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BIO-PROSPECTING, LAND DEVELOPMENT, AND
BIOLOGICAL DIVERSITY UNDER FREE TRADE
RAFAT ALAM
University of Ottawa
N.V. QUYEN University of Ottawa
1. INTRODUCTION
In the early development of medicines, higher plants have played a vital role in providing
biologically active compounds for producing pharmaceuticals. With the advent of
synthetic chemical design, the role of plant-based agents in the development of new and
clinically effective pharmaceutical products declined significantly. In the last two
decades, there was a resurgence of interest in the potential of the chemical compounds
manufactured by higher plants to provide proto-types for new pharmaceuticals,
agrochemicals, and consumer products. The tropical forests in developing countries,
which house more than half of the world’s estimated 500, 000 plant species, represent a
potentially unlimited pool of novel structures – if discovered – as blueprints for the
development of marketable drugs.
To serve as a pool of novel structures, which constitute the target of the bio-prospecting
process, these higher plants must be protected. There are direct costs of biodiversity
protection. Because land has alternative uses, such as housing development or food
production, there is also an opportunity cost involved in maintaining tropical forests as
reservoirs of biodiversity. An economic analysis must take into consideration all these
costs, and the conservation of biodiversity can only be justified if there are sufficient
benefits to warrant its conservation. Because the knowledge about a species and the bio-
chemicals it manufactures might serve as the basis for discovering and developing
marketable drugs, the developing countries with tropical forests have a legitimate claim
on the profits made by these pharmaceutical companies. In this chapter, we present an
economic model in which the bio-prospecting process, its costs, and its benefits, as well
as the opportunity cost of biodiversity conservation are formalized. Now most models
that attempt to measure the value of biodiversity – whether in terms of the revenues
generated by tourism activities or in terms of the monetized value of the medicinal plants
the biodiversity houses – adopt the partial-equilibrium approach. The model of the
present chapter, in contrast, is formulated from a general equilibrium perspective in a
two-country trade framework.
The chapter is organized as follows. In Section 2, the model is presented.
2. THE MODEL
In the model we build, economic activities take place over two periods – called period 0
and period 1. There are two countries called the North and the South, respectively. In
what follows, we also refer to the North as country 1 and the South as country 2. There
are two types of goods in the model: a consumption good and a number of drugs. Each
country produces a consumption good – taken to be the numeraire – from land and labor.
Existing drugs are produced by pharmaceutical companies in the North. Pharmaceutical
companies in the North also carry out bio-prospecting programs using plant samples
obtained from the biodiversity resources of the South to search for new drugs. It is
assumed that labor is the only input used in bio-prospecting and in drug manufacturing.
Furthermore, at the beginning of period 0 there exist already 0n drugs which are labeled
drug1, drug 2,…, drug .0n We shall let },...,2,1{ 00 nJ = denote the set of drugs that have
already existed at the beginning of period 0. Also, we let },,...,1,,...,1{ 00 nnnJ += with n
being a positive integer greater than .0n Bio-prospecting activities are carried out during
period 0 and whose outcomes are only known at the end of this period. The set of drugs
that are available for production at the beginning of period 1 is denoted by ,1J with
.10 JJJ ⊂⊂ Note that 1J includes both 0J and the set of newly discovered drugs
.01 JJ −
Let iA be the land endowment of country .2,1, =ii . In each country, part of the land
endowment has already been developed and is ready for use as input in the production
process. The remaining part is still in a state of wilderness and must be cleared before
being used as a factor of production. The area of the developed land available for food
production in country ,2,1, =ii in period 0 is denoted by .0,iA We shall assume that all
the land in the North has been developed, i.e., 10,1 AA = In the South, the area of
wilderness land that houses its biodiversity resources at the beginning of period 0 is thus
given by .0,22 AA − This wilderness land is rich in biological diversity and can be
conserved or cleared in any period for use as input in food production.
2.1. Preferences and Utility Maximization
We assume that the population of each country is a continuum of measure 1 and an
individual is characterized by her type .10, ≤≤θθ The type of an individual
characterizes her ownership of the means of production and her claim to the profits of the
firms. The distribution of types in country ,2,1, =ii is described by a distribution
function, say ).(θiF Each individual – in the North or in the South – has one unit of labor
that she supplies in-elastically in the labor market in each period. The income of an
individual from the South comes from two sources: labor and land ownership.1 For
consumers in the North, there is another source of income: ownership of pharmaceutical
firms. The pattern of land ownership in each country is assumed to be captured by a
function that depends on the types of the individuals that constitute its population. More
specifically, the amount of land owned by an individual of type θ in country ,2,1, =ii is
assumed to be given by ).(θia Thus in period 0, the stock of developed land in country
,2,1, =ii satisfies the following stock constraint .)()(1
00, ∫= θθ iii dFaA Furthermore, it is
1 The profits made by the representative firm that produces the consumption good in the South is zero under perfect competition and constant returns to scale.
assumed that in the North a consumer of type θ owns a fraction )(θjb of the
pharmaceutical firm that produces drug .,...,1, njj =
Consumers are assumed to derive utility from the consumption good and the drugs that
are consumed. The type of drug a consumer will consume depends on her health
characteristics. We shall assume that for a particular drug, a consumer either consumes
one unit of the drug or none of the drug at all. A drug consumption plan for an individual
can be represented by a list, say ( ) ,Jjjx
∈ where 0=jx indicates that drug j is not
consumed and 1=jx indicates that one unit of the drug j is consumed. The set of
possible drug consumption plans, say X, consists exactly of n2 elements, with the null
drug consumption plan represented by the list ).0,...,0( Given a drug consumption plan
( ) ,Jjjx
∈ we assume that the composite good – called drugs – that is associated with this
drug consumption plan is given by ,∑ ∈Jj jjx ε where ,, Jjj ∈ε is a positive parameter
representing the contribution to the composite good drugs by one unit of drug .j This
specification of the composite drug implies that the individual drugs are imperfect
substitutes for each other.
The preferences of a consumer – in the North as well as in the South – are represented by
the following utility function:
(3) ( )( ) ,][, 100
α
α ε ⎥⎦
⎤⎢⎣
⎡= ∑
∈
−∈
JjjjJji xxxxu
where 0x is the consumption of the numeraire and α is a parameter strictly between 0
and 1.
Consider a consumer in period 0, who has an income level m and who faces
,,...,1, 0njp j = as the price of drug .j She solves the following utility maximization
problem:
(4) ( )
α
α ε ⎥⎦
⎤⎢⎣
⎡∑∈
−
⎟⎠⎞⎜
⎝⎛
∈000
10,][max
Jjjjxx
xxJjj
subject to the budget constraint
(5) .0
0 ∑ ∈+=
Jj jj xpxm
To solve the utility maximization constituted by (5) and (6), let
( )( ) ( ){ }0,000
≤−= ∑ ∈∈∈mxpxmp
Jj jjJjjJjjX
be the set of drug consumption plans that is affordable, given drug prices and income.
This set is finite. Next, let ( )0Jjjx
∈ be an affordable drug consumption plan that the
consumer chooses. Then the income left to be spent on the consumption good is
,0
∑ ∈−
Jj jj xpm and the utility that the consumer obtains by making this choice is
(6) ( )( ) ( ) .,0
00
1α
α εφ ⎥⎦
⎤⎢⎣
⎡−= ∑∑
∈
−
∈∈Jj
jjJj jjJjj xxpmmx
The optimal drug consumption plan is the drug plan in ( )( )mpJjj ,
0∈X that maximizes (6).
