Group Title: Working paper - International Agricultural Trade and Policy Center. University of Florida ; WPTC 05-11
Title: How cool is C.O.O.L.?
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Title: How cool is C.O.O.L.?
Series Title: Working paper - International Agricultural Trade and Policy Center. University of Florida ; WPTC 05-11
Physical Description: Book
Language: English
Creator: Dinopoulos, Elias
Livanis, Grigorios
West, Carol
Publisher: International Agricultural Trade and Policy Center. University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: September 2005
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WPTC 05-11

I 'ional Agricultural Trade and Policy Center

Elias Dinopoulos, Grigorios Livanis, & Carol West

WPTC 05-11 September 2005





Institute of Food and Agricultural Sciences



The International Agricultural Trade and Policy Center (IATPC) was established in 1990
in the Institute of Food and Agriculture Sciences (IFAS) at the University of Florida
(UF). The mission of the Center is to conduct a multi-disciplinary research, education and
outreach program with a major focus on issues that influence competitiveness of specialty
crop agriculture in support of consumers, industry, resource owners and policy makers.
The Center facilitates collaborative research, education and outreach programs across
colleges of the university, with other universities and with state, national and
international organizations. The Center's objectives are to:

* Serve as the University-wide focal point for research on international trade,
domestic and foreign legal and policy issues influencing specialty crop agriculture.
* Support initiatives that enable a better understanding of state, U.S. and international
policy issues impacting the competitiveness of specialty crops locally, nationally,
and internationally.
* Serve as a nation-wide resource for research on public policy issues concerning
specialty crops.
* Disseminate research results to, and interact with, policymakers; research, business,
industry, and resource groups; and state, federal, and international agencies to
facilitate the policy debate on specialty crop issues.

How Cool is C.O.O.L.?

Elias Dinopoulos Grigorios Livanis Carol West*
University of Florida

Original Version: November 22, 2004
Current Version: July 12, 2005

Abstract: This paper develops a partial equilibrium model of a small open-economy producing
and trading an unsafe product that is supplied by perfectly competitive producers. The presence
of product safety considerations, in this case risks to health, introduces a wedge between the
market prices producers receive and the higher risk-adjusted prices consumers respond to. The
size of the wedge depends positively on the per-unit cost of illness and the proportion of unsafe
units embodied in the parent risky product. The model is used to analyze the welfare effects of
trade with and without a country-of-origin labeling (COOL) program. Assuming imports are less
safe than domestic production, the welfare gains from trade in the absence of COOL are
ambiguous and may justify the imposition of a trade ban. Even if a full ban does not improve
welfare, some restriction of trade is always welfare-enhancing. These outcomes derive from an
informational distortion that prevents consumers from distinguishing the different country-
specific risks embodied in the foreign and domestic products resulting in a pooling equilibrium.
The presence of a COOL program removes the informational distortion and generates a welfare
maximizing separating equilibrium in which the safer (domestic) product commands a higher
market price. In the presence of a COOL program, more trade- caused by a reduction in
protection- is better than less trade.

Key Words: Country-of-origin labeling, protection, product safety, welfare.
JEL Classification: F10, F13, L15.
Address for Correspondence: Elias Dinopoulos, Department of Economics, University of
Florida, Gainesville, Fl 32611. E-mail: elias.dinopoulos( An electronic version of
the paper is available at

* Elias Dinopoulos and Carol West are Professors of Economics at the University of Florida. Grigorios Livanis is
postdoctoral research associate at the International Agricultural Trade and Policy Center, Department of Food and
Resource Economics, at the University of Florida.

How Cool is C.O.O.L.?

1. Introduction
The incidence of foodborne diseases has dramatically increased in the past fifteen years in
the United States and in other industrialized countries. According to the Centers for Disease
Control and Prevention (CDC 2004), foodborne infections in the United States annually cause
approximately 76 million illnesses, costing $23 billion per year. Widely publicized outbreaks
such as "Mad Cow" disease (Bovine Spongiform Encephalopathy or BSE), avian influenza
("bird flu") and the contamination of animal feed with cancer-causing dioxin and polychlorinated
biphenyls (PCBs) have led to greater consumer awareness of potential food hazards and
increased consumer demand for safer products. Concomitantly, these outbreaks have triggered
national revisions in trade policies. The efficacy of these policy responses is the focus of this
The imposition of temporary import bans has been one response. BSE outbreaks resulted
in a spate of such bans in 2003. A virtually worldwide ban on Canadian beef exports followed
the May 20, 2003 announcement that a single breeder cow in Alberta had tested positive for
BSE. By August, Canada's beef export market had dwindled from $4.1 billion annually to near
zero. In less than ten days following the December 23, 2003 diagnosis of a BSE case in the
United States, over 30 countries had banned US imports, including Japan, traditionally the
largest buyer of American beef. More recently, outbreaks of bird flu in Delaware and Texas
prompted the European Union to ban imports of poultry from the United States. Country-of-
origin labeling (COOL) is another policy measure addressing the problem of potentially unsafe
food imports. COOL allows consumers to differentiate products that may embody different
health risks as a consequence of the uneven geographical origins of foodborne diseases. Japan
has mandated a COOL for all meat imports since 1997. In the U.S., the 2002 Food Security and
Rural Investment Act called for voluntary COOL on September 30, 2002 and mandatory COOL
by September 30, 2004 for a number of food products such as beef, pork, fresh fruit and
vegetables (Federal Register 2003). Recently, Congress approved a two-year delay for COOL
Juxtaposed against the emotional intensity that often surrounds health-related issues and
the sometimes extreme measures that have been implemented to deal with foodborne diseases in

particular, is a relatively scant literature analyzing the economics of trade policy in risky food-
products. Many questions remain unanswered. From an economic welfare perspective, are trade
embargoes rational when there is a food safety concern? Perhaps under some circumstances but

not others? What are the welfare effects of policies such as COOL? Should a COOL be
augmented by traditional protectionist trade policy instruments (e.g., tariffs)?
Product safety, and in particular food safety, issues have been analyzed theoretically and
empirically, but primarily in the context of closed-economy, partial-equilibrium models.1 In the

international context, there are three related literatures. First, considerable attention has been
given to product quality and government intervention to help exporters overcome informational
barriers that impede foreign market entry (in particular, adverse country-of-origin reputations).2
While this set of studies and the current one each embodies a type of endogenous quality

determination, the nature and consequences of product quality differences, key decision-making
units, international trade context, and pertinent policy analyses differ substantially.3
Second, consumer inability to distinguish safe and unsafe products in the marketplace
resembles consumer inability to distinguish goods by production process (eco-friendly,

sweatshop, etc.) which, if known, would affect willingness to pay.4 Since welfare analyses of
trade policy in the latter context lack explicit representation of how production process affects
consumer utility, it is difficult to directly compare these studies with the present model. In
addition, "labeling" in this literature is standard-conforming certification, a process that allows
the consumer to definitively separate products of different "quality" in the marketplace. In

contrast, in the current model, risk of purchasing and consuming an unsafe product cannot be

