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

Grigorios Livanis

Carol West*

University of Florida

Current Version: June 27, 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 presenceof product safety considerations, in this case risks to health, introduces a wedge between themarket 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 oftrade with and without a country-of-origin labeling (COOL) program. Assuming imports are lesssafe than domestic production, the welfare gains from trade in the absence of COOL areambiguous and may justify the imposition of a trade ban. Even if a full ban does not improvewelfare, some restriction of trade is always welfare-enhancing. These outcomes derive from an
informational distortion that prevents consumers from distinguishing the different countryspecific 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 inprotection– is better than less trade.

Key Words: Country-of-origin labeling, protection, product safety, welfare.
JEL Classification:
Address for Correspondence: Elias Dinopoulos, Department of Economics, University of
Florida, Gainesville, Fl 32611. E-mail: elias.dinopoulos@cba.ufl.edu. An electronic version of
the paper is available at http://bear.cba.ufl.edu/dinopoulos/research.html.

__________________* 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 andResource 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 polychlorinatedbiphenyls (PCBs) have led to greater consumer awareness of potential food hazards andincreased 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 thisresearch.
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 nearzero. 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 thelargest 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-oforigin labeling (COOL) is another policy measure addressing the problem of potentially unsafe
food imports. COOL allows consumers to differentiate products that potentially 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 andmandatory 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 implementation.
Juxtaposed against the emotional intensity that often surrounds health-related issues andthe sometimes extreme measures that have been implemented to deal with foodborne diseases in1

particular, is a relatively scant literature analyzing the economics of trade policy in risky foodproducts. Many questions remain unanswered. From an economic welfare perspective, are tradeembargoes 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 beaugmented by traditional protectionist trade policy instruments (e.g., tariffs)?
Product safety, and in particular food safety, issues have been analyzed theoretically andempirically, but primarily in the context of closed-economy, partial-equilibrium models.1 In theinternational 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 marketplaceresembles consumer inability to distinguish goods by production process (eco-friendly,
sweatshop, etc.) which, if known, would affect willingness to pay.4 Since welfare analyses oftrade 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
1See, 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 foodsafety on meat demand and for a partial review of empirical studies on food safety, see Piggott and Marsh (2004).
For extensive theoretical analysis in a domestic context, see Fulton and Giannakas (2004) 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.
3
An interesting extension of the present research would link to these previous analyses by incorporating thepossibility 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 thefeasibility of its plausible incorporation into the potential exporter’s explicit choice between “high quality” and “lowquality” production, the situation could have similarities to examples that motivate the analyses of country-of-origin
reputations.
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 nonconforming goods, including effects of certification labeling.

2

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 situationa 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 productsafety. Price consequences are only indirect, as the change in consumer information altersdemand 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 productionthat 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 associatedwith 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, weconsider a product with an inherent health risk that is measured by the proportion of its unsafe
units supplied in the market. 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 origin.
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.

3

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 (closedeconomy) 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 costof illness, leads to a decrease in social welfare (Proposition 2).
For a small country that imports a riskier product than it produces, movement from theautarky 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 aninformational distortion associated with the inability of consumers to assign the correct risk levelto domestic and foreign goods that leads to a pooling equilibrium and ambiguous gains fromtrade. This result allows for the possibility of welfare-enhancing import bans. Even in the casewhere an import ban does not dominate un-COOL free trade, some restriction of un-COOL tradeis always welfare-enhancing.
We then analyze the effects of introducing a COOL program that permits the consumer todifferentiate 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 theprice 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 areduction 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 ofautarky or un-COOL trade.
While no model can thoroughly address the multiplicity of issues regarding food safety andglobal 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 approach4

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 closedeconomy 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 outsidecomposite 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 thatwages are equal to unity. To focus on the analysis of product safety we assume that perfectcompetition prevails in all markets and consumers have identical preferences.
The risk associated with a purchase X of the unsafe good is captured by the assumptionthat it embodies a certain proportion, λ , of safe units, Z = λ X , and a remaining unsafe portion,(1 − λ ) with 0 ≤ λ ≤ 1 . Consumption of safe units yields positive utility, but consumption ofunsafe 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 byparameter λ 7, 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 facesa (1 − λ ) = 3.5 × 10−6 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, λ , of safe units in any purchase X and a resultant (1 − λ ) 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 λdepends on self-protection actions and on a set of information (i.e. past experience) that each consumer uses informing 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.

5

proportion of unsafe units, the consumer making a purchase of X faces an exogenous
probability (1 − λ ) the purchase will make him/her ill. Concomitantly, with probability λ , thepurchase can be expected to be consumed without adverse health consequences. If a particularexpenditure on X turns out to be a “bad lot,” then the associated cost of illness is proportional tothe volume of X purchased and consumed. Both interpretations yield the same key relationshipsthat are used in the subsequent model analysis, but formal presentation is restricted to the firstinterpretation.
We postulate the existence of a competitive health (medical) insurance market thatprovides insurance to all consumers in the market against the loss L caused by the consumptionof 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 “MadCow” disease) and in principle depends on the quality of the health system. Following theinsurance literature, we further assume that the insurance offered to the consumers is full andactuarially fair in the sense that the insurance premium equals the expected value of theinsurance claims.8 In the case of eggs, one can measure the expected damage cost to theconsumer 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 ofillness 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 partialequilibrium 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 andindicates that the consumer does not receive any utility from the unsafe units X − Z 9. In thisformulation, 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 andactuarially 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.