We denote by ( )( ) ,,, 00
JjmpxJjjj ∈
∈ the optimal consumption of drug j and
( )( )mpxJjj ,
00 ∈
the optimal consumption of the numeraire. The indirect utility function of
the individual is then given by
(7) ( )( ) ( )( )[ ] ( )( ) .,,,0
000
10
αα ε ⎥
⎦
⎤⎢⎣
⎡= ∑
∈∈
−
∈∈Jj
jJjjjJjjJji mpxmpxmpv
2.2. The Consumption Good Sector
The consumption good in country ,2,1, =ii is produced with the help of land and labor
according to the following production function:
(8) ,10,
ii LAYiββ −=
where A and L denote, respectively, the land and labor input. Also, iβ is a parameter
strictly between 0 and 1. Note that the subscript 0 in 0Y indicates that this is the output of
the consumption good, namely good 0.
Consider a period in which the representative firm that produces the consumption good in
country i faces the rental rate of land ir and the wage rate .iω The representative firm
solves the following profit maximization problem:
(9) ( ) .max 1), LArLA iiLA
ii ωββ −−−
The following firs-order conditions characterize, respectively, the land and labor inputs
that maximize profit:
(10) ,011 =−−−ii rLA ii βββ
and
(11) .0)1( =−− −ii
ii LA ωβ ββ
2.3. The Bio-Prospecting Process
In their struggle for survival, plants manufactures biologically active compounds –
known as secondary metabolites – to defend themselves against insects, herbivores,
diseases, and harsh environmental conditions. Each species has a unique profile of
secondary metabolites, and it is in this pool of bio-chemicals that bio-chemical
compounds with the desired medicinal properties can be discovered through bio-
prospecting activities.
The search for novel biochemical structures by a bio-prospecting firm is systematic, not
random. A bio-prospecting program consists of three stages. In the first stage, the plants
whose secondary metabolites are expected to have the desired bio-chemical activity are
identified. Shaman, a pharmaceutical company, employs a network of ethno-botanists
and physicians to seek out plant remedies used by generations of native populations.2
Specific plants that are related to plants with proven bio-chemical activity might also be
the target of a systematic investigation. Samples of the identified plants are then collected
and screened for the desired novel bio-chemical structures. Each of these steps just
described takes time and involves enormous costs. At the end of each step, the results are
evaluated and the bio-prospecting program might be terminated – and all the resources
spent up to this point wasted – if it is judged that the leads turn out not to be as promising
as expected. Principe (1991) used the National Institute of Health experience with the
screening process in bio-prospecting and arrived at an estimate that from 1000 to 10,000
chemicals must be evaluated before a lead is found. In the second stage, the leads are
used to develop a drug with the desired properties. The drug thus designed must not be
toxic to the patient, and the development stage involves many clinical trials. If the clinical
trials are satisfactory and if the drug is not too expensive to produce, then the
pharmaceutical company can embark on the last stage of the bio-prospecting process:
marketing the drug. According to McChesney (1996), on average it takes about 10 years
and costs between 100 and 225 million dollars to discover, develop, and bring to the
market a new drug.
2.4. Pharmaceutical Firms and the Search for New Drugs
Recall that the set of drugs that already exist at the beginning of period 0 is
}.,...,1{ 00 nJ = The pharmaceutical companies that own patents for these drugs are
assumed to be distinct and each of these firms owns exactly one drug.3 Recall also that
the set of drugs – existing or yet to be discovered – is }.,...,1,,...,1{ 00 nnnJ += We shall
assume that in period 0 there are 0nn − other pharmaceutical companies, with each
company engaging in a bio-prospecting program in the South to find a new drug.
2 Conte, Lisa A. (1996): “Sharman Pharmaceuticals’ Approach to Drug Development,” in Medicinal Resources of the Tropical Forests, ed. by Michael J. Ballick, Elaine Elisabetsky, and Sarah A. Laird, Columbia University Press, New York, pp. 94-100. 3 It is simple to extend our model to the case of a pharmaceutical companies markets more than one drug or the case several pharmaceutical companies manufacturing the same or similar drugs. In the latter case, the same drugs marketed by different pharmaceutical companies can be considered as differentiated products.
Presumably, for each ,0JJj −∈ the pharmaceutical company that searches for drug j
among the flora of the South has won the right – before period 0 and over numerous
competitors – to obtain plant samples from the government of the South to screen for
desired bio-chemical compounds. In exchange for these plant samples, a bio-prospecting
company often pays up front a lump sum and promises to pay royalties in the future if its
bio-prospecting program results in a marketable drug. The company, under this scenario,
owns the intellectual property right to the novel bio-chemical structure it has discovered.
Competition among bio-prospecting firms will drive the net expected payoff – the profits
that remain after royalties have been paid in the production stage minus the lump sum
payment and the bio-prospecting costs – of obtaining the right for using the biodiversity
of the South down to zero. We shall ignore the lump sum payment and assume that the
bio-prospecting firm that discovers a marketable drug, say drug ,j pays the country from
the South a royalty of jτ per unit of the drug sold.
As discussed in Subsection 2.4, bio-prospecting is a long and costly process, with the
decision taken at each step in the process depending on the outcomes of all the previous
steps. We shall not attempt to model the sequential nature of the bio-prospecting process.
Instead, we take a very abridged view of the bio-prospecting process and assume that bio-
prospecting activities last one period and that labor is the only input used in this process.
Furthermore, we assume that the labor input needed in the search for drug ,, 0JJjj −∈
is jB and that the probability of success is .jq We shall also assume that bio-prospecting
activities are carried out during period 0; that the outcomes of the various bio-prospecting
programs are independent; and that the outcomes are only known at the end of period 0.
As for production costs for existing or newly discovered drugs, we shall assume that
drugs – existing or yet to be discovered – are produced with labor as the only input and
that it requires jl units of labor to produce one unit of drug ., Jjj ∈
2.5. General Equilibrium in the Second Period
Let 1J be the set of drugs that are available at the beginning of period 1. Included in 1J
are the drugs available in period 0 and the newly discovered drugs, with 01 JJ − as the set
of newly discovered drugs. The probability of the event 1J is
(12) .)1()()( 101
1 ⎟⎟⎠
⎞⎜⎜⎝
⎛−⎟
⎟⎠
⎞⎜⎜⎝
⎛= ∏∏
−∈−∈ JJjj
JJjjJ qqq
There are two possibilities to consider. The South can honor its agreements with the bio-
prospecting firms and conserve its biodiversity or the South can abandon these
agreements and clear the land for agricultural uses. In what follows, we shall assume that
wilderness land can be cleared at negligible costs.
2.5.1. General Equilibrium in the Second Period when Biodiversity is not Conserved
When the South decides not to maintain the biodiversity that could support the
production of the newly discovered drugs, the land that houses the biodiversity can be
cleared and used for food production. The total supply of land in period 1 in the South is
then equal to .2A Under such a scenario, the output of the consumption good is given by
(13) .220,2βAY =
Furthermore, the equilibrium rental rate of land and the equilibrium wage rate in the
South are given, respectively, by
(14) ,1222
2 −= ββ Ar
and
(15) .)1( 2222
ββω −−= A
The income of a consumer of type θ in the South is
(16) ].[)()( 2222222 AArarm −++= ωθθ
In (16) the last term on the right side represents the transfer from the government of the
South. Here we have assumed that the income generated by the land that used to house
the biodiversity resources is distributed equitably to all the consumers in the South.