1 See, for instance, Oi (1973), Epple and Raviv (1978), Spence (1977), Shapiro (1983), Daughety and Reinganum
(1995), and Boom (1998) for theoretical analyses on product safety, among many others. For the impact of food
safety on meat demand and for a partial review of empirical studies on food safety, see Piggott and Marsh (2"'1 4).
For extensive theoretical analysis in a domestic context, see Fulton and Giannakas (21'" 4) and references therein.
2 See Grossman and Horn (1988), Bagwell and Staiger (1989), Falvey (1989), Bagwell (1991), Raff and Kim
(1999), and Chisik (2003) among many others.
3An interesting extension of the present research would link to these previous analyses by incorporating the
possibility of consumer misperceptions of the safety of a specific country's exports as a consequence of the
publicized outbreak of a foodborne disease in that country. Depending upon the nature of the disease, and the
feasibility of its plausible incorporation into the potential exporter's explicit choice between "high quality" and lo\\
quality" production, the situation could have similarities to examples that motivate the analyses of country-of-origin
4 Haener and Luckert (1998) and Blend and Ravensway (1999) provide empirical evidence of consumer willingness
to pay a "green premium." Theoretical foundations of the literature date from the classic Akerlof (1970) study of the
"hidden quality" problem associated with lemons in the used car market. Recent work by Gaisford and Lau (2000)
and Beaulieu and Gaisford (2002) address welfare implications of indistinguishable standard-conforming and non-
conforming goods, including effects of certification labeling.

completely eliminated. If the only labeling possibility is country of origin, and if the consumer
knows the proportion of imports that are standard-conforming versus non-standard conforming,
then straightforward representation of how production process affects utility renders the situation
a special case of this study's more general model.
A third strand of literature analyzes rules of origin (ROO) that prevent transshipment in a
Free Trade Area (FTA). The effects of ROO on trade, welfare and distribution of rents in the
supply chain under various market structures have been extensively examined in the literature.5
While both ROO and COOL involve "country labeling," there are critical distinctions for policy
analysis modeling. ROO impacts the consumer directly via price (higher or lower depending
upon eligibility for tariff-free shipment). COOL, in contrast, directly influences consumer
behavior by expanding information on product attributes he/she associates with expected product
safety. Price consequences are only indirect, as the change in consumer information alters
demand conditions. More basically, the unobservable product-quality differences inherent in a
COOL analysis give rise to the possibility of different prices for domestic and foreign production
that do not characterize homogeneous ROO markets.
This paper develops a partial equilibrium model to analyze the welfare effects of a COOL
program in the presence of risky foods supplied by domestic and/or foreign producers under
perfect competition. The theoretical model uses building blocks from the seminal study by Oi
(1973), who established that in the presence of insurance markets, the uncertainty associated
with the risk of consuming an unsafe product is reflected in the risk-adjusted price (RAP)6.
Higher than the market price, the RAP includes the proportion of unsafe units in the parent
product and expected damage costs of consuming those hazardous units. In this paper, we
consider a product with an inherent health risk. The consumer knows with some exogenous
probability (equal to the proportion of unsafe units) that the product is risky, but cannot
determine whether the consumption of any particular unit will lead to adverse health outcomes.
The primary focus of the research is the welfare effects of international trade in such a product
and international trade policies with regard to such a product, when safety varies by country of

5 Krueger (1993, 1997), Lloyd (1993), Lopez-de-Silanes, Markusen and Rutherford (1996), Rodriguez (2001),
Falvey and Reed (2002). For a recent literature review see Krishna (2005).
6 In this paper we use the terminology of risk-adjusted price instead of full price, because it is more self-explanatory.
The full price concept was developed by Becker (1965) to analyze the ultimate consumption flow.

We first analyze the effects of product risk and severity of the disease (as measured by the
per-unit opportunity cost plus monetary cost of illness) on social welfare for the autarky (closed-
economy) equilibrium. Because the presence of safety risk creates a difference between the
consumer (RAP) and the producer (market) price, the market for a risky product might not exist
(Proposition 1). As intuitively expected, an increase in the riskiness of the product, or in the cost
of illness, leads to a decrease in social welfare (Proposition 2).
For a small country that imports a riskier product than it produces, movement from the
autarky equilibrium to free-trade in the absence of a COOL program (i.e., un-COOL trade) leads
to a decrease in the production of safer domestic units and to a decrease in producer surplus. The
effect of un-COOL free trade on expected consumer surplus is ambiguous and the welfare
ranking between un-COOL trade and autarky is also ambiguous (Proposition 3). This result is
consistent with the theory of distortions (Bhagwati 1971): Un-COOL trade involves an
informational distortion associated with the inability of consumers to assign the correct risk level
to domestic and foreign goods that leads to a pooling equilibrium and ambiguous gains from
trade. This result allows for the possibility of welfare-enhancing import bans. Even in the case
where an import ban does not dominate un-COOL free trade, some restriction of un-COOL trade
is always welfare-enhancing.
We then analyze the effects of introducing a COOL program that permits the consumer to
differentiate safer domestically produced goods and less safe imports. Equilibrium requires
equalization of the RAPs between the domestic and foreign goods resulting in an increase in the
price and quantity of the healthier domestic product and an increase in the producer surplus
(Proposition 4). Simultaneously, the implementation of COOL leads to a decrease in aggregate
safe quantities of the product consumed and a decline in the expected consumer surplus. COOL
removes the informational distortion associated with differential risk levels and reestablishes the
traditional gains from trade (Proposition 5): In the presence of COOL, more trade (caused by a
reduction in a tariff) increases the welfare of a small country even if it imports riskier goods.
More COOL trade is better than less COOL trade and welfare under COOL trade exceeds that of
autarky or un-COOL trade.
While no model can thoroughly address the multiplicity of issues regarding food safety and
global commerce, the current theoretical model sheds some light on the efficacy of trade policies
commonly proposed to deal with those issues. It is a first step in developing a rational approach

to the economic cost-benefit analysis of COOL programs that several industrial countries,
including the US, are considering implementing or have recently implemented.
Section 2 of the paper develops the model and studies the properties of the closed-
economy equilibrium. Section 3 introduces the economics of un-COOL free-trade, and derives
its welfare implications, for a small country importing a riskier product than it produces
domestically. Section 4 analyzes the economic effects of COOL trade. Conclusions are provided
in the last section and some proofs are relegated to appendixes.

2. Closed-Economy Equilibrium
Consider an economy producing an unsafe (risky) good denoted by X and an outside
composite safe good Y, which will be used as the numeraire. Assume that labor is the only
factor of production, and that each unit of good Y requires one unit of labor, implying that
wages are equal to unity. To focus on the analysis of product safety we assume that perfect
competition prevails in all markets and consumers have identical preferences.
The risk associated with a purchase X of the unsafe good is captured by the assumption
that it embodies a certain proportion, A, of safe units, Z = AX, and a remaining unsafe portion,
(1- A) with 0 < A < 1. Consumption of safe units yields positive utility, but consumption of

unsafe units not only results in no addition to utility, but simultaneously incurs a cost L per unit
of unsafe good consumed. While the consumer knows the risk of becoming ill, captured by
parameter A7, he/she cannot differentiate between a safe and an unsafe unit. For instance,
according to the Food Safety and Inspection Service (FSIS 2004) of the USDA, a consumer faces

a (1- A)=3.5 x106 probability of becoming ill from Salmonella, if he/she eats one egg. This

probability is obtained by dividing 174,356, the estimated number of annual illnesses attributed
to Salmonella for 2000, by the U.S. population to obtain the per-capita chance of becoming ill
and then dividing the resulting expression by 178, the annual per-capita consumption of eggs .
An alternative interpretation of the risk embodied in X is as follows: Rather than an
expected proportion, A, of safe units in any purchase X and a resultant (1- A) expected

7 In our formulation the probability of the adverse health outcome is treated as "objective" information. Thus, any
consumer who faces the same problem will assign the same probability. One could introduce the case where )
depends on self-protection actions and on a set of information (i.e. past experience) that each consumer uses in
forming risk perceptions. This is an interesting generalization that is left for future research. Notice, though that any
valuation of a public policy change should be based on objective risks.