6

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 λ X will yield positive
utility. Insuring against the expected cost of illness (or setting aside the funds to pay for it)
requires expenditure of (1 − λ )LX . Assuming a total budget M , and a price P of X , theconsumer’s maximization problem is as follows:
Max ⎡⎣u ( λ X ) + M − PX − (1 − λ ) LX ⎤⎦X(2)

The first-order condition for (2) can be written asu′ ( Z ) =

P

λ

+

(1 − λ )

λ

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 = λ X ). Concavity of u (.) guarantees that thesecond-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) isˆ +Y ,
identical to maximizing U ( Z , Y ) = u ( Z ) + Y subject to the budget constraint M = PZ

where
P (1 − λ )Pˆ = +
L

λ

λ

(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: P̂ is the risk-adjusted
price (expected cost) of obtaining a safe unit of a risky product, P / λ is the warranty price, andthe term (1 − λ ) L / λ 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 ofcontracting Salmonella. Substituting the risk of becoming sick ( 1 − λ = 3.5 × 10 −6 ), the cost ofillness ( 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.

7

becomes Pˆ =0.081
+ 2,126*3.5 × 10−6 = $0.088 . In other words, the consumer behaves as if
0.999997

the risk of Salmonella generates an 8.6% increase in the market price for safe eggs with acorresponding 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 P̂ , and is denoted by Z D Pˆ . This relationship will be used in calculating
the expected consumer surplus in the welfare analysis. Recalling the relationship between thesafe and unsafe quantities of a risky product, Z = λ X , the demand for the risky product X can

( )

( )

be obtained then by X D Pˆ = Z D Pˆ λ . Substituting λ X = Z into the left-hand side of (3)yields the inverse market demand function of the risky good X , where the dependent variable isthe market price (as opposed to the RAP):P = λu′ ( λ X ) − (1 − λ ) L(5)Equation (5) yields the first result of our model which is stated in the following
proposition:
Proposition 1: A market for an unsafe product does not exist if the following condition holds:

P = λu′ ( 0 ) − (1 − λ ) 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 λ0 = L /( L + u′ ( 0 )) < 1
which varies positively with L and negatively with the marginal utility of consuming the firstsafe 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 theoutput of good X supplied is given by

X S ( P)

(6)

where ∂X S ( P ) / ∂P > 0 , and X S ( P ) = 0 for a non-negative price P ≥ 0 : The supply curve isupward 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

8price of X .11 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 / λ)(7)where ∂P ( X ) / ∂X > 0 and P ( 0 ) = P > 0 . The supply of safe units Z S ( λ , P ) is straightforwardly
obtained by multiplying (6) by the proportion of safe units λ , i.e., Z S ( λ , P ) = λ X S ( P ) .
The autarky (closed-economy) equilibrium condition requires equality between thequantity supplied and the quantity demanded for the tradeable good X :X S ( P ) = X D ( P, λ , L )(8)

Condition (8) determines the market equilibrium price PA (where subscript A denotes theautarky equilibrium) and the equilibrium quantity of X , X A . In addition, multiplying both sidesof equation (8) by λ , evaluated at PA , yields(

Z S ( λ , PA ) = λ X D ( PA , λ , L ) ≡ Z D Pˆ ( PA , λ , L )

)

.

(9)

which implies equality between the equilibrium level of safe units of good X produced andconsumed. Having determined the producer price PA , one can calculate the consumer RAP, P̂A ,directly by setting P = PA in (4).
Figure 1 illustrates the closed-economy equilibrium. The horizontal axis measures theamount of safe and total units, Z and X respectively, and the vertical axis denotes prices (bothmarket and risk adjusted). The upward-slopped curve X S ( P ) illustrates the supply (and inverse
supply) curve of the risky good, and the downward-slopped curve X D ( P, λ , L ) is the market
demand curve for the risky good X , which is implicitly defined by equation (5).12 Theintersection of these two curves illustrates geometrically the solution of (8), which yields theclosed-economy market-equilibrium price PA and quantity produced X A . Having determined theequilibrium quantity of the risky good produced X A , one can readily determine the equilibrium

One could introduce the assumption that the supply of a risky good is a decreasing function of λ and analyze theeffects 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.
119amount of safe units Z A = λ X A by subtracting horizontally the amount of unsafe units (1 − λ ) X Afrom X A (i.e., the intersection of PA and Z S ( λ , P ) ).
Z S (λ, P )P

X S ( P)

α

PˆA

P

PA

β

γ

( )

Z D Pˆ

X D ( λ , L, P )

P
0

Z, X

XA

ZA

Figure 1: Closed-Economy Equilibrium( )The downward-slopped curve Z D Pˆ illustrates the demand curve for safe units Z as a functionof the risk-adjusted price P̂ (defined in equation (3)). Evaluating this inverse demand curve at
the equilibrium level of safe units Z A yields the equilibrium RAP, P̂A , which exceeds the market( )price. Area (α) that is located below curve Z D Pˆ and above the equilibrium RAP, P̂A , is equal
to the expected consumer surplus.
Area (β+γ), which is located below the market equilibrium price PA and above the supply
curve X S ( P ) , measures producer surplus. In our analysis producer surplus captures the rents tospecific factors (or industry profits) associated with the supply of X A risky units, given ourassumption that consumers bear all the risks and so producers are not concerned with thedistinction between safe and unsafe units. Consequently, the closed-economy equilibrium levelof social welfare is measured by area (α+β+γ). This geometric property will be utilized later inthe welfare analysis of various public policies. We need to emphasize that the use of this10

standard measure of producer surplus implies that producers are not liable for the production ofunsafe 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 “taxrevenue” is not a transfer but a pure welfare loss associated with the production and consumptionof unsafe units. This welfare loss is measured by the area ( PˆA − PA ) Z A in Fig. 1 and depends onthe 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 perfectcompetition, the market solution maximizes social welfare (defined as the sum of expectedconsumer plus producer surplus). In other words, unless the social planner can alter the risk
parameter λ (perhaps though testing) or the per-unit cost of illness L (through health carereforms or development of better treatments), the market solution coincides with the
maximization of social welfare. To establish this property, denote with C ( X ) the aggregatesocial (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 = λ X andincurs two types of costs, health insurance costs (1 − λ )LX and production costs C ( X ) . Hence,the social planner’s problem is
Max ⎡⎣u (λ X ) + M − (1 − λ ) LX − C ( X ) ⎤⎦X

which yields the first-order conditionu′ ( Z ) =C′( X )

λ+(1 − λ )

λ

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.

