1. TRADE, TRAGEDY, AND THE COMMONS
B. Copeland & S. Taylor, NBER WP 10836, 2004
simplified version prepared by J-M Grether
December 2004
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2. TRADE AND TRAGEDY OF THE COMMONS
Property rights (PRs) over renewable resources (fishes, forests) are difficult to define and often poorly enforced.
 tragedy of the commons = over-exploitation of resources because each agent ’s harvest affects the productivity of future harvests .
+ trade liberalization may exacerbate the effect  stock depletion and reduction of real income in resource-exporting countries (eg. Chichilnisky, 1994 or Brander & Taylor, 1997)
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3. ENDOGENOUS PROPERTY RIGHTS
Enforcement of PRs vary enormously across communities, over time and by resource type.
 here: PRs are endogenous = government takes into account the agents’ incentive to cheat.
= model: add an (efficiency wage-type) incentive constraint to an existing ricardian framework (Brander & Taylor, 1997)  3 main results:
determinants of PRs enforcement
typology of countries (Hardin, Ostrom and Clark economies)
trade liberalization may be beneficial after all
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4. A SIMPLIFIED PRESENTATION
1. Resource dynamics
2. Optimal resource management vs. Open access
3. The incentive constraint
4. Typology of countries
5. Effects of trade liberalization
6. North-South trade and resource management
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5. Logistic growth function:
1. RESOURCE DYNAMICS
Logistic growth function:
where r: intrinsic rate of resource growth, S: resource stock level, K: carrying capacity
in terms of growth rates: S K
 K is the “natural” steady state stock level (without human intervention)
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6. RESOURCE DYNAMICS (ct ’d)
Harvesting (: productivity parameter, L: labor allocated to harvesting ):
in terms of growth rates: L
 steady state stock level: S K S*
exhaustion of the resource:
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7. RESOURCE DYNAMICS (end)
Harvest at steady state: H
Lmax
½Lmax K
S*(L)
= inverted-u shaped, with maximum obtained at:
H*(L)
 which level of harvesting?
depends on incentives and PRs enforcement in a general equilibrium framework
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8. 2. RESOURCE MANAGEMENT MODEL
Hypos:
2 sectors: H and M (manufactures)
one factor: N = L+LM, 1 unit to each agent
small open economy, p is international price of H
M sector has CRTS, with M=LM
M sector is numéraire, pM=w
analysis at steady state (transition dynamics in companion paper)
agents are infinitely patient (relaxed later)
government is infinitely patient (relaxed in paper)
positive or zero depending on resource management
Rents in H sector:
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9. RESOURCE MANAGEMENT (ct’d)
PPF: given by H*(L) H
(w/p)L
A: optimal management (perfect enforcement of PRs): real income and rents are maximized A L*
Rents: given by the difference between H(L) and the opportunity cost line, (w/p)L
B: open access (no PRs at all, developing country): rents are totally dissipated: resource depletion and lower real income = tragedy of the commons B L0  N
two cases:
½Lmax
Lmax M
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10. RESOURCE MANAGEMENT (end)
Impact of trade liberalization: suppose the country is resource-exporting and p
(w/p0)L H
A: optimal management: real income  (usual gains from trade) A A’
B: open access: more resource depletion and real income  B’ B
(w/p1)L N
½Lmax
Lmax M
But: what if resource management is endogenous?
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11. limited harvest time: /N per agent
3. INCENTIVE CONSTRAINT
Hypos:
limited harvest time: /N per agent
if caught: looses forever access to harvest
dt: probability of getting caught over dt
dt: probability of death over dt
: rate of time preference
to cheat (C) or not to cheat (NC) ?
where:
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12. INCENTIVE CONSTRAINT (ct’d)
At steady state, after simplification, the no-cheating condition becomes:
present value if caught forever in manufacturing
present value of
rents from harvesting
This is equivalent to:
= to make cheating unattractive, the access rule must be sufficiently generous given agent’s impatience (), their expected lifetime (1/) and their probability of being caught ()
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13. INCENTIVE CONSTRAINT (end)
Is the incentive constraint biting? Three cases: H
unconstrained first best = optimal harvesting restriction is incentive compatible
constrained optimum = limited harvesting restriction
(w/p)L N
de facto open access = no harvesting restriction compatible with positive rents L* L0
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14. Depending on the magnitude of Lc relative to Lmax:
4. TYPOLOGY OF COUNTRIES
Depending on the magnitude of Lc relative to Lmax:
3 types (with government infinitely patient)
1. Clark
2. Ostrom H
3. Hardin
½Lmax N
Lmax
For each type of country, PR enforcement will depend on international price.