proportion of unsafe units, the consumer making a purchase of X faces an exogenous
probability (1- A) the purchase will make him/her ill. Concomitantly, with probability A, the

purchase can be expected to be consumed without adverse health consequences. If a particular
expenditure on X turns out to be a "bad lot," then the associated cost of illness is proportional to
the volume of X purchased and consumed. Both interpretations yield the same key relationships
that are used in the subsequent model analysis, but formal presentation is restricted to the first
We postulate the existence of a competitive health (medical) insurance market that
provides insurance to all consumers in the market against the loss L caused by the consumption
of the unsafe product. Loss L is given exogenously and captures the direct (i.e., medical
treatment) costs and the indirect (i.e., lost wages) costs of illness per-unit of unsafe X
consumed. Parameter L can be as large as the economic cost of life (as in the case of the "Mad
Cow" disease) and in principle depends on the quality of the health system. Following the
insurance literature, we further assume that the insurance offered to the consumers is full and
actuarially fair in the sense that the insurance premium equals the expected value of the
insurance claims.8 In the case of eggs, one can measure the expected damage cost to the
consumer using the cost of illness (COI) data available on the ERS website Foodborne Illness
Cost Calculator (FCOI 2004). The COI method includes both direct and indirect costs of an
illness. In the case of Salmonella in eggs, the ERS website data imply that the average cost of
illness is $2,126.
Assuming the representative consumer derives utility only from the safe units Z of
product X and from the outside (safe) good Y; and, following the standard approach to partial-
equilibrium analysis, suppose that the utility function is separable in X and Y

U(Z,Y)=u(Z)+Y (1)

where u(Z) is an increasing and concave function of the safe quantity of the risky good X and

indicates that the consumer does not receive any utility from the unsafe units X Z 9. In this
formulation, the price of product Y is equal to unity (numeraire), while the market price of

8 The absence of an actuarially fair and full insurance complicates the analysis. See Oi (1973) and especially Epple
and Raviv (1978) among others for more details on this issue. Oi (1973) adopts the assumption of full and
actuarially fair insurance, while Epple and Raviv (1978) provide also results for the case of partial insurance.
9 The analysis can be generalized to the case of severe risky products that result in a negative utility level if one
risky unit is consumed. This novel extension is beyond the scope of the present paper.

product X is denoted by P. Since Y enters the consumer's utility linearly, equation (1) allows
us to focus on partial-equilibrium analysis, while the assumption of a single unsafe product will
be relaxed in section 4 that analyzes the economic effects of COOL.
The above notation and assumptions imply the following maximization problem for the
representative consumer. For a given amount of X purchased, only AX will yield positive
utility. Insuring against the expected cost of illness (or setting aside the funds to pay for it)
requires expenditure of (1-A)LX. Assuming a total budget M, and a price P of X, the
consumer's maximization problem is as follows:

AlMax[u(AX)+M-PX-(- A)LX] (2)

The first-order condition for (2) can be written as

u'(Z) = + (- L (3)
where a prime superscript denotes a partial derivate and the argument in the left-hand side of (3)
is equal to the amount of "safe" food consumed (Z = AX). Concavity of u(.) guarantees that the

second-order condition for (2) is satisfied.
Recalling that the consumer derives utility only from good Y and the safe units Z of
product X, it is obvious from (3) that the solution to the utility maximization problem (2) is

identical to maximizing U(Z,Y)=u(Z)+Y subject to the budget constraint M=PZ+Y,


P =-+ (I )L (4)
is the risk-adjusted price (RAP) of an unsafe good. In the presence of actuarially fair insurance,

the economic interpretation of (4) is described elegantly by Oi (1973)10: P is the risk-adjusted
price (expected cost) of obtaining a safe unit of a risky product, P / A is the warranty price, and
the term (1- A)L / A is the actuarially fair insurance premium rate per "safe" unit.
We illustrate the relative magnitude of the RAP for the case of eggs embodying the risk of
contracting Salmonella. Substituting the risk of becoming sick (1- = 3.5 x10 6), the cost of
illness (L= $2,126), the market price of one grade A shell egg (P = $0.081), the RAP of eggs

10 See also Becker (1965) who developed the technique of decomposing the full price of an ultimate consumption
flow. Notice that the full price concept in these studies is termed as risk-adjusted price in our paper.

becomes P=- + 2,126*3.5x106 =$0.088. In other words, the consumer behaves as if
the risk of Salmonella generates an 8.6% increase in the market price for safe eggs with a
corresponding decrease in the quantity of eggs consumed.
Equation (3) defines the demand function for the safe quantity of a risky product X as a

function of its RAP P, and is denoted by ZD (). This relationship will be used in calculating

the expected consumer surplus in the welfare analysis. Recalling the relationship between the
safe and unsafe quantities of a risky product, Z = AX, the demand for the risky product X can

be obtained then by XD (P)= ZD (P)/A. Substituting AX= Z into the left-hand side of (3)

yields the inverse market demand function of the risky good X, where the dependent variable is
the market price (as opposed to the RAP):
P= Au'(AX)- (1- A)L (5)

Equation (5) yields the first result of our model which is stated in the following

Proposition 1: A market for an unsafe product does not exist if the following condition holds:
P = Au'(0) (1 A)L < 0, i.e., the vertical intercept of its market demand curve is non-positive.

The condition in proposition 1 defines a lower bound of product safety Ao = L/(L +u'(0)) <1

which varies positively with L and negatively with the marginal utility of consuming the first
safe unit of the good.
The supply side of the economy is modeled as follows: We assume that producers
maximize profits with respect to a given market price P of the risky product X and that the
output of good X supplied is given by
Xs (P) (6)

where 8XS(P))/ P> 0, and Xs (P) 0 for a non-negative price P >0: The supply curve is

upward sloping and has a non-negative vertical intercept. The assumption of a non-negative
vertical intercept is not critical for the analysis. Implicit in (6) is the assumption that the supply
of a risky good does not depend on the proportion of "safe" units, but simply on per unit market

price of X .1 For welfare analysis purposes, it is useful to invert (6) and define the inverse
supply of a risky good X
P=P(X)= P(Z/A) (7)

where 8P(X) / X > 0 and P(0) = P > 0. The supply of safe units Zs (A,P) is straightforwardly

obtained by multiplying (6) by the proportion of safe units A, i.e., Zs (A,P) = Xs (P).

The autarky (closed-economy) equilibrium condition requires equality between the
quantity supplied and the quantity demanded for the tradeable good X :
XS (P)= XD (P,A,L) (8)

Condition (8) determines the market equilibrium price P, (where subscript A denotes the

autarky equilibrium) and the equilibrium quantity of X, XA. In addition, multiplying both sides

of equation (8) by A, evaluated at P,, yields

Z (A,P,)=AXD(P,,A,L)-ZD (P,(A,,L)) (9)

which implies equality between the equilibrium level of safe units of good X produced and

consumed. Having determined the producer price P,, one can calculate the consumer RAP, PA,

directly by setting P = PA in (4).