11

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 thecomparative 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 ↑ shifts the market demand curve in Fig. 1,
X D (λ , L, P) , downward and generates: a decline in the market-equilibrium price PA ; a fall inthe equilibrium quantities X A and Z A ; an increase in the risk-adjusted price P̂A ; and areduction the social welfare, measured by expected consumer plus producer surplus.
(b) A decline in product safety, measured by a reduction in parameter λ ↓ , reduces social
welfare.
(c) If the market price elasticity for

product

X

is not numerically small, i.e.,−ε P = −(∂X D ∂P )( P X D ) > P ( P + L ) , then a decline in product safety, measured by areduction in parameter λ ↓ , shifts the market demand curve in Fig. 1, X D (λ , L, P) , downward
generating declines in the market-equilibrium price PA , the market-equilibrium quantity X A andthe amount of safe quantity Z A and a rise in the equilibrium risk-adjusted price P̂A .
Part (a) follows straightforwardly from (5) and Figure 1. For part (b), differentiate welfare ( W =u (λX ) + M − (1 − λ ) LX − C ( X ) ) with respect to λ and simplify using (10) to verify dW d λ > 0 .

For (c), substitute λ X for Z in (10) and then differentiate totally to determine dX d λ whose
sign depends upon the sign of u ′′(.)λX + u ′(.) + L . Use (5) differentiated with respect to X ( λfixed) 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 issusceptible to any new information concerning the way consumers perceive objective (orsubjective) threats to food safety as measured by the parameters λ and L . For instance,
according to Piggott and Marsh (2004) the public will generally respond to a foodborne outbreakby decreasing its consumption, at least in the short run. Moreover, if the food-safety problem isrecurring, it can result in an inward shift of consumer demand for a specific good. In the case of12the 1996 outbreak of BSE (“Mad Cow” disease) in the United Kingdom, both the product risk
(1- λ ) 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- λ ) is very small then even forlarge L the difference between the RAP and the market price will be small and the demand for arisky product will be determined by its market price. This is consistent with the findings of areport 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-oforigin 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 thepooling 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 forthe case of a country that imports an unsafe good at a fixed international market price P * (thesmall-country case). This implies that the home country faces a horizontal supply curve ofimports at the international market price P * and each unit of imports carries a risk of becoming
ill equal to 1 − λ * .14
Denote with X T the market quantity of the domestic risky product and with X T * thecorresponding 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
ZT = λ X T be the domestic “safe” quantity consumed that does not result in any adverse healthoutcomes. Similarly, assume that ZT * = λ * X T * 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 withdifferent safety parameters λ * . This case can be analyzed, but it is beyond the scope of the present paper.

13

(imported) safe food so the aggregate consumption of safe units is given by ZT + ZT * . Assume,for simplicity that parameters λ , λ * ∈ [0,1] are exogenous and may differ from each other.
Without loss of generality, assume max ( λ0 *, λ0 ) < λ* < λ < 1 , which implies markets exist foreach 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 inequalization of the domestic and world prices, i.e., P = P * . The market quantity supplied will be
X T + X T * , where the domestic quantity supplied X T is given by X S ( P *) —the domestic
supply curve evaluated at the world market price. The domestic supply of safe units isconsequently given by ZT = λ X T . To determine the market-equilibrium quantity of imports
X T * note that imported and domestic goods are indistinguishable in the marketplace and theircosts of illness per unsafe unit consumed are identical. This implies consumer demand will
depend on the average probability of becoming ill λT = ( ZT + ZT *) /( X T + X T *) . In this case, thesolution to the consumer problem can be obtained by assuming that he/she maximizes utilityu ( ZT + ZT *) by choosing the aggregate quantity consumed ZT + ZT * subject to the nonstochastic budget constraint M = Y + PˆT ( ZT + ZT *) . The first-order condition of the consumer’s
maximization problem is then given byu′ ( ZT + ZT *) = PˆT = [ P * +(1 − λT ) L] / λT

(11)where P * is the common market price, PˆT is the free-trade risk-adjusted price,

λT =ΖT + Z T * Z T + Z T *== (1 − s*)λ + s * λ *ΧT + X T * ZT + Z T *
λ
λ*

(12)

is the free-trade consumption safety level, and s* = X T * /( X T + X T *) is the consumption share ofimports. Un-COOL free-trade yields a common market price P * and a common RAP given by(11). Substituting (12) and ZT = λ X S ( P *) into (11) determines the un-COOL free-tradeequilibrium value of safe imports ZT * , which can readily be transformed into the marketequilibrium quantity of imports X T * = ZT * / λ * .