In the North, the calculations of the equilibrium prices and outputs are much more
complex because each pharmaceutical company is a monopoly for the drug it sells. Thus
each existing pharmaceutical company can control the price it charges for its own drug.
Furthermore, because drugs are imperfect substitutes for each other, the price charged by
one pharmaceutical company for the drug it manufactures influences its own demand as
well as the demand for all the other drugs. Thus the pricing strategy of a pharmaceutical
company must be strategic.
By a marketing plan for the pharmaceutical company that manufactures drug ,, 0Jjj ∈
we mean a pair ( ),, jj Yp where jp is the price the company charges for its drug and jY is
the planned output of the drug. An arbitrary list of drug marketing plans ( )( )0
,Jjjj Yp
∈
does not automatically imply that all the single plans in the list can be realized because
the drug prices set by all the pharmaceutical firms in question determine jointly the
demands for all the drugs, in addition to part of the incomes – the dividends distributed
by these pharmaceutical companies – received by the consumers who are their owners.
Loosely speaking, a general equilibrium occurs when this list of drug prices induces an
equilibrium on the market for land, the market for labor, and the market for the
consumption good in each country. Furthermore, demand must also be equal to supply in
each drug market and no pharmaceutical firm wants to change its marketing plan.
Now the labor input used in the marketing plan ( )), jj Yp is equal to
(17) ,j
jj
YL
l= ).( 0Jj∈
Using (17) and assuming that the land and labor markets both clear, we obtain the
following expression for the rental rate of land and the wage rate in the North:
(18) ( )( ) ,1,1
0
1
0
1
1111
β
ββ−
∈
−
∈ ⎟⎟⎠
⎞⎜⎜⎝
⎛−= ∑ Jj
j
jJjjj
YAYpr
l
and
(19) ( )( ) .1)1(,1
0
1
0111
β
ββω−
∈∈ ⎟⎟⎠
⎞⎜⎜⎝
⎛−−= ∑ Jj
j
jJjjj
YAYp
l
The profit this marketing plan makes if it is realized is
(20) ( )( ) ,1)1(
,
1
0
1
0
11
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛−−
−=
−
∈
∈
∑
j
Jjj
j
jjJjjjj
YA
pYYpl
l
β
ββπ ).( 0Jj∈
Using (18), (19), and (20), we obtain the following expression for the income of a
consumer of type θ in the North:
(21)
( )( )
.1)1(
)(
1)1(
1)(,
0
1
0
1
1
0
1
1
0
1
0
1
1
1
11111
∑∑
∑
∑
∈
−
∈
−
∈
−
∈
−
∈
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛−−
−+
⎟⎟⎠
⎞⎜⎜⎝
⎛−−+
⎟⎟⎠
⎞⎜⎜⎝
⎛−=
Jjj
Jjj
j
jjj
Jjj
j
Jjj
jJjjj
YA
pYb
YA
YAaYpm
l
l
l
l
β
β
β
β
β
β
βθ
β
βθθ
The following condition must hold if the market for drug j clears:
(22) ( ) ( )( )[ ] ( )[ ] ),()(,)(,, 2
1
021
1
01
000θθθθ dFmpxdFYpmpxY
JjjjJjjjJjjjj ∫∫ ∈∈∈+= ).( 0Jj∈
Given ( ) ,0Jjjp
∈ (22) represents a system of 0n equations in the 0n unknowns ( ) .
0JjjY∈
We shall assume that this system has a unique solution and denote it by ( )( )( )00'' JjJjjj pY
∈∈
to indicate its dependence on ( ) .0Jjjp
∈ We call ( )( )( )
00'' JjJjjj pY∈∈
the list drug outputs
induced by ( )0Jjjp
∈ in the second period, given that the biodiversity is not conserved. The
profits made by the drug companies under ( )( )( )00'' JjJjjj pY
∈∈ are then given by
(23) ( )( ) ( )( )( )( )
,
1)1(1
0
01
00
''11
''''
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−−
−=
−
∈
∈
∈∈
∑
j
Jjj
Jjjj
jJjjjJjjj
pYA
ppYpl
l
β
ββ
π ).( 0Jj∈
DEFINITION 1: A list of drug prices ( )0Jjjp
∈is said to constitute part of an equilibrium
price system in the second period under the scenario that the South converts the land that
houses the biodiversity resources into agricultural land if the following conditions are
satisfied:
(24) ( )( ),,maxarg0','' Jjjjjjjpj ppp
j ∈≠= π ).( 0Jj∈
Let ( )0Jjjp
∈ be an equilibrium list of drug prices in the second period, given that the
South chooses not to conserve its biodiversity resources. Then the social welfare of this
region is given by
(25) ( ) ),())(,( 22
1
01,2
0θθ dFmpvV
Jjj ∈∫=
and the social welfare of the North is given by
(26) ( ) ( )( )( ) ).(),,( 1''1
1
01,1
000θθ dFpYpmpvV
JjJjjjjJjj ⎟⎠⎞
⎜⎝⎛=
∈∈∈∫
Note that in 1,1V and 1,2V the first subscript indicates country of origin while the second
subscript indicates time, i.e., the period.
2.5.2. General Equilibrium in the Second Period when Biodiversity is Conserved
Suppose now that 1J is the set of drugs available at the beginning of period 1, where, we
recall, 1J includes both the drugs that already exists in period 0 and the newly discovered
drugs. Also, suppose that the South honors its agreements with the pharmaceutical
companies that discovered the new drugs. The definition of general equilibrium under
this scenario is the same as the one given in Sub-subsection 2.5.1, except for some minor
modifications in the incomes of the consumers in the North and in the South. In
particular, the transfer that a consumer in the South receives now comes from the
royalties paid by the pharmaceutical companies that produce the newly discovered drugs.
To define the trade equilibrium under this scenario, let ( )1
,Jjjj Yp
∈ be a list of marketing
plans chosen by the various pharmaceutical companies for their own products. When the
South decides to conserve the biodiversity resources to support the production of the
newly discovered drugs, the total supply of land for use in the production of the
consumption good in period 1 in the South is then equal to .0,2A Under such a scenario,
the output of the consumption good is given by
(27) .20,20,2βAY =
Furthermore, the equilibrium rental rate of land and the equilibrium wage rate in the
South are given, respectively, by
(28) ,10,2222 −= ββ Ar
and
(29) .)1( 20,222ββω −−= A
The income of a consumer of type θ in the South is
(30) ( )( ) ,)(,)(
222201
1∑
−∈∈
++=JJj
jjJjjj YarYpm τωθθ
where ),(, 01 JJjj −∈τ is the royalty – paid to the South by the pharmaceutical company
that produces drug j – for each unit of the drug it sells. Note that in (30) we have
assumed that these royalties are distributed equitably to all the consumers in the South.