Figure 1 illustrates the closed-economy equilibrium. The horizontal axis measures the
amount of safe and total units, Z and X respectively, and the vertical axis denotes prices (both
market and risk adjusted). The upward-slopped curve Xs (P) illustrates the supply (and inverse

supply) curve of the risky good, and the downward-slopped curve XD (P, A,L) is the market

demand curve for the risky good X, which is implicitly defined by equation (5).12 The
intersection of these two curves illustrates geometrically the solution of (8), which yields the
closed-economy market-equilibrium price P, and quantity produced XA. Having determined the

equilibrium quantity of the risky good produced XA, one can readily determine the equilibrium

1 One could introduce the assumption that the supply of a risky good is a decreasing function of A and analyze the
effects of policies that provide direct incentives to producers to increase the safety of their products. This
generalization is beyond the scope of the present paper and constitutes an interesting topic for further research.
12 These curves are not straight lines in general, but the use of linear curves in all figures of the paper is based on
expositional considerations.

amount of safe units ZA = AXA by subtracting horizontally the amount of unsafe units (1- A)XA

from XA (i.e., the intersection of PA and Zs (, P))

P (A P)

P / y


Figure 1: Closed-Economy Equilibrium

The downward-slopped curve ZD () illustrates the demand curve for safe units Z as a function

of the risk-adjusted price P (defined in equation (3)). Evaluating this inverse demand curve at

the equilibrium level of safe units ZA yields the equilibrium RAP, PA, which exceeds the market

price. Area (a) that is located below curve ZD () and above the equilibrium RAP, PA, is equal

to the expected consumer surplus.
Area (P+y), which is located below the market equilibrium price PA and above the supply

curve Xs (P), measures producer surplus. In our analysis producer surplus captures the rents to

specific factors (or industry profits) associated with the supply of XA risky units, given our

assumption that consumers bear all the risks and so producers are not concerned with the
distinction between safe and unsafe units. Consequently, the closed-economy equilibrium level
of social welfare is measured by area (a+P+y). This geometric property will be utilized later in
the welfare analysis of various public policies. We need to emphasize that the use of this

standard measure of producer surplus implies that producers are not liable for the production of
unsafe units and our analysis abstracts from moral hazard and principal-agent considerations
associated with the production of unsafe products. These issues have been analyzed in closed
economy models and constitute an important direction for future research.13
It is apparent from Fig. 1 that, in the presence of foodborne risk, the closed-economy
equilibrium involves two distinct types of welfare distortions. First, consumer behavior depends
on the RAP, which exceeds the market price. This discrepancy between the two prices is similar
to the welfare effects of a specific tax incidence that reduces total welfare. Second, unlike a tax
incidence, in the present model the "tax revenue" is proportional to the value of the unsafe units
which does not yield any utility to the consumer. In other words, the corresponding "tax
revenue" is not a transfer but a pure welfare loss associated with the production and consumption

of unsafe units. This welfare loss is measured by the area (PA -PA)ZA in Fig. 1 and depends on

the market quantity of Z, the proportion of unsafe units, and the per-unit cost of illness.
In addition, for any given parameters of the model and in the presence of perfect
competition, the market solution maximizes social welfare (defined as the sum of expected
consumer plus producer surplus). In other words, unless the social planner can alter the risk
parameter A (perhaps though testing) or the per-unit cost of illness L (through health care
reforms or development of better treatments), the market solution coincides with the

maximization of social welfare. To establish this property, denote with C(X) the aggregate

social (and private) costs of producing X units of the risky good. Assuming a total budget of
M, the social planner derives utility from the amount of safe units consumed Z= AX and
incurs two types of costs, health insurance costs (1 A)LX and production costs C(X). Hence,

the social planner's problem is
Max [u(AX)+M -(1- )LX-C(X)]

which yields the first-order condition

u'(Z) = '(x)+ (I L (10)

13 Spence (1977), Epple and Raviv (1978), and Boom (1998) among others have developed closed-economy models
that explicitly analyze producer liability issues.

In the competitive market equilibrium, P = C'(X). Comparing (10) with (3) yields the desired
result, namely that, under consumer liability and full insurance, the market equilibrium
maximizes the level of national welfare.
Differentiating the equilibrium conditions (8) and/or (9) totally, one can derive the
comparative statics properties of the closed-economy equilibrium.

Proposition 2: The closed-economy equilibrium is characterized by the following properties:
(a) An increase in per-unit damage cost L T shifts the market demand curve in Fig. 1,
XD (A, L,P), downward and generates: a decline in the market-equilibrium price PA; a fall in

the equilibrium quantities XA and Z ; an increase in the risk-adjusted price P; and a

reduction the social welfare, measured by expected consumer plus producer surplus.

(b) A decline in product safety, measured by a reduction in parameter A 4-, reduces social
(c) If the market price elasticity for product X is not numerically small, i.e.,
-Ep=-(aXD/IP)(P/XD)> P/(P+L), then a decline in product safety, measured by a

reduction in parameter A 1 shifts downward the market demand curve in Fig. 1, XD (A, L, P),

and shifts inward the supply of safe units, Zs(A, P), generating declines in the market-

equilibrium price PA, the market-equilibrium quantity XA and the amount of safe quantity ZA

and a rise in the equilibrium risk-adjusted price P,.

Part (a) follows straightforwardly from (5) and Figure 1. For part (b), differentiate welfare (W=
u(AX)+M -(1-A)LX-C(X)) with respect to A and simplify using (10) to verify

dW/dA > 0. For (c), substitute AX for Z in (10) and then differentiate totally to determine

dX/dA whose sign depends upon the sign of u"(.)AX + u'(.) + L. Use (5) differentiated with

respect to X (A fixed) to establish (c). For the rest of the analysis we assume 2.c holds.
These results are consistent with the empirical evidence that consumer demand is
susceptible to any new information concerning the way consumers perceive objective (or
subjective) threats to food safety as measured by the parameters A and L. For instance,
according to Piggott and Marsh (2004) the public will generally respond to a foodborne outbreak
by decreasing its consumption, at least in the short run. Moreover, if the food-safety problem is

recurring, it can result in an inward shift of consumer demand for a specific good. In the case of
the 1996 outbreak of BSE ("Mad Cow" disease) in the United Kingdom, both the product risk
(1-A) and loss L (equal to the statistical value of life) were large and caused a substantial
decline in the demand for beef. However, if the product risk (1- A) is very small, then even for
large L the difference between the RAP and the market price will be small and the demand for a
risky product will be determined by its market price. This is consistent with the findings of a
report by the Foreign Agricultural Service of the USDA (FAS 1998), which indicated that while
E.U. consumers are concerned with food safety, price of beef is also important in deciding
whether or not to purchase beef. That is, if the price of beef is low enough, consumers may buy it
despite any remaining concerns over BSE.

3. Un-COOL Free Trade
Having established the welfare properties and comparative statics of the closed economy
equilibrium, we now analyze the benchmark free-trade equilibrium in the absence of country-of-
origin labeling (COOL). We assume that the consumer cannot distinguish imports and domestic
goods in the marketplace although he/she knows all the parameters of the model and the market
equilibrium values of the relevant endogenous variables. Consequently, this section analyzes the
pooling equilibrium associated with an informational distortion: The inability of the domestic
consumer to differentiate between imports and domestic products. To facilitate the economic
intuition and the clarity of the geometric analysis, we will illustrate the free-trade equilibrium for
the case of a country that imports an unsafe good at a fixed international market price P (the
small-country case). This implies that the home country faces a horizontal supply curve of
imports at the international market price P and each unit of imports carries a risk of becoming
ill equal to 1- A* .14

Denote with X, the market quantity of the domestic risky product and with X, the

corresponding quantity of risky imports coming from the rest of the world, where subscript T
will be used to indicate function and variables associated with the (free) trade equilibrium. Let
Z, = AX, be the domestic "safe" quantity consumed that does not result in any adverse health

outcomes. Similarly, assume that Z,*= A*X, is the corresponding quantity of the foreign

14 Here we abstract from analyzing the case in which a country's imports originate from a variety of countries with
different safety parameters *. This case can be analyzed, but it is beyond the scope of the present paper.

(imported) safe food so the aggregate consumption of safe units is given by Z, + Z, *. Assume

for simplicity that parameters A, A* [0,1] are exogenous and may differ from each other.