14

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

λT ( ZT *) =P*+ Lu ′ ( Z T ( P *) + Z T *) + L(13)and, for clarity of exposition, we replicate equation (12) below

λT =

ZT + ZT *.
ZT ZT *
+
λ
λ*

(14)

Because the domestic quantity of safe units ZT ( P *) = λ X S ( P *) is a function only of the world
price and λ, (13) and (14) constitute a system of two simultaneous equations in two unknowns

λT and ZT * . The solution is illustrated in Fig. 2. The upward-slopped curve is the graph ofequation (13). It has a positive vertical intercept defined by setting ZT * = 0 in equation (13), anda positive slope:

λT
Eq. (13)λλT(

Eq. (14)P *+Lu′ λ XS( P *) ) + L
0

Z T*

Z*

Figure 2. Determination of Free-Trade Equilibrium ofImports 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 ( λT , ZT *) space under15

the assumption that domestically produced goods are safer than imported ones ( λ * < λ < 1 ). The
vertical intercept of the downward-slopped curve equals λ : For any level of safe domestic units
ZT ( P *) , as the amount of imports increases, the level of product safety declines. Theintersection of these two curves determines the free-trade equilibrium quantity of safe imports
ZT * and the level of λT . The total quantity of imports is given by X T * = ZT * / λ * .
Note that if P* ≥ PA , the graph of equation (13) in Fig. 2 lies above that of equation (14)for non-zero ZT * and the free-trade equilibrium reduces to the autarky equilibrium. If
X S ( P *) = 0 , (14) in Fig. 2 is undefined at Z*=0 and otherwise horizontal at λT = λ * . The free-

trade equilibrium reduces to one of solely purchasing imports. We abstract from theseuninteresting degenerative equilibria by assuming:
P* < PA and X S ( 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 ofimports, which is a horizontal line intersecting the vertical axis at P * .

P
X S ( P)

α
PˆA

δ

PˆT

PA

γ

( )

Z D Pˆ

P*
β

P
0

XT

XA

Z T + ZT *Z, X

Figure 3. Un-COOL Free-Trade Equilibrium

16

The closed-economy equilibrium corresponds to the market price PA , and the RAP P̂A
where Z D ( PˆA ) = λX A . Price PA determines the producer surplus (β+γ) and RAP P̂A determines

expected consumer surplus (α). The opening of trade establishes a lower producer price P * andresults in the importation of ZT * = λ * X T * units of safe imports and (1 − λ *) X T * units of unsafe
imports. Under un-COOL free trade, domestic producers face a lower price and reduce thequantity of unsafe and safe food produced, and therefore the producer surplus is equal to area (β).
The move from autarky to free trade results in a decline in the producer surplus which equals
area (γ) 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-tradeequilibrium, one has to add the safe quantity embodied in imports ZT * , which is determined inFig. 2, to the domestic quantity of safe units ZT . The RAP under free trade PˆT corresponds to( )the total safe quantity consumed ZT + ZT * . The area (α+δ), which is below curve Z D Pˆ andabove the RAP PˆT 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 movefrom 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 (γ). This reduction in welfare is the same as theincrease in expected consumer surplus measured by area (δ), caused by a reduction in the RAP
from P̂A to PˆT . Thus, even if imports are more risky than domestic products, the economy isindifferent between imposing an import ban and engaging in free trade. Of course, in this caseconsumers 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 λ * does not affect the graph of equation (13) in Fig. 2, but rotatesclockwise from its intercept the graph of equation (14) and results in a lesser safe quantity of17

imports ZT * , for any given market price P * . This implies that the total safe quantity available
to consumers ZT + ZT * declines in Fig. 3, and the expected consumer surplus under free unCOOL trade falls. Since the expected producer surplus depends on the market price P * , a
reduction in λ * leaves this component of national welfare unaffected. Consequently, theexpected gain from trade measured by area (δ-γ) is negative and an import ban improves welfare.
One can readily construct other scenarios that justify the ban of unsafe imports based on otherparameter 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 aresummarized in the following proposition:
Proposition 3: Starting at the autarky equilibrium and assuming that the domestically produced

good is safer than the imported product ( λ > λ * ), 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
surplus.
(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 of free 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 acommon (average) safety risk. The model is consistent with the evidence of import bansfollowing outbreaks of foodborne disease abroad. These bans can be modeled as a move fromun-COOL free trade (with safe domestic and risky imported goods, λ = 1, λ* < 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 safety18

captured by the risk parameter λ * and the damage costs L . For example, the larger thedifferential of safety risk between domestic and imported goods measured by λ − λ * , 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 theimports. In particular, from the individual consumer perspective, the marginal unit of X carries
a risk (1 − λT ) < (1 − λ*) . However, for society, the marginal unit of X is imported and carries
the higher illness risk (1 − λ*) . 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 theconditions 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 formallyanalyze the effects of costs associated with implementation of a COOL program. If the costs ofinstituting 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 candistinguish whether a good is imported or domestic, allowing the two types of X to havedifferent prices. Denoting COOL values by subscript C , maximizing the consumer’s utility
function u ( Z C + Z C *) + Y subject to a deterministic budget constraint M = PˆC Z C + Pˆ * Z C * + Y
yields the following first-order conditions for an interior solution :P (1 − λ )u′ ( Z C + Z C *) = PˆC = C +L(16)

P * (1 − λ *)u′ ( Z C + Z C *) = Pˆ * =
L
+
λ*
λ*

(17)

λ

λ

19

where PC denotes the producer price of domestically produced X , P * the producer price ofimports and “^” indicates associated RAP. Under COOL trade, the consumer buys the productwith 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 thedomestic 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 thatPˆC = [ PC + (1 − λ ) L] / λ = [ P * + (1 − λ *) L] / λ *(18)which determines PC and equilibrium RAPs, PˆC = Pˆ * .
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 thedomestically produced good yields⎡P* ⎛ λ −λ *⎞ ⎤PC = λ ⎢+⎜⎟ L⎥⎣ λ * ⎝ λ *λ ⎠ ⎦(19)According to equation (19), the good with the lower safety risk (in this case the domestic productsince λ > λ * by assumption) commands a higher market price at equilibrium because theconsumer 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
Z C = Z S ( λ , PC ) = λ X S ( PC )(20)