The labor input used by the pharmaceutical company that produces drug j is thus equal
to
(31) ,j
jj
YL
l= ),( 1Jj∈
Using (31), we obtain the following expressions for the rental rate of land and the wage
rate that clear the factor markets:
(32) ( )( ) ,1,1
1
1
1
1
1111
β
ββ−
∈−
∈ ⎟⎟⎠
⎞⎜⎜⎝
⎛−= ∑ Jj
j
jJjjj
YAYpr
l
and
(33) ( )( ) .1)1(,1
1
1
1111
β
ββω−
∈∈ ⎟⎟⎠
⎞⎜⎜⎝
⎛−−= ∑ Jj
j
j
Jjjj
YAYp
l
The profit made by the pharmaceutical company that produces drug j is
(34) ( )( ) ,1)1(
,
1
1
1
1
11
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛−−
−=
−
∈
∈
∑
j
Jjj
j
jjJjjjj
YA
pYYpl
l
β
ββπ ),( 0Jj∈
,1)1(
1
1
111
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛−−
−−=
−
∈∑
j
Jjj
j
jjj
YA
pYl
l
β
ββτ )).(( 01 JJj −∈
Using (32), (33), and (34), we obtain the following expression for the income of a
consumer of type θ in the North:
(35)
( )( )
.1)1(
)(
1)1()(
1)1(
1)(,
)(
11
11
11
1
11111
01
1
1
1
0
1
1
1
1
1
1
1
1
1
1
∑∑
∑∑
∑
∑
−∈
−
∈
∈
−
∈
−
∈
−
∈−
∈
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛−−
−−+
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛−−
−+
⎟⎟⎠
⎞⎜⎜⎝
⎛−−+
⎟⎟⎠
⎞⎜⎜⎝
⎛−=
JJjj
Jjj
j
jjjj
Jjj
Jjj
j
jjj
Jjj
j
Jjj
jJjjj
YA
pYb
YA
pYb
YA
YAaYpm
l
l
l
l
l
l
β
β
β
β
β
β
β
β
βτθ
βθ
β
βθθ
The following condition must hold if the market for drug j clears:
(36) ( ) ( )( )[ ]
( ) ( )( )[ ] ),(,,
)(,,
2
1
02
1
1
01
11
11
θθ
θθ
dFYpmpx
dFYpmpxY
JjjjJjjj
JjjjJjjjj
∫
∫
∈∈
∈∈
+
=
).( 1Jj∈
Given ( ) ,1Jjjp
∈ (36) represents a system of 11 Jn = equations in the 1n unknowns
( ) .1JjjY
∈ We shall assume that this system has a solution and denote it by ( )( )( )
11'' JjJjjj pY∈∈
to indicate its dependence on ( ) .1Jjjp
∈ We call ( )( )( )
11'' JjJjjj pY∈∈
the list drug outputs
induced by ( ) .1Jjjp
∈ The profits made by the drug companies under ( )( )( )
11'' JjJjjj pY∈∈
are
then given by
(37) ( )( ) ( )( )( )( )
,1)1(
1
1
11
11
''11
''''
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛−−
−=
−
∈
∈
∈∈
∑
j
Jjj
Jjjj
jJjjjJjjj
pYA
ppYpl
l
β
ββ
π ).( 0Jj∈
( )( )( )( )
,1)1(
1
1
11
1
''11
''
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛−−
−−=
−
∈
∈
∈
∑
j
Jjj
Jjjj
jjJjjj
pYA
ppYl
l
β
ββ
τ ).(( 01 JJj −∈
DEFINITION 2: A list of drug prices ( )( )1
1 Jjj Jp∈
is said to constitute part of an equilibrium
price system in the second period under the scenario that the South conserves the land
that houses the biodiversity resources if the following conditions are satisfied:
(38) ( ) ( )( )( ),,maxarg)(','1'1
01 JJjjjjjjpj JppJpj −∈≠
= π ).( 1Jj∈
Let ( )( )1
1 Jjj Jp∈
be an equilibrium list of drug prices in the second period, given that the
South chooses to preserve her biodiversity resources. Then the social welfare of this
region is given by
(44) ( )( ) ( ) ( )( )( )( ) ),(,,)( 2
1
0112111,2
111θθ dFJpYJpmJpvJV
JjJjjjjJjj∫ ⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛=
∈∈∈
and the social welfare of the North is given by
(45) ( )( ) ( ) ( )( )( )( ) ),(,,)( 1
1
0111111,1
111θθ dFJpYJpmJpvJV
JjJjjjjJjj∫ ⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛=
∈∈∈
2.6. The Conservation of Biodiversity: Decision Making in the Second Period
Suppose that at the beginning of period 0 the South agreed to let a number of
pharmaceutical firms use plant samples from its flora to search for drugs
.,...,2,1 00 nnn ++ Let 1J be the set of drugs – old as well as newly discovered – that are
available at the beginning of period 1. If the South honors the agreements it signed with
the bio-prospecting firms at the beginning of period 0, then the social welfare this region
will obtain in period 1 is given by (44). On the other hand, if the South does not honor the
agreement and converts the land that used to house the biodiversity resources into
agricultural land, then the payoff it obtains in the second period is given by (25). Thus the
South will conserve the biodiversity resource if and only if .)( 1,211,2 VJV ≥ The optimal
value social welfare function for the South in the second period is thus given by
(46) { }.),(max)( 1,211,21*1,2 VJVJV =
The expected payoff for the South in the second period, given that it signed an agreement
with the bio-prospecting firms at the beginning of period 0, is then given by
(47) ).( 1*1,2
10
1JVq
JJJJ∑
⊂⊂
2.7. General Equilibrium in the First Period
Let us now situate ourselves at the beginning of period 0 and analyze the problem of the
South at this point in time. If the South chooses not to conserve the biodiversity
resources, then the international trade equilibrium in period 0 is exactly the same as the
one analyzed in Sub-subsection 2.5.1, and the social welfare this region obtains in period
0 is also given by (25), namely .1,2V On the other hand, if the South allows the bio-
prospecting firms to search for the new drugs among its flora, then the general
equilibrium can be found as follows.
In period 0, if the South decides to conserve the biodiversity resources for bio-
prospecting, then its total supply of land for use in the production of the consumption
good in this period is equal to .0,2A Under such a scenario, the output of the consumption
good, the rental rate of land, and the wage rate are given, respectively, by (27), (28), and
(29). Furthermore, the income of a consumer of type θ in the South is given by
(48) .)1()(
)()(22
0,2221
0,22
2222ββ βθβ
ωθθ−− −+=
+=
AaA
arm
Next, let ( )0
,Jjjj Yp
∈ be a list of marketing plans for the drugs that exist at the beginning
of period 0. The total demand for labor by the bio-prospecting firms and the firms that
manufacture the existing drugs is
(49) ( )
.00
∑∑−∈∈
+JJj
jJj j
j BYl
The residual demand for labor by the representative firm producing the consumption
good is thus given by
(50) ( )
.100
∑∑−∈∈
+−JJj
jJj j
j BYl
If the land and labor markets in the North are to clear, then the rental rate of capital and
the wage rate must be given, respectively, by
(51) ( ) ( ) ( )( )( )
,1,1
00
1
00
1
1111
β
ββ−
−∈∈
−−∈∈ ⎟
⎟⎠
⎞⎜⎜⎝
⎛−−= ∑∑
JJjj
Jj j
jJJjjJjjj B
YABYpr
l
and
(52) ( ) ( ) ( )( )( )
.1)1(,1
00
1
00111
β
ββω−
−∈∈−∈∈ ⎟
⎟⎠
⎞⎜⎜⎝
⎛−−−= ∑∑
JJjj
Jj j
jJJjjJjjj B
YABYp
l
The profit made by the pharmaceutical company that produces drug j is
(53)
( ) ( ) ( )( )
( ) ,1)1(
,
1
00
1
00
11
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛−−−
−=
−
−∈∈
−∈∈
∑∑
j
JJjj
Jj j
j
jj
JJjjJjjjj
BY
ApY
BYp
l
l
β
ββ
π
),( 0Jj∈
Using (51), (52), and (53), we obtain the following expression for the income of a
consumer of type θ in the North:
(54)
( ) ( ) ( )( )
( )
( )
( )
.)(
1)1()(
1)1(
1)(
,,
)(
11
11
1
1111
1
01
0
1
00
1
1
00
1
1
00
1
00
∑
∑∑∑
∑∑
∑∑
−∈
∈
−
−∈∈
−
−∈∈
−
−∈∈
−
−∈∈
−
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛−−−
−+
⎟⎟⎠
⎞⎜⎜⎝
⎛−−−+
⎟⎟⎠
⎞⎜⎜⎝
⎛−−=
JJj jj
Jjj
JJjj
Jj j
j
jjj
JJjj
Jj j
j
JJjj
Jj j
j
JJjjJjjj
Bb
BY
ApYb
BY
A
BY
Aa
BYpm
θ
βθ
β
βθ
θ
β
β
β
β
β
β
l
l
l
l
The following condition must hold if the market for drug j clears:
(55) ( ) ( ) ( ) ( )( )[ ]
( )[ ] ),()1()(,
)(,,,
2
1
00,222
10,22
1
1
01
22
1
011
θβθβ
θθ
ββ dFAaApx
dFBYpmpxY
Jjjj
JJjjJjjjJjjjj
∫
∫
−−∈
−∈∈∈
−++
=
).( 0Jj∈
Given ( ) ,0Jjjp
∈ (55) represents a system of 0n equations in the 0n unknowns ( ) .