Without loss of generality, assume max (A *, A0) < A* < A <1, which implies markets exist for

each of the two products and home produces a safer product than the rest of the world. Assume
finally that damage costs L associated with consumption of unsafe domestic and imported goods
are equal-i.e., the illness imports carry is the same as that of domestic production.
Since consumers cannot distinguish between the two risky goods, free-trade will result in
equalization of the domestic and world prices, i.e., P = P*. The market quantity supplied will be
X,+X, *, where the domestic quantity supplied X, is given by Xs (P*) -the domestic

supply curve evaluated at the world market price. The domestic supply of safe units is
consequently given by Z, = AX,. To determine the market-equilibrium quantity of imports

X, note that imported and domestic goods are indistinguishable in the marketplace and their

costs of illness per unsafe unit consumed are identical. This implies consumer demand will
depend on the average probability of becoming ill AT = (Z, + Z,*)/(X, + X *). In this case, the

solution to the consumer problem can be obtained by assuming that he/she maximizes utility
u(Z, +Z, *) by choosing the aggregate quantity consumed Z +Z subject to the non-

stochastic budget constraint M = Y + P (Z, + Z, *). The first-order condition of the consumer' s

maximization problem is then given by

u'(Z, + Z *) = P = [P* +(1- 4)L]/ AT (11)

where P is the common market price, P, is the free-trade risk-adjusted price,
Z7+Z Z7+Z *
T +Z Z Z = (1-s*)A+s*A* (12)
T X,+XT Z1 Z1
A A*

is the free-trade consumption safety level, and s* = X, */(X, + X *) is the consumption share of

imports. Un-COOL free-trade yields a common market price P* and a common RAP given by
(11). Substituting (12) and Z =AXs (P *) into (11) determines the un-COOL free-trade

equilibrium value of safe imports Z, *, which can readily be transformed into the market-

equilibrium quantity of imports X = Z, / A *.

Fig. 2 illustrates the determination of the un-COOL free-trade equilibrium values of safe
imports and A, in the (A,,Z, *) space. Specifically, equation (11) can be written as

T (ZT *)= (13)
u'(Z, (P *)+ Z, *)+ L

and, for clarity of exposition, we replicate equation (12) below
Z, + Z *
T = Z (14)

Because the domestic quantity of safe units Z, (P*)= AXs (P *) is a function only of the world

price and A, (13) and (14) constitute a system of two simultaneous equations in two unknowns
A, and Z, *. The solution is illustrated in Fig. 2. The upward-slopped curve is the graph of
equation (13). It has a positive vertical intercept defined by setting Z* = 0 in equation (13), and

a positive slope:


Eq. (13)

P*+L Eq. (14)
u'(XS (P*))+L

0 Z,* Z*

Figure 2. Determination of Free-Trade Equilibrium of
Imports and Food Safety

As the quantity of safe imports increases the marginal utility declines, and the denominator of
(13) decreases. Equation (14) defines a downward-slopped curve in the (A,,Z, *) space under

the assumption that domestically produced goods are safer than imported ones (A* < A <1). The
vertical intercept of the downward-slopped curve equals A : For any level of safe domestic units

Z, (P*), as the amount of imports increases, the level of product safety declines. The

intersection of these two curves determines the free-trade equilibrium quantity of safe imports
Z, and the level of A,. The total quantity of imports is given by X* = Z / A *

Note that if P* > PA, the graph of equation (13) in Fig. 2 lies above that of equation (14)

for non-zero Z, and the free-trade equilibrium reduces to the autarky equilibrium. If

Xs (P*) = 0, (14) in Fig. 2 is undefined at Z*=0 and otherwise horizontal at = A *. The free-

trade equilibrium reduces to one of solely purchasing imports. We abstract from these
uninteresting degenerative equilibria by assuming:
P*0 (15)

Fig. 3 illustrates the welfare effects of unsafe food imports and the autarky welfare level. It
does this by superimposing on the closed-economy equilibrium in Fig. 1, the market supply of
imports, which is a horizontal line intersecting the vertical axis at P *.


s (P)


Figure 3. Un-COOL Free-Trade Equilibrium


The closed-economy equilibrium corresponds to the market price PA, and the RAP PA

where ZD (P) = AXA. Price PA determines the producer surplus (P+y) and RAP PA determines

expected consumer surplus (a). The opening of trade establishes a lower producer price P* and
results in the importation of Z, = A X, units of safe imports and (1 A*)X, units of unsafe

imports. Under un-COOL free trade, domestic producers face a lower price and reduce the
quantity of unsafe and safe food produced, and therefore the producer surplus is equal to area (0).
The move from autarky to free trade results in a decline in the producer surplus which equals
area (y) in Fig. 3.
The effects of un-COOL free trade on the expected consumer surplus (and the total
welfare) are in general ambiguous. In order to calculate the RAP associated with the free-trade
equilibrium, one has to add the safe quantity embodied in imports Z, *, which is determined in

Fig. 2, to the domestic quantity of safe units Z,. The RAP under free trade P, corresponds to

the total safe quantity consumed Z, + Z, *. The area (a+6), which is below curve ZD (P and

above the RAP P, corresponds to the expected consumer surplus under un-COOL free trade. In

general, the consumer welfare ranking between autarky and free-trade is ambiguous and depends
on the ranking of the RAPs under the two regimes. The ranking is unclear because the move
from autarky to free trade lowers price, but increases risk of illness.
Fig. 3 illustrates a case in which the move from autarky to un-COOL free trade leaves the
economy's welfare unchanged: Un-COOL free-trade reduces the market price from PA to P*

and reduces the producer surplus by area (y). This reduction in welfare is the same as the
increase in expected consumer surplus measured by area (6), caused by a reduction in the RAP

from PA to PT Thus, even if imports are more risky than domestic products, the economy is

indifferent between imposing an import ban and engaging in free trade. Of course, in this case
consumers like free trade more than the import ban (free trade results in higher consumer surplus
than autarky), while producers would advocate an import ban based on the effects of trade on
producer surplus. It is straightforward to show the existence of cases for welfare improving
import bans. For example, starting at an equilibrium of indifference between a ban and free trade,
a decline in import safety A* does not affect the graph of equation (13) in Fig. 2, but rotates
clockwise from its intercept the graph of equation (14) and results in a lesser safe quantity of

imports Z, *, for any given market price P*. This implies that the total safe quantity available

to consumers Z, + Z, declines in Fig. 3, and the expected consumer surplus under free un-

COOL trade falls. Since the expected producer surplus depends on the market price P*, a
reduction in A leaves this component of national welfare unaffected. Consequently, the
expected gain from trade measured by area (6-y) is negative and an import ban improves welfare.
One can readily construct other scenarios that justify the ban of unsafe imports based on other
parameter changes.
Note finally that even if free trade is preferred to a ban, there always exists a restriction of
trade that improves welfare-i.e., free un-COOL trade is never welfare maximizing for a small
country. (Proof is given in the Appendix A). The effects of moving from autarky to free-trade are
summarized in the following proposition:

Proposition 3: Starting at the autarky equilibrium and assuming that the domestically produced
good is safer than the imported product (A > A *), the introduction of free-trade by a small
country results in:
(a) A decline in the market price and market quantity of the safer domestic product.
(b) An increase in the market quantity and safe quantity of the less safe imported product.
(c) An ambiguous effect on the total safe quantity consumed and on the expected consumer
(d) A decrease in the safe quantity of the domestic good and a decrease in the producer surplus.
(e) An ambiguous effect on national welfare measured by producer plus expected consumer
surplus, but if welfare improves as a result of free trade, it can always be raised further by some
restriction offree un-COOL trade.