Since the introduction of COOL raises the market price of the domestic product relative to thedomestic 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 λT = (1 − s*)λ + s * λ * > λ * . It follows from (11) and (17) that20

u ′ ( Z C + Z C *) =⎛ P * (1 − λ*) ⎞ ⎛ P * (1 − λT ) ⎞ ˆPˆC = ⎜
L⎟ > ⎜
L ⎟ = PT =
+
+
λ*
λT
⎝ λ*
⎠ ⎝ λT⎠(21)u ′ ( Z T + Z T *)The total amount of safe quantity consumed under COOL free trade is strictly less than thecorresponding quantity under un-COOL free trade, i.e. Z C + Z C * < ZT + ZT * . This inequality
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 theconsumption of the safer domestic good increases with the introduction of COOL, (i.e.,
Z C > ZT ), the safe (and market) quantity of imports declines (i.e., Z C * < ZT * ). Thus, COOL
increases the domestic market price of the safer (domestic) product, reduces the quantity of theless 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 thatsummarizes the economic effects of introducing a COOL program.
Proposition 4: Starting at the un-COOL free-trade equilibrium and assuming that thedomestically produced good is safer than the imported product ( λ > λ * ), 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
surplus.
We are now in a position to establish the optimality of COOL. With a price P * forimports, X * , and P for domestically produced X , X d , and a domestic cost of producing X d ,C ( X d ) , the level of national welfare in general is given by:
W = u ( λ X d + λ * X *) + M − [(1 − λ ) LX d + (1 − λ *) LX *] − C ( X d ) − P * X *(22)An interior maximum for W ( X d > 0, X * > 0 ), requires:

λ u′ ( λ X d + λ * X *) − (1 − λ ) L − C ′ ( X d ) = 0 and

(23)

21

λ * u′ ( λ X d + λ * X *) − (1 − λ *) L − P* = 0(24)

The concavity of u and C ′′ > 0 assure second order conditions are satisfied. Given that both C ′and u ′ are monotonic, if an interior maximum exists, it is unique. Since C ′( X C ) = PC , (16) and(17) imply an interior COOL equilibrium is this unique maximum. Note that un-COOL trade cannever maximize welfare since joint satisfaction of (23) and (24) at ( X d > 0, X * > 0 ) requires
C ′( X d ) > P * (assuming λ > λ * ) and in the un-COOL trade equilibrium C ′( X T ) = P * .
Appendix B establishes that if an interior maximum exists, it dominates corner solutions of
X d = 0 and X * = 0 . Hence, if an interior COOL equilibrium exists, it dominates both autarky
and the un-COOL trade equilibrium. A corner COOL equilibrium at all imports is precluded by(15).15 A corner COOL equilibrium at the autarky solution can be consistent with (15). In thatcase,
PA + (1 − λ ) L

λ= u ′(λX A ) <P * + (1 − λ*) L
λ*i.e., at the autarky solution, the marginal utility of an additional unit of Z is less than the RAP ofbuying it as an import and hence, there is no market for imports. In this situation, clearly theequivalent autarky and corner COOL equilbria dominate the un-COOL trade equibrium because
no interior maximum exists. Hence, welfare under a COOL regime always exceeds that of unCOOL 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 , Z C , and Z C * . Substituting
Z C = λ X C and Z C * = λ * X C * in (17) and differentiating totally the system of these equations
yields15

A corner COOL equilibrium at all imports can exist only if

P * + (1 − λ *) L

λ*<C ′(0) + (1 − λ ) L

λwhich is precludedby (15) and C ′′(.) > 0 which imply C ′(0) < P * , and λ > λ * .
For this derivation we assume an interior COOL solution since imposing tariffs in the corner COOL solution ofautarky is uninteresting.

16

22

dX C
λ ∂X C=>0
dt t ≥0 λ * ∂PC(25)

dX C *∂X ⎤1 ⎡ 1=− λ2 C ⎥ < 0 .
2 ⎢dt t ≥0 (λ *) ⎢⎣ u ′′ (.)∂PC ⎥⎦(26)

Because the safe quantities of domestic and imported products are proportional to X C and X C * ,an increase in protection increases Z C and reduces Z C * . 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 consumedu ( λ X C + λ * X C *) and faces insurance costs (1 − λ ) LX C + (1 − λ*) LX C * to cover the costs ofillness from domestic and imported risky products. In addition, the social planner faces domestic
production costs C ( X C ) and import costs ( P * + t ) X C * . Since the government collects the tariff
revenue t ⋅ X C * , which is distributed back to consumers, under the standard assumption, the net
social costs of imports are simply P * X C * . The level of national welfare as a function of thespecific tariff is
W (t ) = u ( λ X C ( t ) + λ * X C * ( t ) ) + M − ⎡⎣(1 − λ ) LX C ( t ) + (1 − λ *) LX C * ( t ) ⎤⎦− C ( X C (t )) − P * X C * (t )Differentiating the above expression with respect to the specific tariff yields:

dX
dX *
dW
= {λu′ − (1 − λ ) L − C ′ (.)} C + [ λ * u′ − (1 − λ *) L − P *] C
dt
dt
dt

(27)

Equation (16) and the property PC = C ′ ( X C ) 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 ofthe specific tariff. Therefore, taking into account the above analysis and using (26) one canderive two standard expressions for the effects of a specific tariff on national welfare in thepresence of COOL17dX *dW=t C <0
dt t >0
dt

(28)

17

See Feenstra (2004, 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.

