2 -7^3) = ( ^ c / ' + ^ c f « Y +

From the first-order conditions we can re-write the current value Hamiltonian in expression (A. 3) as,

H = U + U cK + S L ( S ^ f d-U cF f^ R + - d - g V U c f ^ ~ ^ c ^ R + A a - d - a g - n L

The Hamiltonian in expression (A.3) is measured in terms o f utility. However, it would be useful to have an expression that is more readily recognisable as a national accounting aggregate. That is, we need a rationale to measure N N P in more familiar terms - i.e. its dollar value. Hartwick (1990) relied on assuming a linear approximation of utility {U{C)=UcC) and then dividing the Hamiltonian by the marginal utility of consumption Ucto derive NNP: i.e. N N P = HUJc ■ While this is a practical proposal that has been used relatively extensively (Hamilton, 1997c) various critiques of this practice have been offered (see, for example, Aronsson et al. 1997).

In particular, Pemberton and Ulph (1998) have proposed that the rationale for measuring N N P does not depend on the specific utility function used. Rather it derives from applying an extended Hicksian concept of income to the accounting problem. This income concept is “extended” Hicksian because income or N N P is defined as that amount of produced output that can be consumed while leaving the present value of

utility (i.e. wealth) instantaneously constant.

Hamilton (1997c) has generalised this approach to a model that allows for both production of natural resources and pollution emissions. The key points, from that contribution, that allow the Hamiltonian to be re-written as N N P are the following. Firstly, the Hamiltonian (e.g. as in expression (A.3)) is simply current welfare plus changes in various assets or ‘genuine’ (or net) saving: U + UcG. For a constant rate of

time preference r, this expression is equivalent to the product o f r and (util- dominated) wealth: U + UqG = rW (for proof, see for example, Dasgupta and Maler,

2000). In turn, the change in wealth can be written as: W = r W - U or U^G = f V . That is, genuine saving, G, can be interpreted as the change in total (net) wealth. Therefore,

fV = 0 if G = 0 (as t/c > 0). In other words, wealth is constant only if genuine saving is zero. Hicksian income or the maximum amount o f produced output that can be consumed (leaving wealth constant) is consumption plus genuine (or net) saving.

Given that NNP = C+G, this provides the rationale for measuring NNP in conventional (i.e. dollar) terms. That is, in the context of current accounting problem , and defining the marginal damages from carbon dioxide to be b = - y the expression for Hicksian income is:

NNP = C ■¥ K + { f + {ccb + F f^— d — 7^ R-\— d — g — b cc—d — ccg — n . (A.7)

L L L

The last term in expression (A.7) is the value of damages from the net accumulation of CO2 in the atmosphere. Slash-and-bum therefore adds to the CO2 stock, while the growth of timber on the remaining forested land and natural dissipation of atmospheric CO2 reduces it. The preceding term is the value of net reduction in the stock of timber. This has two components: net harvest of timber on forested land {R~ g)\ and, timber on deforested land (S/Lxd). Before that is the term representing the difference in the shadow prices of agricultural land and forested land. Here, marginal clearance costs (f), damages from carbon dioxide emissions (ab) and the rental value of the timber that was burned are all part of the difference in prices between these two different uses of land.

It is also worth noting how, for example, global preferences for standing forest relate to the expression for NNP in expression (A.7). There are two points that need discussing in this respect:

Firstly, it might be argued that, for example, the welfare that residents in the rest of the world currently derive from standing forest needs to be accounted for: i.e. as a “consumption-like” item. An estimate of these (non-market) benefits would certainly be of interest if we wished to measure of economic welfare (see, for example.

Hamilton, 1996a). However, given the definition of Hicksian income as the maximum amount of produced output that can be consumed (while leaving wealth constant), this offers a rationale as to why the value of the current flow of these (non-market) benefits might not be measured in NNP.

Secondly, in this model, land is an asset which can be used to for crop production or standing forest. In turn, the price of land under these distinct uses will depend on different factors. In particular, we can infer more about what factors determine these prices if we examine the steady-state conditions in expressions (A.8) and (A.9) below. In expression (A.8), we can see that (steady-state) yi, the (steady-state) shadow price of agricultural land, is related to the marginal returns to agricultural land {Fa). In expression (A.9), (steady-state) the (steady-state) shadow price of forestland, is related to a range of factors such as the welfare enjoyed by citizens in the rest of the world from a hectare of land under standing forest (t/J^ ).

At the margin, if land clearance is costless, we would expect the value of land under these two competing uses to be equal. In other words, for the marginal hectare, we would expect that (in the steady-state) yi = y}, and that farmers are indifferent between land clearance and forest conservation (i.e. the marginal benefits of clearance are just equal to the marginal costs). When land clearance is costly there is some additional term reflecting investment in land-use change that we must be taken account of. In terms of our forestry model, it can be recalled from expression (A.7) that this investment term is related not only to marginal clearance costs i f ) but to damages from carbon dioxide emissions {ab) and the rental value of the timber that was burned. This term drives a wedge between the value of land used for agricultural production and value of land under standing forest. Hence, if land clearance is costly, and we observe deforestation (i.e. d>0) then we can reasonably assume that agricultural returns less the costs of that investnlent must at least just equal the returns (and all of the marginal values this is made up of) from keeping the land under standing forest.