The reason for the ambiguous welfare ranking between the autarky and pooling equilibria
can be traced to the theory of market distortions: While free trade introduces standard efficiency
gains, it simultaneously introduces an informational distortion forcing consumers to act on a
common (average) safety risk. The model is consistent with the evidence of import bans
following outbreaks of foodborne disease abroad. These bans can be modeled as a move from
un-COOL free trade (with safe domestic and risky imported goods, A = 1, A* < 1) to the autarky

equilibrium. The welfare consequences of this move are in general ambiguous, and depend on
the magnitudes of demand and supply elasticities, the severity in the reduction of food safety

captured by the risk parameter A* and the damage costs L. For example, the larger the
differential of safety risk between domestic and imported goods measured by A- *, the more
likely it is that a trade ban will be welfare improving.
The reason for the existence of a welfare enhancing trade restriction (even if free trade
dominates an import ban) also derives from the informational distortion introduced by the
imports. In particular, from the individual consumer perspective, the marginal unit of X carries
a risk (1- A) < (1- A*). However, for society, the marginal unit of X is imported and carries

the higher illness risk (1- *) Alternatively, the RAP associated with a marginal unit of Z for

the consumer is less than the RAP associated with a marginal unit of Z for society.
Consequently, consumers over-consume Z in the free-trade equilibrium, setting up the
conditions for welfare-enhancing trade restrictions.

4. COOL Trade
We are now in a position to analyze the economic effects of introducing country-of -origin
labeling (COOL). In order to keep the analysis as simple as possible, we will not formally
analyze the effects of costs associated with implementation of a COOL program. If the costs of
instituting and maintaining a national COOL system are fixed or sunk costs, they constitute an
additional welfare cost that can readily be incorporated in the cost-benefit calculations without
altering the qualitative conclusions of the analysis. We will also treat COOL as a government
policy introduced after the country has engaged in free trade and will maintain the small-country
assumption for comparison purposes. The introduction of COOL removes the informational
distortion associated with the inability of consumers to incorporate the safety risk differential
between imports and domestic goods. In the presence of COOL trade, the consumer can
distinguish whether a good is imported or domestic, allowing the two types of X to have
different prices. Denoting COOL values by subscript C, maximizing the consumer's utility

function u(Zc + Zc *)+ Y subject to a deterministic budget constraint M = PcZc + P* Zc + Y

yields the following first-order conditions for an interior solution :

u'(Zc + Zc *) = Pc + (1-A) L (16)

u'(Z+Z* *= P L (17)
Z A* Z*

where Pc denotes the producer price of domestically produced X, P* the producer price of

imports and "A" indicates associated RAP. Under COOL trade, the consumer buys the product
with the lower risk-adjusted price, since a safe unit gives the consumer the same utility, whether
it is produced domestically or imported. The different country-specific health risks generate
perceived quality differences that are reflected in different market prices. Coexistence of both
goods in the market requires that consumers derive the same marginal utility from the two risky
products (that is, the consumer must be indifferent between consuming a safe unit of the
domestic good and a safe unit of the imported good). This implies that the introduction of COOL
results in equalization of RAP between the domestic and imported product. Formally, equations
(16) and (17) imply that

Pc = [P +(1- A)L]/A=[P*+(- A*)L]/A* (18)

which determines Pc and equilibrium RAPs, Pc = P*

Unlike the equilibrium analyzed in the previous section, COOL trade introduces a market
price differential in favor of the safer product. Solving equation (18) for the producer price of the
domestically produced good yields

P =A -+ -Q L] (19)

According to equation (19), the good with the lower safety risk (in this case the domestic product
since A > by assumption) commands a higher market price at equilibrium because the
consumer perceives it as a higher quality (healthier) good. Substituting (19) into the domestic
supply of the risky good yields the equilibrium safe domestic quantity produced
Zc = z (A,Pc) = AXS (Pc) (20)

Since the introduction of COOL raises the market price of the domestic product relative to the
domestic price of imports (Pc > P*), the introduction of COOL generates a higher producer

surplus compared to the free-trade equilibrium without COOL. Therefore, abstracting from
implementation costs, the introduction of COOL will be supported by producers of domestic
goods that are safer than imported ones.
COOL effects on expected consumer surplus depend on COOL effects on the RAP. From
(12) it is obvious that 4 = (1- s*)A +s* A* > A*. It follows from (11) and (17) that

u'(Z +Z )=

P = +(l_) L> + ( L = P (21)

u'(Z, + Z, *)

The total amount of safe quantity consumed under COOL free trade is strictly less than the
corresponding quantity under un-COOL free trade, i.e. Zc +Zc*
follows from the concavity of the consumer's utility function. The result implies that, starting at
the un-COOL free-trade equilibrium, the introduction of COOL reduces the expected consumer
surplus, which is an increasing function of the aggregate safe quantity consumed. Since the
consumption of the safer domestic good increases with the introduction of COOL, (i.e.,
Zc >Z,), the safe (and market) quantity of imports declines (i.e., Zc*
increases the domestic market price of the safer (domestic) product, reduces the quantity of the
less safe (imported) product by more than the increase in domestic production, and results in a
reduction of expected consumer surplus. These results lead to the following proposition that
summarizes the economic effects of introducing a COOL program.

Proposition 4: Starting at the un-COOL free-trade equilibrium and assuming that the
domestically produced good is safer than the imported product (A > A *), the introduction of
COOL by a small country results in:
(a) An increase in the market price and market quantity of the safer domestic product.
(b) A decline in the market quantity and safe quantity of the less safe imported product.
(c) A decline in the total safe quantity consumed and a decline in the expected consumer surplus.
(d) An increase in the safe quantity of the domestic good and an increase in the producer
We are now in a position to establish the optimality of COOL. With a price P* for
imports, X *, and P for domestically produced X, Xd, and a domestic cost of producing Xd,

C (Xd), the level of national welfare in general is given by:

W =u(AXd + A*X*)+M-[(1- )LXd + (1-*)LX*]-C(Xd)-P*X* (22)

An interior maximum for W (Xd > 0, X* > 0), requires:

Au'(AXd + A*X*)-(1- A)L -C'(Xd)=0 and (23)

A*u'(AXd +A* X*)- (1- A*)L -P*= 0 (24)

The concavity of u and C" > 0 assure second order conditions are satisfied. Given that bothC'

and u' are monotonic, if an interior maximum exists, it is unique. Since C'(Xc) = Pc, (16) and

(17) imply an interior COOL equilibrium is this unique maximum. Note that un-COOL trade can

never maximize welfare since joint satisfaction of (23) and (24) at (Xd> 0,X*>0) requires

C'(Xd) > P* (assuming A > A*) and in the un-COOL trade equilibrium C'(X) = P*

Appendix B establishes that if an interior maximum exists, it dominates corner solutions of

Xd= 0 and X* = 0. Hence, if an interior COOL equilibrium exists, it dominates both autarky

and the un-COOL trade equilibrium. A comer COOL equilibrium at all imports is precluded by
(15).15 A comer COOL equilibrium at the autarky solution can be consistent with (15). In that

PA + (1 A)L '( < P +(1 *)L
A A A*
i.e., at the autarky solution, the marginal utility of an additional unit of Z is less than the RAP of
buying it as an import and hence, there is no market for imports. In this situation, clearly the
equivalent autarky and comer COOL equilbria dominate the un-COOL trade equibrium because
no interior maximum exists. Hence, welfare under a COOL regime always exceeds that of un-
COOL trade and it exceeds that of autarky except in cases the two are equivalent.
Furthermore, it is straightforward to establish that any restriction of COOL trade reduces
welfare16. If a non-prohibitive specific tariff, t, is imposed on imports, the COOL equilibrium
can be determined as above by replacing P* by P*+ t. Equations (17), (19) and (20) with P*

replaced by P*+ t determine the market-equilibrium values of Pc, Zc, and Zc *. Substituting