23

dX *
dW
=t C =0
dt t =0dt(29)Inequality (28) states that national welfare is a decreasing function of the specific tariff forstrictly 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 ( λ > λ * ), 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 andreestablishes the traditional optimality of trade which asserts that more trade is better than lesstrade for a country that cannot change the terms-of-trade. This proposition also implies that if thecosts 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 bestpolicy 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 thesmall country produces an unsafe product and imports another riskier product under conditionsof perfect competition. Product risk was modeled as the exogenous proportion of units of theparent 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 orunsafe. 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 thethird was a free-trade regime coupled with a COOL program.
18

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

24

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 andproducer surplus. The presence of insurable risk creates a wedge between the producer andconsumer price that depends positively on the per-unit cost of becoming ill and on the proportionof unsafe units embodied in the risky product. In the absence of a COOL program, the openingof 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 tradebans 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 haveassumed 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 behigher or lower than the objective risk assumed in this paper. We have also abstracted fromanalyzing the more realistic case of multiple import suppliers and multiple levels of countryspecific 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 fullconsumer liability and abstracted from principal-agent and moral hazard issues associated withproducer incentives. All these important topics represent very fruitful avenues for future research

25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!

26

References

Akerlof, G.A. “The Market for Lemons: Quality Uncertainty and the Market Mechanism.”
Quarterly Journal of Economics, 1970, 84, pp. 488-500.
Bagwell, Kyle and Staiger, Robert W. “The Role of Export Subsidies when Product Quality is
Unknown.” Journal of International Economics, 1989, 27, pp.69–89.
Bagwell, Kyle. “Optimal Export Policy for a New-Product Monopoly.” American Economic
Review, 1991, 81(5), pp.1156–1169.
Beaulieu, E. and J. Gaisford. “Labour and Environmental Standards: The ‘Lemons Problem’ inInternational Trade Policy.” World Economy, 2002, 25(1), pp.59–78.
Becker, Gary S. “A Theory of the Allocation of Time.” Economic Journal, 1965, 74(295),
pp.493–517.
Bhagwati, Jagdish. “The Generalized Theory of Distortions and Welfare”, in Jagdish N.
Bhagwati, Ronald W. Jones, Robert A. Mundell and Jaroslav Vanek, eds., Trade, Balance ofPayments and Growth; Papers in International Economics in Honor of Charles P.
Kindleberger. Amsterdam, North-Holland Pub. Co., 1971.
Blend, J.R. and van Ravenswaay, E.O. “Measuring Consumer Demand for Ecolabeled Apples.”American Journal of Agricultural Economics, 1999, 81, pp.1072–7.
Boom, Anette. “Product Risk Sharing by Warranties in a Monopoly Market with Risk-Averse
Consumers.” Journal of Economic Behavior and Organization, 1998, 33, pp.241–257.
CDC, Centers for Disease Control and Prevention. Infectious Disease Information. Internet
address: http://www.cdc.gov/ncidod/diseases/food/index.htm, last accessed: Dec.1 2004.
Chisik, Richard. “Export Industry Policy and Reputational Comparative Advantage.” Journal ofInternational Economics, 2003, 59(2), pp.423–451.
Daughety, Andrew F. and Reinganum, Jennifer F. “Product Safety: Liability, R&D, andSignaling.” American Economic Review, 1995, 85(5), pp.1187–1206.
Donnenfeld, Shabtai; Weber, Shlomo and Ben-Zion, Uri. “Import Controls under Imperfect
Information.” Journal of International Economics, 1985, 19, pp.341–354.
Epple, Dennis and Raviv, Artur. “Product Safety: Liability Rules, Market Structure, andImperfect Information.” American Economic Review, 1978, 68(1), pp.80–95.

27

Falvey, Rod and Reed, Geoff. ‘‘Rules of Origin as Commercial Policy Instruments.’’
International Economic Review, 2002, 43(2), pp. 393–407.
Falvey, Rodney. “Trade, Quality, Reputations and Commercial Policy.” International Economic
Review, 1989, 30(3), pp.607–622.
FCOI, Economic Research Service (ERS). Foodborne Illness Cost Calculator. United States
Department of Agriculture, Internet address: http://www.ers.usda.gov/data/foodborneillness/,last accessed Dec. 1 2004.
Federal Register. Mandatory Country of Origin Labeling of Beef, Lamb, Pork, Fish, Perishable
Agricultural Commodities, and Peanuts; Proposed Rule. U.S. Department of Agriculture,
Agricultural Marketing Service, 68 (210), October 30, 2003, Internet address:www.ams.usda.gov/cool/ls0304.pdf.
Feenstra, Robert. Advanced International Trade: Theory and Evidence, 2004, Princeton
University Press.
Foreign Agricultural Service (FAS). The Continuing Effects of BSE Beef Market, Trade, andPolicy. Livestock and Poultry - World Markets and Trade, U.S. Department of Agriculture,
Washington D.C., March 1998, available at: http://www.fas.usda.gov/dlp2/circular/1998/9803LP/bse.html.
FSIS, Food Safety and Inspection Service. Risk Assessments. United States Department ofAgriculture, Internet address: http://www.fsis.usda.gov/Science/Risk_Assessments/index.asp,
last accessed November, 29 2004.
Fulton, Murray and Giannakas, Konstantinos. “Inserting GM Products into the Food Chain: The
Market and Welfare Effects of Different Labeling and Regulating Regimes.” American
Journal of Agricultural Economics, 2004, 86(1), pp.42–60.
Gaisford, J.D. and Lau, C. “The Case For and Against Import Embargoes on Products ofBiotechnology.” The Estey Journal of International Law and Trade Policy, 2000, 1(Spring),
pp.83–98, www.esteyjournal.com.
Grossman, Gene M. and Horn, Henrik. “Infant-industry Protection Reconsidered: The Case ofInformational Barriers to Entry.” The Quarterly Journal of Economics, 1988, 103(4),pp.767–787.
Haener, M.K. and Luckert, M.K. “Forest Certification: Economic Issues and Welfare
Implications.” Canadian Public Policy, 1998, 24, pp. S83-S94.

