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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
Transcript

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

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(

ˆˆ

)1)1(

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

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

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

.

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

.

.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,

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,

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.


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