0JjjY∈
We shall assume that this system has a solution and denote it by
( ) ( ) ( )( )( )0
00''JjJJjjJjjj BpY
∈−∈∈ to indicate its dependence on ( ) .
0Jjjp∈
We call
( ) ( ) ( )( )( )0
00''JjJJjjJjjj BpY
∈−∈∈ the list drug outputs induced by ( ) .
0Jjjp∈
The profits made by
the drug companies under ( ) ( ) ( )( )( )0
00''JjJJjjJjjj BpY
∈−∈∈ are then given by
(56)
( ) ( ) ( )( )( ) ( ) ( )( )
( ) ( ) ( )( )( )
,
1)1(
1
00
011
00
00
''
''''''''''
11
''''
''''
⎟⎟⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜⎜⎜
⎝
⎛
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛−−−
−
×=
−
∈−∈
−∈∈
−∈∈
−∈∈
∑ ∑
j
JjJJj
jj
JJjjJjjj
j
JJjjJjjj
JJjjJjjj
BBpY
A
p
BpY
Bp
l
l
β
ββ
π
).( 0Jj∈
DEFINITION 3: A list of drug prices ( )0
#Jjjp
∈is said to constitute part of an equilibrium
price system in period 0 under the scenario that the South conserves the land that houses
the biodiversity resources if the following conditions are satisfied:
(57) ( ) ( ) ( )( ),,maxarg00 ''','
#'
#JJjjJjjjjjjpj Bppp
j −∈∈≠= π ).( 1Jj∈
Let ( )0
#Jjjp
∈ be an equilibrium list of drug prices in period 0, given that the South
chooses to conserve her biodiversity resources in this period. Then the social welfare
obtained in period 0 by this region is given by
(58) ( )[ ] ),()1()(, 2
1
00,222
10,22
#0,2
22
0θβθβ ββ dFAaApvV
Jjj∫ −−∈
−+=
and the social welfare of the North is given by
(59) ( ) ( ) ( ) ( )( )( ) ( ) ( ) ),(,,, 1
1
0'''''
#'
#1
#0,1
000θθ dFBBpYpmpvV
JjjJjJjjJjjjjJjj∫ ⎥
⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛=
−∈∈−∈∈∈
3. COMPARATIVE ANALYSIS
3.1 Conservation Decision
To conserve the biodiversity rich land in the South, the decision rule will be: whether the
expected social welfare in the South from biodiversity conservation is greater than the
social welfare from non-conservation. That is,
(60) 1,220,21,220,2~ VVVV δδ +>+ .
Here, ∑⊂⊂
=JJJ
j JVqV10
1)(~
11,21,2 , the expected social welfare in the South from conservation.
The above expression can be written as the following:
(60A) )()~( 0,20,21,21,22 VVVV −>−δ , as 0,21,2 VV = .
Expression (60A) implies that the discounted second period expected utility difference
between conservation and non-conservation has to be greater than the first period utility
difference between non-conservation and conservation scenarios. The present value of
second period utility gain from conservation has to be greater than the first period utility
loss from conservation.
1,2~V has to be large enough and 1,2V has to be small enough to maintain the inequality in
(60A) as it will ensure that the left hand side is relatively larger than the right hand side.
Now by analyzing the factors that affect 1,2~V and 1,2V , we can show the impact of other
factors on the conservation decision. For this comparative analysis, we can expand (60A)
as the following:
(60B)
( )( ) ( )( ) ( )( )( )( )( )( ) ( )( ) ( )( )( )( )
( )( ) ( )( ) ( )( )( )( )( )( ) ( )( ) ( )( )( )( ) ⎪
⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
⎟⎠
⎞⎜⎝
⎛⎟⎠⎞
⎜⎝⎛
−⎟⎠
⎞⎜⎝
⎛⎟⎠⎞
⎜⎝⎛
>
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
⎟⎠
⎞⎜⎝
⎛⎟⎠⎞
⎜⎝⎛
−⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛
∈∈∈∈
∈∈∈∈
∈∈∈∈
∈∈∈∈
0000
0000
0000
1111
,,,
,,,
,,,
,,,~
0#
0#
20#
0,2
00200,2
00201,2
11211,2
2
JjjJjjjJjjJjj
JjjJjjjJjjJjj
JjjJjjjJjjJjj
JjjJjjjJjjJjj
JpYJpmJpV
JpYJpmJpV
JpYJpmJpV
JpYJpmJpV
εθ
εθ
εθ
εθδ
3.2 Impact of Discount Rate and Probability of Success on Conservation Decision
From (60A), we find that there are two obvious factors that affects conservation decision:
Southern discount factor (inverse of the discount rate) and the probability of success in
new drug discovery. A high discount rate and a corresponding low discount factor on the
left hand side and a relatively large size of social welfare loss in the first period from
conservation on the right hand side can reverse (60A) and lead to land conversion and
corresponding destruction of biodiversity.
The search for new drugs by a bio-prospecting firm is not random. The firm relies heavily
on the local and traditional knowledge of the people living in the biodiversity rich areas
and on the prior scientific research on plant species. Moreover, the firm also relies on the
information about the health characteristics of the Southern and Northern consumers and
matches the disease with the search process. So, at first it chooses the disease for which it
will look for drugs depending on the health characteristics of the consumers and then
starts the search process using the already available scientific and traditional knowledge.
During the search process, the pharmaceutical companies do not analyze each and every
plant species for a new drug. Rather, the plants whose secondary metabolites are
expected to have the desired bio-chemical activity or specific plants that are related to
plants with proven bio-chemical activity are identified. Then if the leads result in the
development of a new drug, it has to go through many clinical trials. At last when the
clinical trials are satisfactory, the pharmaceutical company decides to market the drug.
This two prior information sets, one on the health characteristics of the consumers and
the other one on the scientific and traditional knowledge on the plant characteristics
makes the search process more systematic and decreases the uncertainty with the
invention of new drug many folds. This systematic search process increases the
probability of success than the random search process i.e. randomj
sustematicj qq
11> .