28

Krishna, Kala. “Understanding Rules of Origin.” NBER Working Paper No. 11150, 2005.
Krueger, Anne O. ‘‘Free Trade Agreements as Protectionist Devices: Rules of Origin.’’ NBER
Working Paper No. 4352, 1993.
Krueger, Anne O. ‘‘Free Trade Agreements versus Customs Unions.’’ Journal of Development
Economics, 1997, 54, pp.169–187.
Lloyd, P.J., “A Tariff Substitute for Rules of Origin in Free Trade Areas”, World Economy,
1993, 16(6), pp.699–712.
Lopez-de-Silanes, Florencio; Markusen, James R. and Ruthenford, Thomas. “Trade Policy
Subtleties with Multinational Firms.” European Economic Review, 1996, 40(8), pp.1605–27.
Oi, Walter Y. “Economics of Product Safety.” The Bell Journal of Economics and Management
Science, 1973, 4, pp.3–28.
Piggott, Nicholas E. and Marsh, Thomas L. “Does Food Safety Information Impact U.S. Meat
Demand?” American Journal of Agricultural Economics, 2004, 86(1), pp.154–174.
Raff, Horst and Kim, Young-Han. “Optimal Export Policy in the Presence of Informational
Barriers to Entry and Imperfect Competition.” Journal of International Economics, 1999,
49(1), pp.99–123.
Rodriguez, Peter L. “Rules of Origin with Multistage Production.” World Economy, 2001, 24(2),pp.201–220.
Shapiro, Carl. “Premiums for High Quality Products as Returns to Reputations.” Quarterly
Journal of Economics, 1983, 98(4), pp 659–680.
Spence, Michael. “Consumer Misperceptions, Product Failure and Producer Liability.” Review of
Economics Studies, 1977, 44(3), pp.561–572.

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

A1. Tariff

Welfare as a function of the specific tariff t , W ( t ) , is given for the un-COOL case by
W (t ) = u ( λ X T ( t ) + λ * X T * ( t ) ) + M − ⎡⎣ (1 − λ ) LX T ( t ) + (1 − λ *) LX T * ( t ) ⎤⎦− C ( X T (t )) − P * X T * (t )Totally differentiating this expression with respect to tariff yields
dX
dX *
dW
= {λu ′ − (1 − λ ) L − C ′(.)} T + [λ * u ′ − (1 − λ *) L − P*] T
dt
dt
dt

(A1)

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 ZT is a function of ( P * + t ). For given
ZT * , the shifts in equations (13) and (14) in Figure 2 as a function of t are readily determinedby differentiation to both be upward, establishing that
dλT
>0
dt

The sign of

λT =

(A2)

dZT *
cannot be definitively established. However, re-writing (14) in terms of X ,dt

λ XT + λ * XT *XT + XT *(A3)

it is straightforward to show (A2), (A3) and λ > λ * , imply the elasticity of X T with respect to t
exceeds the elasticity of X T * with respect to t or:dX T
X dX T *> T
dt
X T * dt

(A4)

From (11), λ * < λT < λ , and C ′( X T ) = P * at t = 0 , it follows at an un-COOL equilibrium witht = 0 , the term in curly brackets in (A1) is strictly positive while the term in square brackets isstrictly negative. Since C ′( X T ) = P * + t and C ′′(.) > 0 ,dX T
dX T *> 0 . If
< 0 , then it follows
dt
dt

30

directly from the signs of the terms in brackets of (A1) thatdW
dX T *> 0 . If
> 0 , then use
dt t =0
dt(A4) to derive at t = 0 ,⎡⎤ dX *X
X
dW> ⎢(λ T + λ *)(u ′ + L) − ( T + 1)( L + P*) ⎥ T
dt t =0 ⎣ X T *
XT *
⎦ dt

Under the assumption(A5)

dX T *> 0 , the sign of the right-hand side of (A5) is determined by thedtsign of the term the square brackets. The latter is the same as the sign of[.] /(

XT+ 1) = λT u′ + λT L − L − P* = 0 . Given the strict inequality of (A5) it follows that
XT *dW
> 0 and imposition of a tariff improves welfare.
dt t =0

Although there is at least a marginal tariff that unambiguously improves welfare, it isquestionable whether or not the tariff constitutes a “trade restriction” in the case ofdX T *>0 —dti.e., the tariff actually increases imports. This outcome can occur because the increase in safetyof the pooled X ,dλT> 0 , increases demand for all X (including imports which are
dt

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 notnecessarily follow thatdW
> 0 . In this case, the term in curly brackets in (A1) remains
dt

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 unrestricted un-COOL trade equilibrium is an unambiguous trade restriction. Hence, we now showthat 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 isless than Z purchased in the un-COOL equilibrium.