Zc = AXc and Z*= A*Xc in (17) and differentiating totally the system of these equations


P P* +(1 *)L C'(0) + (1- )l)L
15 A comer COOL equilibrium at all imports can exist only if < which is precluded
2" 2
by (15) and C"(.) > 0 which imply C'(0) < P*, and 2 > *.
16 For this derivation we assume an interior COOL solution since imposing tariffs in the corer COOL solution of
autarky is uninteresting.

dXc 2 c8Xc
SdX >0 (25)

dX* I A2 <. (26)
t to (A*)2 u"(.) P,

Because the safe quantities of domestic and imported products are proportional to Xc and Xc *,

an increase in protection increases Zc and reduces Zc *. As a result, protection has the standard

effects of increasing the domestic production and reducing the level of imports.
For any given budget M, the social planner derives utility from the safe units consumed
u(AXc +A Xc *) and faces insurance costs (1 -)LX + (1 A*)LX to cover the costs of

illness from domestic and imported risky products. In addition, the social planner faces domestic
production costs C (Xc) and import costs (P* + t)Xc *. Since the government collects the tariff

revenue t. X *, which is distributed back to consumers, under the standard assumption, the net

social costs of imports are simply P* X *. The level of national welfare as a function of the

specific tariff is
W(t) = u (AXc (t) + A (t)) +M [(1- A)Lxc (t) + (1- A*)LXc *(t)]

-C(Xc (t))-P*Xc*(t)

Differentiating the above expression with respect to the specific tariff yields:
dW dX, dX *
{ Au'-(1- A)L -C'(.)I +[A*u'-(1-A*)L-P*] c (27)
dt dt dt
Equation (16) and the property Pc = C'(Xc) imply that, under COOL, the term in the curly

bracket of (27) is zero. From (17), the expression in the square bracket is equal to the value of
the specific tariff. Therefore, taking into account the above analysis and using (26) one can
derive two standard expressions for the effects of a specific tariff on national welfare in the
presence of COOL1
dW. dX *
=i t <0 (28)
dt o dt

17 See Feenstra ( 2" 14, Chapter 7) for a derivation of an identical expression in the case of a small country imposing
a specific tariff in the absence of unsafe food trade.

dW dX *
= t =0 (29)
dt t dt

Inequality (28) states that national welfare is a decreasing function of the specific tariff for
strictly positive values of t and equation (29) implies that welfare is maximized under COOL
free trade. In words, there is no need for COOL trade import bans! We have established formally
two key welfare results which are summarized in the following proposition.18

Proposition 5: In the presence of country-of-origin labeling (COOL), even if the domestically
produced good is safer than the imported product (A > A *), a reduction in protection increases
a small country's level of national welfare: More COOL trade is better than less COOL trade,
and COOL free trade is the best policy for a small country.

Proposition 5 is consistent with the theory of trade distortions applied to this particular
informational welfare distortion. The introduction of a COOL policy removes this distortion and
reestablishes the traditional optimality of trade which asserts that more trade is better than less
trade for a country that cannot change the terms-of-trade. This proposition also implies that if the
costs of maintaining a COOL policy are unaffected by changes in the level of protection, more
COOL trade is better even if a small country imports riskier goods. COOL seems to be the best
policy instrument to offer protection from unsafe imports, assuming of course that the consumer
is as informed as the policy makers about the potential risk of imports.

4. Concluding Remarks
The present study developed a small open-economy partial-equilibrium model in which the
small country produces an unsafe product and imports another riskier product under conditions
of perfect competition. Product risk was modeled as the exogenous proportion of units of the
parent good that lead to adverse health outcomes. Consumers were assumed to know this
proportion, but they could not distinguish whether a particular unit of the good was safe or
unsafe. The model was used to analyze three cases. The first was the closed-economy
equilibrium, the second a free-trade regime without country-of-origin labeling (COOL), and the
third was a free-trade regime coupled with a COOL program.

18 If the COOL equilibrium with no tariff is a corer solution, the argument doesn't technically hold. However, if it
is a corer at the autarky solution, the issue of tariffs is superfluous. If it is a corer with imports only, then a tariff
which does not change the nature of that equilibrium leaves welfare unchanged-the consumer pays more for
imports, but is returned the tariff revenues.

We established that the competitive equilibrium maximized social welfare for the closed
economy situation where social welfare is measured by the sum of expected consumer and
producer surplus. The presence of insurable risk creates a wedge between the producer and
consumer price that depends positively on the per-unit cost of becoming ill and on the proportion
of unsafe units embodied in the risky product. In the absence of a COOL program, the opening
of trade with another country that produces a riskier good at a lower price results in a reduction
in expected producer surplus and an ambiguous effect on expected consumer surplus. An
ambiguous welfare outcome leaves open the possibility of welfare-improving trade bans. Even if
free un-COOL trade dominates an import ban, welfare can always be increased by some
restriction of un-COOL trade. The outcomes are consistent with the generalized theory of
distortions: Un-COOL trade introduces an informational distortion to the open economy because
the consumer cannot distinguish and incorporate into his/her behavior the differential risk
between imports and domestic goods.
The introduction of COOL addresses the source of the distortion directly, maximizes
welfare and reestablishes the traditional insight that more (COOL) trade is better than less
(COOL) trade for a small country even if imports are riskier. As a policy, COOL dominates trade
bans and un-COOL trade. We suspect that this property would hold in a general equilibrium
framework and in the case of a large country.
Of course the model's properties and results depend on several assumptions. We have
assumed that the consumers are fully informed about the safety risk of the two products.
However, consumers could form a subjective estimate of the risk of the product, which may be
higher or lower than the objective risk assumed in this paper. We have also abstracted from
analyzing the more realistic case of multiple import suppliers and multiple levels of country-
specific risky products. We have also avoided incorporating the effects of costs associated with
implementation and maintenance of national COOL programs and the introduction of costly
testing and disposal of unsafe units. Further, we have assumed that a competitive insurance
market exists that offers an actuarially fair insurance premium to the consumers in order to cover
the damages from consumption of unsafe goods. Finally we have analyzed the case of full
consumer liability and abstracted from principal-agent and moral hazard issues associated with
producer incentives. All these important topics represent very fruitful avenues for future research

some of which constitute work in progress by the authors. We complete the paper by addressing
the title question for the demanding reader:
How cool is COOL trade? Pretty cool indeed!


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Appendix A
At any unrestricted un-COOL trade equilibrium, there always exists a trade restriction
that improves welfare.