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15. TYPOLOGY OF COUNTRIES (ct’d)
(w/p+)L
1. Clark economies H
if p<p+: not possible to deter cheating = de facto open access
if p+<p<p++: some restriction, but not optimal = constrained optimum
if p>p++: optimal restriction is incentive-compatible = first best
(w/p++)L N M Lc
Lmax
p++ p+
H/M
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16. TYPOLOGY OF COUNTRIES (ct’d)
2. Ostrom economies H
if p<p+: not possible to deter cheating = de facto open access
(w/p+)L
if p>p+: some restriction, but not optimal = constrained optimum Lc
Lmax
but: never possible to achieve first best p+
H/M
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17. TYPOLOGY OF COUNTRIES (ct’d)
3. Hardin economies H
for any p: not possible to deter cheating = de facto open access
= neither constrained optimum nor first best
backward-bending relative supply
(w/p*)L
Lmax Lc N p*
H/M
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18. TYPOLOGY OF COUNTRIES (ct’d)
open access
Hardin
Lc=L0
Ostrom
constrained optimum
Lc=L*
Clark
first best
p+C
p+O
p++C p
= for given value of other parameters, N determines country type, while N and p determine PRs enforcement
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19. TYPOLOGY OF COUNTRIES (end)
EPR 1
Clark
Effective property rights:
Ostrom
Hardin
EPR=L*/L
p+C
p+O
p++C p
Hardin economies cannot improve resource management, but Ostrom and Clark economies can, depending on international prices.
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20. if p+<p0<p++ (constrained optimum): welfare increasing
5. TRADE LIBERALIZATION
Hypos:
Clark
resource-exporting
marginal increase in p H
(w/p+)L
if p+<p0<p++ (constrained optimum): welfare increasing
if p0<p+ (open access): welfare decreasing
if p0>p++ (first best): welfare increasing
(w/p++)L Lc
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21. TRADE LIBERALIZATION (ct’d)
welfare decreasing
Hardin
Lc=L0
Ostrom
welfare increasing
Lc=L*
Clark
p+C
p+O
p++C p
Moreover, for an Ostrom or Clark economy, a non-marginal increase in p may lead not only to a welfare increase but also to the emergence of a management regime.
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22. 6. NORTH-SOUTH TRADE AND RESOURCE DEPLETION
Usual story (eg Chichilnisky,1994): because of imperfect PRs, poor South country has a comparative advantage in H. Free trade with North amplifies the problem, leading to welfare losses for the South and more stock depletion.
Is it still valid when PRs are endogenous?
Hypos:
2 countries, one Hardin, one Clark
only source of difference: r  Lmax different ; Lc identical
Which country has a comparative advantage in H?
What are the welfare and stock depletion consequences of free trade?
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23. NORTH-SOUTH TRADE (ct’d)
(w/p+)L
(w/p++)L
Clark H
(w/p*)L
Hardin Lc N
For any p, clear that H/M supply is larger in Clark …
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24. NORTH-SOUTH TRADE (ct’d)
Supply curves
and comparative
advantage:
 Clark is both high income and resource-exporter at free trade equilibrium
(H/M)D
Hardin
Clark p*
H/M
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25. NORTH-SOUTH TRADE (end)
Impact of free trade:
Clark: higher or identical real income, more (optimal) harvesting
Hardin: higher real income, less (over-)harvesting
Also valid if N is the source of difference!
In fact: remains valid if country characteristics are correlated in such a way that the strong PRs’ country is both high-income and resource-exporting (not necessarily always the case).
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26. PRs enforcement depends:
SUMMING UP
PRs enforcement depends:
positively on: intrinsic rate of resource growth
negatively on: population size, impatience of agents, monitoring costs, harvest technology
New results:
trade liberalization may result in more efficient management of the resource
free trade may be welfare enhancing and reduce resource depletion in the South
neutral technological progress may reduce PRs enforcement
Further research: growth in capital stock, different trade policy instruments, etc.
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