Yet like any other scientific research, there is always an uncertainty with the innovation
of any new drugs. This uncertainty affects the conservation decision. The conservation
decision in (60A) is positively related with the probability of success of innovating new
drugs i.e.
(61) .0~
1
1,2 >∂
∂
jqV
3.3 Impact of Drug Price on the Conservation Decision
Using (44), we can express the welfare of a consumer as:
(44A) ( )( ) ( )( ) ( )( )( )( ) ⎟⎠⎞
⎜⎝⎛
⎟⎠⎞
⎜⎝⎛=
∈∈∈∈1111
11211,21,2 ,,JjJjjjJjjJjj JpYJpmJpvv θ
The impact of any drug price, jp , on 1,2v can be shown as:
(62) j
j
jjj pY
Ym
mv
pv
dpdv
∂
∂
∂∂
∂
∂+
∂
∂= 2
2
1,21,21,2 .
In the above expression,
(62A) 01,2 <∂
∂
jpv
and,
(62B) 0,0,0 2
2
1,2 <∂
∂>
∂∂
>∂
∂
j
j
j pY
Ym
mv
.
So, drug price has a dual impact on the social welfare of the South. Through (62A), it
affects the social welfare negatively. On the other hand (62B) implies that the price of the
drug also negatively affects the Southern social welfare through a chain link: 1,2~V is
positively related to the Southern income level 2m , income level is positively related to
the royalty payments∑ jjYτ and demand of drug jY , and demand of drug, jY , is
negatively related to the drug price.
It follows from (62A) and (62B) that:
(62C) 01,2 <jdp
dv.
It implies if the new drug price is greater than the old drug price, the welfare of the
consumers who consume the new drug will decrease and vise-versa. So, the variables and
parameters that affect the drug price will also affect the conservation decision.
From (37), the profit maximization problem for the old drugs with no conservation and
the new drugs with conservation can be written as:
(63A) ⎥⎥⎦
⎤
⎢⎢⎣
⎡−=Π
j
jjjjj
Yj
Y lY
YpYpMaxMaxjj
)()( 1ω , for an already available drug with
no-conservation.
(63B) ⎥⎥⎦
⎤
⎢⎢⎣
⎡−−=Π jj
j
jjjjj
Yj
Y
Yl
YYpYpMaxMax
j
ˆˆ
ˆ)ˆ(ˆ)ˆ(ˆˆˆ
1ˆˆ
1
τω , for a new drug with
conservation.
The above profit maximizing problems lead to the general solution for the price of an
existing drug with no-conservation and a new drug with conservation as the following:
(64A) ( )
⎟⎟⎠
⎞⎜⎜⎝
⎛−
+=
dj
yj
el
ep j
11
1 ,1 1ωω
, price of drug j under non-conservation scenario,
(64B) ( )
⎟⎟⎠
⎞⎜⎜⎝
⎛−
++=
dj
jyj
el
ep j
ˆ11ˆ
ˆ1ˆˆ ˆ,ˆ1 1
τω ω , price of drug j under conservation scenario.
Using (64A) and (64B), we can explain the factors that affect the drug prices and how it
changes.
Impact of Drug Demand on Drug Price
The variables and parameters in (64A) and (64B) can be expressed as the following:
(65)
)1(
1
)1(
1ˆ
ˆˆ
)1)1(
)ˆ
ˆ1)1(ˆ
1
11
1
11
1
1
1
1
1,
1ˆ,ˆ
111
111
∑
∑
∑
∑
−=
−=
⎟⎟⎠
⎞⎜⎜⎝
⎛−−=
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−−=
−
−
j j
jj
jy
j j
jj
jy
j
j
j
j
lYl
Ye
lYl
Ye
lY
A
l
YA
β
β
βω
βω
ω
ω
β
β
β
β
The drug demand jY affects all of the above parameters and also the elasticity of
demand de . From (65), we can show that:
(66) 0
0
,
1
1 >∂
∂
>∂∂
j
Y
j
Y
eY
jω
ω
Using (64A), (64B) and (66), we can state that,
.ˆ,,ˆ,ˆ,
.),(,
:1
,ˆ,ˆ11
1,
11
1
versaviseandppsoandeethenYYwhenimpliesIt
versaviseandpsoandethenYIf
Fact
jjYYjj
jYj
jj
j
−>>>>
−↑↑↑
ωω
ω
ωω
ω
The increased drug demand also has impact on the elasticity of demand which is
negatively related to the drug price jp i.e.
(67) .0<∂∂
j
d
Ye
As the drug market is a monopoly for every unique drug, firm will only sell drug at
prices when demand is elastic or 1>de . New drug prices will increase as the demand for
the drug becomes less and less elastic. Elasticity of demand will be less elastic and close
to one when the new drug contributes highly to the utility or jε is high. This can be true
for a drug that has more life saving capacities.
By solving the profit maximizing problem described by equations (4) and (5), we get the
demand for new drug for any representative consumer in the North or the South as the
following:
(68) ji
jjijii
j
jjijii
jiother
otherother
other
otherotherx
p
xpmx
,
,,,
,
)1()(
ε
εαα ∑∑ −−
−=
We know that,
(69) ( )( )[ ] ( )( )[ ] )(,, )(,, 22
1
0,222,211
1
0,111,1 θθθθ dFYpmpxdFYpmpxY jjjjjjjjj ∫∫ +=
From (68) and (69) we can derive:
(70) 0>∂
∂
j
jYε
(71) 0<∂
∂
otherj
jYε
(72) .0<∂
∂
otherj
j
pY
Equation (70) implies that jε and jY is positively related. Equations (68) - (72) imply
that demand for new drug is negatively related with the following:
i. The price of the other drugs otherjp
ii. Total expenditure for the other drugs ∑other
otherotherj
jij xp ,
iii. The importance of the other drugs otherjε .
Using (67), (70) and the intuition that when jε is high, de is low, we can state that:
.ˆˆ,ˆ,ˆ
.,,,
:2
versaviseandppsoandeethenYYwhenimpliesalsoIt
versaviseandpsoeYWhen
Fact
jjddjjjj
jdjj
−><>>
−↑↓↑↑
εε
ε .
Using facts 1 and 2, we can state the following:
Statement 1: Between an old drug and a new drug, if the demand for the new drug jY is
lower than the old drug jY , then the price for the new drug will be lower than the old drug
and that may increase the expected utility from conservation.
Impact of Labour Productivity on the Drug Price
From (64A), (64B) and (65), we get:
(73) 0
0
,
1
1 <∂
∂
<∂∂
j
Y
j
l
el
jω
ω
It implies that labor required for per unit of drug production, jl , has several impacts on
price of the drug:
i. a negative indirect impact through the wage rate
ii. a negative indirect impact through the elasticity of wage rate
iii. a direct negative impact.
The overall relationship of jl with the drug price is negative i.e. 0<∂
∂
j
j
lp
. jl represents
the productivity of labor for each drug. So, the impact of jl on the drug price is the
supply-side impact. If the productivity is lower, the cost is higher and that will lead to a
higher price and vise-versa. So, we can state the following:
Statement 2: Between an old drug and a new drug, if the labor needed per unit of drug
production for the new drug jl is higher than the old drug jl , then the price for the new
drug will be smaller than the old drug and that may increase the expected utility from
conservation.