31

Consider a quota in the latter that restricts Z * to Z * = Z C + Z C * − ZT < ZT * . It is assumed
the quota amount of X * , Z * / λ * is purchased at world price P * , mixed with domestic
production and then sold to consumers. Price ( Pq ) of both imported X and domestic X ( X q ), is
determined by supply equals demand given the quota and domestic production determined
by C ′( X q ) = Pq . Profit on the quota purchase and resale ( Pq − P*) X * is returned to theconsumer. The general expression for welfare given in (22) is unaffected. To distinguish pooled

λ in general from its specific value of λT in the unrestricted un-COOL equilibrium, define:Zd + Z * λX d +λ* X *=λp = dX +X*
Xd + X *(A6)

Where superscript d denotes supply of Z or X from domestic sources and superscript * denotes
supply from imports. With the quota, Pq and λ p , must simultaneously satisfy:()

u′ λ X S ( Pq ) + Z * =Pq + (1 − λ p ) L

λp

(A7)

and

λ X S ( Pq ) + Z *λp = S
X ( Pq ) + ( Z * / λ*)(A8)Equations (A7) and (A8) define two relationships between λ p and Pq that must hold in
equilibrium. Each individually defines a relationship Pq ( λ p ) . It is straightforward to show bydifferentiation that for both (A7) and (A8), Pq ( λ p ) is upward sloping, raising the question ofwhether they intersect and the nature of that intersection. Note, however, that by choice of Z * ,( λ*, P *) satisfies (A7): From the unrestricted, un-COOL trade equilibrium, λ X S ( P *) = ZT ,ZT + Z * = Z C + Z C * and from the COOL trade equilibrium condition (17), it then follows( λ*, P *) satisfies (A7). In contrast, at P * , since λ X S ( P *) = ZT but Z * < ZT * , it follows that
λ p in (A8) corresponding to P * must exceed λT . Denote this value of λ p by λ p*8 . Since bothcurves are strictly upward sloping ( λ p*8 , P *) satisfying (A8) lies below (A7) at λ p*8 .

32

At λ p = λ , there is finite Pq that satisfies (A7): By selection of Z * and the fact ZT < Z C ,it follows that Z * + Z C > Z * + Z T = Z C + Z C * . The COOL market equilibrium implies at the
point ( λ , PC ) , the left-hand side of (A7) (equal to u ′( Z C + Z *) ) is less than the right-hand side
(equal to u ′( Z C + Z C *) ). At ( λ , P *) , the left-hand side of (A7) (greater than u ′( Z T + Z T *))exceeds the right-hand side (less than ( P * + (1 − λT ) L) / λT ) ). Hence, there exists P , P* < P < PCsuch that (λ, P ) satisfies (A7). Given Z * >0, there is no Pq that satisfies (A8) at λ p = λ . For(A8), Pq → ∞ as λ p → λ .
From: (a) Pq ( λ p ) strictly increasing for both (A7) and (A8); (b) ( λ p*8 , P *) satisfying (A8),()

but lying below (A7) at λ p*8 > λT ; (c) λ , P satisfying (A7) for P* < P < PC ; and (d) for (A8), ( λ , P ) , jointly satisfying (A7) and (A8) and

Pq → ∞ as λ p → λ , it follows there exists

p

q



characterized by λT < λ p < λ and P* < Pq < PC .

Letting WT and Wq 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 Z q denote domestic production of Z under the quota, and noting since P* < Pq , ZT < Z q
and by construction Z * < Z T * :
ZT

ZT

0

0

WT = M + ∫ u ′( Z )dZ − ∫ZT + ZT *∫ u′(Z )dZ − P *ZT + Z *

ZT

ZT

0

0

∫

ZT + Z *Zqu ′( Z )dZ − ∫

ZT

1

λ

λ

Z

C ′( )dZ − (1 − λ ) L

λ

ZT

λ

+

ZT + Z *

Z*

Z*

Z*

Z*

∫ u′(Z )dZ − P * λ * − (1 − λ*) L λ * +ZT( ZT * − Z *)( Z * − Z *)− (1 − λ *) L T
λ*λ*

Wq = M + ∫ u ′( Z )dZ − ∫Zq + Z *

1

1

λ

Z

C ′( )dZ − (1 − λ ) L

λ

ZT

λ

+

ZT + Z *∫ u′(Z )dZ − P * λ * − (1 − λ*) L λ * +ZT( Z q − ZT )Z
C ′( )dZ −(1 − λ ) L

λ

λ

33

The first seven terms in WT and Wq are identical. Combined, the last three terms of WT arestrictly negative since by selection of Z * , u ′( Z T + Z *) =P * + (1 − λ*) L
and u ′′ < 0 . Combined,
λ*the last three terms of Wq are positive. From the quota equilibrium,
Pq + (1 − λ p ) L Pq + (1 − λ ) Lu ′( Z q + Z *) =
>


λ

λp

and C ′(

Zq

λ

(A9)


) = Pq , the combined positive sign of the final three terms in Wq follow fromu ′′ < 0 and c ′′ > 0 . Hence Wq > WT .

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 ifdW> 0 . Similarly, assuming a market of only imports
dX * X *=0

would yield a non-corner solution, a corner solution defined by X d = 0 cannot be a maximum ifdW>0.
dX d X =0d

Suppose a critical point ( X d > 0, X * > 0 ) exists satisfying (23) and (24). Then, from theautarky solution compared with (23):λu ′(λX A ) − (1 − λ ) L − C ′( X A ) = 0

and

(B1)

λ u′(λ X d + λ * X *) − (1 − λ ) L − C ′( X d ) = 0
Since C ′′ > 0 and X * > 0 and u ′′ < 0 , X d < X A and u′(λ X d + λ * X *) < u ′(λ X A ). It then follows
from (24):

λ * u ′(λX A ) − (1 − λ*) L − P* > 0 ⇒dW> 0.
dX * X *=0

Let X * denote the level of imports that maximizes W given that X d = 0 . Again assume acritical point ( X d > 0, X * > 0 ) satisfying (23) and (24). Then34

C ′( X d ) + (1 − λ ) L

λ=P * + (1 − λ *) L
= u′(λ * X *) orλ*λ u′(λ * X *) − (1 − λ ) L − C ′( X d ) = 0
Since C ′( X d ) > C ′(0) , (B3) implies

(B2)
(B3)

dW
> 0 . Thus, if an interior maximum to W exists, itdX d X =0ddominates corner solutions.

35