Expression (A.7) is an expression for income that we would expect to prevail if deforestation was optimal. However, there is a strong rationale for arguing that the income measure that we should be interested in is one where deforestation is non- optimal. Thus, in the real world we would expect that a variety of policy distortions and market imperfections can easily lead to excess deforestation. In the current context, “excess” can be interpreted as deforestation over and above that which would have prevailed on the optimal path. In such circumstances, the income measure in expression (A.7) might not be not a good indicator of the change in the value of the land asset. Put another way, a proper evaluation of the social costs of land clearance would make NNP reflect better the change in land asset value.

To characterise “excess deforestation” it helps to derive the efficiency condition for harvesting the marginal hectare in the steady state. At this point the marginal returns to agriculture must just equal the marginal returns to standing forest. This can most straightforwardly be done by examining the following dynamic first order conditions.

First recall that the expression for y2 - y^ can be written as follows, after substituting

in the expression for b:

( r 2 - r , ) = U c ( f ' + ( F , + b a ) j )

The dynamic first order conditions for these shadow prices are given by:

h = r y , ~ ^ r y , - U , F , (A.8)

r , = r r , ~ = ry^ - u '[ - U [ - U ^ F , ~ U c F „ g , - U ^bag , (A.9)

oL

These are the standard first order conditions for the maximisation problem that can be used to be derive the steady-state conditions for the accounting model. Hence, each shadow price change ( / , ) is defined in terms of the product of the rate of time

preference, r, and shadow price, y t, and the change in the Hamiltonian with respect to the appropriate stock z.

However, in what follows, we are interested in how these conditions can be used to define “excess deforestation” and therefore Hicksian income or NNP away from the optimum. Subtracting expression (A.8) from expression (A.9), and substituting the

expression for y2 ~ Xs gives.

n - r , = r U ^ (.f' + ( F , + b a ) j ) + U c (.F ,+ F ,g , + b a g , - F , ) + U'[ +U[ (A. 10)

We define one more dynamic first order condition for the shadow price of produced capital, = U c ‘

That is, the rate of change of marginal of utility of consumption is equal to the rate of time preference minus the marginal productivity of capital (or the interest rate). Expression (A.l 1) implies that r = in the steady state where all rates of change fall to 0. Therefore expression (A. 10) reduces to the follo’wing in the steady state:

e

p K i f ' + iFR + b a ) - ) ^ F , - ^ F ^ g , + b a g , + = 0 (A.12)

^ ^ c ^ c

This expression for the shadow prices of agricultural and forested land in the steady state can be re-written as follows,

+ + + + - F ^ . (A.13)

These terms are relatively simple to interpret. Starting with the left-hand side of the expression, the first two terms are, respectively, the (marginal) willingness to pay (WTP) o f foreigners and national residents for a unit of standing forest. Fl is the

production externality provided by a unit of forest. FRgi is the rental value of the natural growth of forest on a unit of land - this is the sustainable harvest or off-take. obgL is the value of the carbon sequestered during natural growth on a unit of land. The next term is interest that would be earned if the sum of the clearance cost, carbon sequestration benefits and timber rental value for the marginal unit of deforested land were put in a bank. Finally, the right hand side is the marginal product of the unit of land under agriculture: i.e. agricultural returns per hectare.

If for a given hectare of land the left-hand side of expression (A.13) is greater than the right, then there is excess deforestation. If it is assumed that there are d* such hectares and that the land use change is permanent, then the value of excess deforestation is given as.

/ r r /

\^U Ur' \ L (A.14)

Note that the terms in Fk cancel and so, when expression (A.14) is subtracted from expression (A.7) to arrive at Hicksian income or NNP when there is excess deforestation, the final expression becomes.

NNP = C + K - F . R — d — g

L - b a - d - a g - nL

(A.15)

where, p[ = U[ UJ^ and l ^ c - Genuine savings, G, in this model is defined as NNP - C.

Appendix 2.2

Figure A2.2.2 Map of Study Area

K UUA L LK A

C a rr c to rj F oderaca B a u c l i c

U cayali

Appendix 2.3

Table A2.3.1 Basic Agricultural Data

Output Unit Price New soles Labour Days/ha/yr Wage New soles Capital Unit Cost Rice 1333 kg 0.79 55 13.00 Seed 8 kg 1.00 Seed Service 1 0 0 .0 0 Corn 1000 kg 0.35 25 13.00 Seed 12 kg 1.00 Sack 20 units 0.30 Yuca 1 0 0 0 0 kg 0 .1 0 34 13.00 Plantain 600 bunches 3.00 29 13.00 Fuelwood 5000kg 25 13.00 Source: Nalvarte (1999)

Appendix 2.4

Figure A2.4.1

Net Carbon Accumulation: farm reverts to (secondary) forest

250 1 200 - E 150 - O 1 0 0 - 2 4 6 22 24 0 8 10 12 14 16 18 20 Year

Chapter 3