3.4 Impact of Consumer Income on the Conservation Decision
Social welfare is positively related with the income of the consumers, 2m :
(74) .02
21 >∂∂
mV
The incomes of a representative Southern consumer in the second period under
conservation and non-conservation scenarios are given as the following:
(30) ( ) ∑−∈
++=)(
222201
)(JJj
jjYarm τωθθ
(16) ][)()( 2222222 AArarm −++= ωθθ
As under non-conservation, there is greater supply of land and rental rate is negatively
related with land supply, it follows that:
22 rr > .
On the other hand, wage rate is positively related with land supply and so it follows that:
.22 ωω <
So, the income under conservation scenario will be greater than the non-conservation
scenario only if the following holds:
(75A) )(])[()()( 22222222 ωωτθ −>−−∑+− AArYarr jj .
As the production of new drugs in the North will deviate labour from the consumption
good sector, the Northern production of the consumption good will be lower under the
conservation scenario in the second period. It will increase the demand for Southern
consumption good in the North. This increased demand for Southern consumption good
will increase the demand for developed land in the South. But as under conservation
scenario, the amount of developed land will remain same and consumption good sector is
more land intensive, the increased demand will increase the rental rate more than the
decrease in the wage rate under conservation i.e. .,)()( 222222 ωωω ∆>∆−>− rorrr
On the other hand, to hold (75), it implies that the royalty income ∑−∈ )( 01 JJj
jjYτ has to be
large enough so that the increased rental income from conservation and the difference
between the royalty income and the lost rental income from land conversion is greater
than the lost wages from non-conservation. The royalty income can be higher in two
ways:
i. A higher jτ can result into higher royalty income
ii. A larger drug sale can result into higher royalty income.
The drug company will be able to pay a high royalty per unit, if the drug price is high and
vise-versa. So, a high royalty per unit of drug with a high drug price and low demand or a
low royalty per unit of drug with a low drug price and a high demand will make the total
royalty payment for the southern consumers higher.
3.5 Impact of jε on the Conservation Decision
jε is a positive parameter representing the contribution to the composite good drugs by
one unit of drug .j Equation (7) expresses the indirect utility of a representative consumer
in the South. As the Southern social welfare is a sum of all the individual indirect utilities
with equal weight, the affect on the representative consumer’s indirect utility can explain
the affect on the social welfare too.
(7) ( )( ) ( )( )[ ] ( )( ) .,,,0
000
10
αα ε ⎥
⎦
⎤⎢⎣
⎡= ∑
∈∈
−
∈∈Jj
jJjjjJjjJji mpxmpxmpv
From equation (7), we get that:
(76) 01,2 >∂
∂
j
vε
.
It implies that besides the drug price and the income of the Southern consumer, the
weight or importance of the new drug in the Southern consumer’s utility function also
decides the social welfare of the South.
3.6 Overall Impact of a New Drug on the Southern Consumer’s Utility
A new drug can affect the utility of the Southern consumer in three ways:
i. There will be an affect through the price of the new drug, i.e.
(62C) 01,2 <jdp
dv
.ˆ, 1,21,2 vvimplywillppor jj >>
ii. There will be an affect through the changed income for the new drug, i.e.
(74) 02
21 >∂∂mv
.ˆ, 1,21,222 vvimplywillmmor >>
iii. There will be an affect due to the importance of the new drug, i.e.
(76) 01,2 >∂
∂
j
vε
.
.ˆ, 1,21,2 vvimplywillor jj >> εε
The overall affect of the invention of a new drug will depend on all the above conditions.
There can be few possibilities (assuming only one new drug is invented):
Fact 3: If the price of the new drug is lower than the old drug, jj pp <ˆˆ , the new drug
is less important than the old drug, 22ˆˆ jj εε < and the new drug increases the income of
the Southern representative consumer, 22ˆ mm > , then 1,21,2 vv > will hold only if,
2ˆ
1,2
2
1,21,2
ˆˆˆjj
vmv
pv
ε∂∂
>∂
∂+
∂
∂.
Fact 4: If the price of the new drug is lower than the old drug, jj pp <ˆˆ , the new drug
is less important than the old drug, 22ˆˆ jj εε < and the new drug decreases the income of
the Southern representative consumer, 22ˆ mm < , then it is most likely that 1,21,2 vv >
will not hold.
Fact 5: If the price of the new drug is higher than the old drug, jj pp >ˆˆ , the new drug
is more important than the old drug, 22ˆˆ jj εε > and the new drug increases the income
of the Southern representative consumer, 22ˆ mm > , then 1,21,2 vv > will hold only if,
2ˆ
1,2
2
1,21,2
ˆˆˆjj
vmv
pv
ε∂∂
+∂
∂<
∂
∂.
Fact 6: If the price of the new drug is higher than the old drug, jj pp >ˆˆ , the new drug
is more important than the old drug, 22ˆˆ jj εε < and the new drug increases the income
of the Southern representative consumer, 22ˆ mm < , then 1,21,2 vv > will not hold.
3.7 Impact of Population Characteristics Parameter θ
The parameter θ shows the characteristics of the population. In reality, θ will be skewed
in distribution i.e. South will have a negatively skewed distribution of θ to indicate its
poverty and the North will have a positively skewed distribution ofθ to indicate its
richness. But θ can represent more than one argument besides richness. If it is possible
to represents the health characteristics of the individual consumers by θ and we can
aggregate the demand for a new drug with respect to both of the two characteristics of the
individual consumer: the richness and the health characteristics, then the aggregate
demand will be able to provide a picture equivalent to one of the five cases described in
section 3.7. Depending on that aggregation, the conservation may or may not take place.
The health characteristics and distribution of income of the Southern and Northern
population are observable. Bio-prospecting firms can do research on these aspects of the
Southern and Northern consumers in advance and find out the drugs that will be most
viable and feasible to bio-prospect. This pre decision and systematic prospecting will
make the success rate of discovering a new drug very high and lead to successful bio-
prospecting contract and biodiversity conservation.
3.8 The first Period Conservation Decision
In the first period, the difference between the conservation and non conservation scenario
is only due to the difference in the income. As in both cases, no new drugs will be
introduced in the market, the drug prices will remain same and will have no impact on the
social welfare. The first-period incomes under conservation and non-conservation
scenarios are expressed as the following:
(48) )()( 2222 ωθθ += arm
(16) ][)()( 2222222 AArarm −++= ωθθ
As 22 rr > and 22 ωω < , the income under non-conservation scenario will be greater than
the conservation scenario only if the following holds:
(75B) )()()(])[ 22222222 θωω arrAAr −>−+− .
It implies that rental income from land conversion and increased wage income under land
conversion scenario have to exceed the decreased rental income from land conservation.
As bio-prospecting by the Northern drug firms will deviate labour from the consumption
good sector, the Northern production of the consumption good will be lower under the
conservation scenario in the first period. It will induce )()( 2222 ωω −>− rr or
22 ω∆>∆r and make the left hand side of (75B) not very large than the right hand side.
This will make the first period loss of social welfare from conservation low enough to
lead to conservation of biodiversity.
3.9 Strategic Pricing, Production Plan and Conservation Decision at the Aggregate level
Biodiversity conservation will depend on whether the present value of second period
utility gain from conservation will be greater than the first period utility loss from
conservation. We get the social welfare of the South by summing up the welfare of
individual consumers with equal weight. The analysis in sections 3.1 to 3.6 shows that
the welfare of a southern consumer is affected by several factors: the drug production
plan ),( jj Yp , the royalty income ∑−∈ )( 01 JJj
jjYτ and the importance of the new drug jε . So,
the social welfare and conservation decision expressed by (60A) will also depend on
these three factors. These will also decide whether the price of the new drug will be
greater than the set of old prices or not.