Al. Tariff
Welfare as a function of the specific tariff t, W(t), is given for the un-COOL case by

W(t)=u(AX, (t)+ A* X, *(t))+M- [(1 )LX, (t)+(1 A*)LX, *(t)]

-c(x (t))- P *X (t)

Totally differentiating this expression with respect to tariff yields

dW dX dX
S{A'- (1- )L-C'(.)} +[ *u'- (1- A*)L-P*] d (Al)
dt dt dt
With un-COOL trade and a specific tariff, t, on imports (13) is modified by replacing P* by
P *+ t and (14) is unchanged except for recognition that Zr is a function of (P + t ). For given

Z, *, the shifts in equations (13) and (14) in Figure 2 as a function of t are readily determined
by differentiation to both be upward, establishing that

d > 0 (A2)
dZ *
The sign of dZ cannot be definitively established. However, re-writing (14) in terms of X,
AX +A*X *
T = + (A3)
XT + X *

it is straightforward to show (A2), (A3) and A > A *, imply the elasticity of X, with respect to t

exceeds the elasticity of X, with respect to t or:

dX, X, dX* (A
> (A4)
dt X dt

From (11), < A < A, and C'(X) = P at t = 0, it follows at an un-COOL equilibrium with

t = 0, the term in curly brackets in (Al) is strictly positive while the term in square brackets is
dX dX *
strictly negative. Since C'(X)=P*+ t and C"(.)> 0, > 0. If < 0, then it follows
dt dt

dW dX *
directly from the signs of the terms in brackets of (Al) that dW > 0. If Td > 0, then use
dt t- dt

(A4) to derive at t = 0,

dwto> (A x +A*)(u'+L)-( x +1)(L+P*)dx (A5)
dt 0 X X dt

dX *
Under the assumption > 0, the sign of the right-hand side of (A5) is determined by the
sign of the term the square brackets. The latter is the same as the sign of
[.]/(- +1) = u'+ 2L-L-P*=0. Given the strict inequality of (A5) it follows that

d >> 0 and imposition of a tariff improves welfare.
dt t=

Although there is at least a marginal tariff that unambiguously improves welfare, it is
dX *
questionable whether or not the tariff constitutes a "trade restriction" in the case of > 0 -
i.e., the tariff actually increases imports. This outcome can occur because the increase in safety
of the pooled X, > 0, increases demand for all X (including imports which are
indistinguishable from domestic production) and the positive safety effect of a tariff can offset
the negative price effect of the tariff. Note that given an equilibrium with t > 0, it does not
necessarily follow that > 0. In this case, the term in curly brackets in (Al) remains
unambiguously positive, but the term in square brackets is not unambiguously negative since it
includes the positive value of the specific tariff

A2. Quota
In contrast to a tariff that can actually raise imports, imposition of a quota on X* at an un-
restricted un-COOL trade equilibrium is an unambiguous trade restriction. Hence, we now show
that at any unrestricted un-COOL trade equilibrium, there exists a quota on X* that reduces
imports and raises welfare. As noted in the text, total Z purchased in the COOL equilibrium is
less than Z purchased in the un-COOL equilibrium.

Consider a quota in the latter that restricts Z to Z* = Zc +Zc *-Z, < Z, *. It is assumed

the quota amount of X*, Z*/A* is purchased at world price P*, mixed with domestic
production and then sold to consumers. Price (P ) of both imported X and domestic X (Xq), is

determined by supply equals demand given the quota and domestic production determined
byC'(X,)=P,. Profit on the quota purchase and resale (PI-P*)X* is returned to the

consumer. The general expression for welfare given in (22) is unaffected. To distinguish pooled
A in general from its specific value of A, in the unrestricted un-COOL equilibrium, define:

Zd +Z* AXd + X*
A = (A6)
P Xd+X* Xd+X*
Where superscript d denotes supply of Z or X from domestic sources and superscript denotes
supply from imports. With the quota, P and Ap, must simultaneously satisfy:

u'AXs (P)+Z*)=- (A7)

AP- -- (A8)
p XS(P)+(Z*/A*)
Equations (A7) and (A8) define two relationships between Ap and PI that must hold in

equilibrium. Each individually defines a relationship P (A,). It is straightforward to show by

differentiation that for both (A7) and (A8), P (Ap) is upward sloping, raising the question of

whether they intersect and the nature of that intersection. Note, however, that by choice of Z *,
(A*, P*) satisfies (A7): From the unrestricted, un-COOL trade equilibrium, AXs (P*)= Z,,

Z,+Z*= Z +Zc and from the COOL trade equilibrium condition (17), it then follows

(A*, P*) satisfies (A7). In contrast, at P*, since AXs (P*)= Z, but Z* < Z *, it follows that

Ap in (A8) corresponding to P*must exceed A Denote this value of Ap by A*,. Since both

curves are strictly upward sloping (Ap,8,P*) satisfying (A8) lies below (A7) at A, .

At A, = A, there is finite PI that satisfies (A7): By selection of Z and the fact Z, < Z,

it follows that Z +Zc > Z +Z, = Zc + Zc *. The COOL market equilibrium implies at the

point (A, Pc), the left-hand side of (A7) (equal to u'(Zc + 7*)) is less than the right-hand side

(equal to u'(Zc +Zc*)). At (A, P*), the left-hand side of (A7) (greater than u'(Z, + Z,*))

exceeds the right-hand side (less than (P +(1 A,)L)A / ,)). Hence, there exists P, P* < P < P

such that (X, P) satisfies (A7). Given Z *>0, there is no PI that satisfies (A8) at A2 = A. For

(A8), P -> oc as 2, -> Z.

From: (a) P% (A) strictly increasing for both (A7) and (A8); (b) (Ap,8,P*) satisfying (A8),

but lying below (A7) at Ap, > T; (c) (A,P) satisfying (A7) for P*

P -> o as A2 2, it follows there exists (Ap,), jointly satisfying (A7) and (A8) and

characterized by AT < Ap < 2 and P* < < P.

Letting W, and W, denote welfare in the original un-restricted un-COOL equilibrium

and the new quota-constrained equilibrium respectively, then, using (22) rewritten in terms of Z,
letting Zq denote domestic production of Z under the quota, and noting since P* < P, Zr < Zq

and by construction Z* < Z *:

ZT 2 *
WT =M+ fu'(Z)dZ- -C'(-)dZ (I A)L f u'(Z)dZ -P* (1- A*)L- +
0 0 Zr

J u'(Z)dZ-P*(Z *Z*) -(1- *)L Z*)
2A* A*

I 1 Z Z Z* Z*
q =M+ u'(Z)dZ- C'(-)dZ-(1-A)L '+ u'(Z)dZ P* (1-*)L
0 0 ZA A A
Zq+Z* Z
(1)d Z (Zq Z )
S'(Z)dZ)d -(1- )L
Z,+Z* z

The first seven terms in W, and W, are identical. Combined, the last three terms of W, are

P +(1 i*)L
strictly negative since by selection of Z u'(Z, + 7*) = +(1 2*)L and u" < 0. Combined,

the last three terms of W, are positive. From the quota equilibrium,

P + (1 A,)L P + (1 A)L
u'(Z +Z*)= > (A9)

and C'( -)= P, the combined positive sign of the final three terms in W follow from

u" < 0 and c" > 0. Hence Wq > W .

Appendix B: If an interior maximum of W in (22) exists, then it is a global maximum.

Since u' and C' are monotonic, (23) and (24) imply that if an interior maximum exists, it
is unique. Assuming the autarky equilibrium is not a corner, a corner solution to (22) defined by
X* = 0 cannot be a maximum if W > 0. Similarly, assuming a market of only imports
dX *=0

would yield a non-corer solution, a corner solution defined by Xd= 0 cannot be a maximum if

dW >0.

Suppose a critical point (Xd > 0, X* > 0) exists satisfying (23) and (24). Then, from the

autarky solution compared with (23):
2u'(AXA)-(1-A)L-C'(XA) 0 and (B1)

u'(AXd + A X*) (1 )L C'(Xd) = 0

Since C" > 0 and X* > 0 and u" < O, Xd < XA and u'(AXd + A* X*) < u'(AXA). It then follows

from (24):
A*u'(X,A) (1 A*)L P*>0-> >0.
dX *X *=0

Let X denote the level of imports that maximizes W given that Xd = 0. Again assume a

critical point (Xd > 0, X* > 0) satisfying (23) and (24). Then

C'(Xd) + (1- )L P* +(1- (B2)L
A u'(**) or (B2)

Au'(A *X *) (1- A)L -C'(Xd) = 0 (B3)

Since C'(X) > C'(0), (B3) implies d0 > 0. Thus, if an interior maximum to W exists, it
odXds c r

dominates corner solutions.

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