But in the case of several new drugs, the prices of new drugs have to be strategic. The
strategic pricing will decide in aggregate whether the social welfare of the Southern
consumer will be higher or not and biodiversity will be conserved or not. Before bio-
prospecting starts, the Northern drug firms will do research on the health characteristics
of the Northern and Southern consumers and chose the diseases. Then it will match the
health information with the information set on plant species. These prior decisions will
increase the success of bio-prospecting and help the firm to maximize their profits.
There are two assumptions of the model in this paper that leads to price and production
decisions of the firms that bio-prospect. First, as the drug market is a monopoly market
and operates only at the elastic demand portion of the demand curve, revenue increases
with a lower price of the product. So, it is most likely that highly demanded drug’s price
will be low. Second, the northern consumers are rich and the Southern consumers are
poor in general. Given these two assumptions, the following statements can be drawn
from the model about the drug price and the conservation decision at the aggregate level:
i. High 1jε , low 1
jY and 02 =jY : If the drug is for a disease specific to the Northern
rich people, the drug company would be able to charge a higher price. Then even
if it is consumed by few people in the North, it can be feasible to produce it. In
this case, there will be no price or drug consumption affects on the Southern
social welfare, but only the income affect. It may lead to 1,21,2~ VV > and ensure
biodiversity conservation.
ii. High 2jε , low 2
jY and 01 =jY : If the new drug is a highly important drug for a few
southern consumers (high 2jε and low 2
jY ) and there is no Northern demand, the
firm has to charge high prices for that drug to make the production plan feasible.
In this scenario, the Southern consumers will not be able to pay the high price due
to low income and the production of the drug may not materialize at all.
iii. High 1jε and 1
jY , low 2jY or High 1
jε , 2jε and low 1
jY , 2jY : If the new drug is a
highly important drug for a large number of Northern consumers (high 1jε and 1
jY )
and a few Southern consumers (low 2jY ) or the drug is highly important for a few
northern and southern consumers (High 1jε , 2
jε and low 1jY , 2
jY ), the drug firm can
discriminate price between the northern and southern consumers – charge a high
price to the northern consumers and a low price to the southern consumers. The
lower price in the south and a high royalty income generated by a high drug price
in the North and the high 2jε will increase the Southern social welfare and lead to
conservation of biodiversity.
iv. High 2jε and 2
jY : If the new drug is a highly important drug for a large number of
Southern consumers the drug company has to charge a relatively lower price due
to the lower purchasing capacity of the southern consumers. A lower price, a high
jε accompanied by a higher royalty income due to large value of jY will increase
the social welfare of the South high enough to lead to conservation of biodiversity
rich land.
v. High 1jε and 1
jY : If the new drug is a highly important drug for a large number of
Northern consumers the drug company can easily charge a relatively lower price
and still make the production plan feasible. In this case, no price or drug
consumption affects accompanied by higher royalty income due to large value of
jY will increase the social welfare of the South high enough to lead to
conservation of biodiversity rich land.
vi. Low jε and high jY : Whenever the importance of the drug is low, the production
plan will only be feasible if the demand for the drug is high, be it from the north
or from the south or by a joint demand from both the north and south. Due to low
value of jε , the drug company has to charge a low price. In these cases, a low
price and a high royalty income due to high demand, may lead to conservation.
vii. On the other hand, higher prices for the new drugs may compel the existing drug
producers to act strategically and charge lower prices. So, in aggregate the
southern social welfare will increase if the loss in welfare due to higher prices for
the new drugs is exceeded by the gain in social welfare from the lower prices of
the existing drugs.
3.10 Strategic Pricing for Several Drugs and Conservation
If there are several new drugs, the pricing of the drugs has to be strategic and it will
depend on the characteristics of the drug consumers and drug demand. We know the from
equations (68) - (72) that drug price has negative relationship with the following:
i. The price of the other drugs otherjp
ii. Total expenditure for the other drugs ∑other
otherotherj
jij xp ,
iii. The importance of the other drugsotherjε .
These relationships decide the strategic prices of a new drug when there are several new
drugs. We can state the following from the model about strategic pricing under several
new drugs:
1. If all the new drugs are for the Northern consumers, the firm will charge higher prices
for all the drugs which have lower demand compared to the drugs which have higher
demands. If the demand for the drugs is similar and from the same groups of people, the
drug price charged has to be relatively low to make each drug affordable to northern
consumers. On the other hand, if the demand for the drugs is similar but from different
groups of people, the firm can charge high price for each drug.
2. If the drug is for the southern consumers, the price charged has to be low due to their
lower purchasing power.
3. If some of the drugs are for the southern consumers and some are for the northern
consumers, the northern drugs will have higher prices than the southern drugs.
4. If the drugs are both for the northern and southern consumers, the monopoly firm can
discriminate price and charge a high price for the Northern consumers and a lower price
for the southern consumers.
5. If all the drugs are for a larger number of consumers, the prices of all the drugs have to
be relatively low so that everyone can afford all the needed drugs and make the demands
high enough for the production plans to be feasible.
But the drug prices have to be strategic only when there are several drugs and a large
number of consumers or same group of consumers need to consume it and the consumers
are not mutually exclusive. For all the above strategic pricing, the firm will do prior
research on the feasibility of the production plans and the pricing strategy accompanied
by the royalty income will ensure conservation.
3.11 Determinants of Terms of Trade and It’s Impact on Conservation Decision
The Southern terms of trade is denoted by jp
1 or the inverse of the drug price. All the
variables that affect price of drug will inversely affect the price of the consumption good,
0x . For facts 3 and 4, the price of drug decreases with the invention of a new drug. But at
the same time it increases the terms of trade for the South. A larger set of new drugs also
lead to low prices for all the new drugs and increase the southern terms of trade. Also
both in the first and second period due to bio-prospecting and production of new drugs,
labour is diverted from the consumption goods sector in the North. It will create higher
northern demand for southern consumption good. A higher southern income from royalty
payment will add another pressure on the demand for southern consumption good. For all
these reasons, the south faces a dual impact: a direct incentive for conservation and an
indirect incentive for land development. If the economy can be modeled for more
periods, the incentive to clear biodiversity rich land may become high enough to make
1,21,2~ VV < and reverse the conservation decision.
4. Conclusion
The paper has shown that with a systematic search process depending on prior
information on the plant species and the health characteristics increases the success of
bio-prospecting and biodiversity conservation. Systematic search process and strategic
drug pricing are key to a successful bio-prospecting. But there are some caveats of this
systematic search process. The drug companies will ignore any of the southern specific
diseases which do not create enough demand. On the other hand if the Southern
governments help the drug companies by decreasing their costs by waiving the royalty
payment for these drugs and make the production plan of these drugs feasible. But as the
south faces a dual pressure for conservation and land development at the same time, bio-
prospecting contracts may break down in longer terms. So, bio-prospecting may be one
of the feasible options for biodiversity conservation, but may not be a strong or only
option.
REFRENCES
PRINCIPE, P.,(1991): “Valuing the biodiversity of medicinal plants,” in The Conservation of Medicinal Plants, ed. by O. Akerele et al., Cam-bridge University Press, Cambridge, 1991. MCCHESNEY, J. D. (1996): “Biological Diversity, Chemical Diversity, and the Search for New Pharmaceuticals,” in Medicinal Resources of the Tropical Forests, ed. by Michael J. Ballick, Elaine Elisabetsky, and Sarah A. Laird, Columbia University Press, New York, pp. 11-18.