2012 年度日本地域学会報告用レジメ
A Strategic Inspection Policy of a Food Importing Country in the Case
Where False Food is Mixed in the Imported Food
Madoka Okimoto

Makoto Tawada

Nagoya University
1. Introduction.
In the age of globalization, the transportation system of the world is becoming
well-developed and free trade is widely promoted, so that many products and resources areable to trade among many countries. This development affects particularly food trade. Many
types of food could not transfer from country to country to consume in past. But, nowadays
most types of food more or less can be consumed in every country thanks of the developmentof transportation system. However, by the rigorous trade activity of food, we have a number ofserious problems on food trade. The consciousness on safety food or healthy food differs fromcountry to country because of the difference in people’s life style. Then the norm on the qualityof food is different from country to country, which causes trouble between trading countries.
Another problem is that consumers usually cannot distinguish which food is produced bywhat production process. Some production processes may give damage to consumers who took
the food produced by those processes. And yet we cannot check the foreign factories. Thus, on
the one hand, we sometime face to a risk to take wrong importing food, bur the other hand,foreign food firm have an incentive to produce wrong food in order to reduce production cost.
In fact, a trouble of this kind appeared between Japan and China concerning toxic
dumplings made in China. A similar trouble is the trade of beef a part of which is made fromcows infected with BSE. The trade of chlorinated chickens and hormone beef also became aninternational trade dispute. Moreover, some chemical fertilizers are prohibited to use for
agricultural production in some countries but allowed in other countries. Thus, a country
taking a severe standard for chemical fertilizers tends to be nerves to the imports from acountry taking a lower standard. The international dispute concerning the geneticallymodified organisms is also in this category.
In our present paper, we investigate how the government of a food importing country deals
with this kind of risk and to promotes a sound food trade. In the case where food a part ofwhich is wrong is imported and consumers cannot recognize which is wrong at sight, theimporting government should take some policies to prevent people from having healthdamage by the consumption of wrong food. The foreign country’s firms compete with the firmsof the importing country, so that they tend to reduce the production cost by mixing wrong
production processes or using wrong materials. Thus the government of the importing country1has to take a policy of checking the quality of the imported food. On the other hand, theforeign firms determine the mixing level of wrong food according to how severe is thedetection policy of the importing country. Thus, we construct a model suitable for thegovernment of an importing country and the exporting firms to play a game with each other.
In this game we derive an equilibrium and investigate the properties of the equilibrium.
Concerning an aspect of illegal economic behavior, the analysis of illegal labor migration
has been explored deeply in many ways. However, our present supposition of the illegal
economic behavior that the foreign firms forge their exporting products has a quite different
aspect from the illegal migration. Illegal migrant workers are employed in firms and thosefirms usually distinguish who is an illegal migrant. In the case of illegal wrong food, however,consumers consume it without noticing that it is wrong food. There are a number of papers
analyzing an economic aspect of food trade. Among them, The analysis of Cardebat andCasaagnard(2010) is similar to ours. But, it focuses illegal production processes and thequality of the product is identical among all firms. Moreover, their model does not mature, sothat they failed to derive the equilibrium of the game properly. Thus, we construct a newmodel to investigate this topic.
2. ModelConsider an economy where countries A and B exist. In each country, there are perfectlycompetitive firms producing food. Consumers of food exist only in country A. Therefore, allamount of food produced in country B is exported to country A, and all amount of foodproduced in country A is domestically consumed.
All firms in country A have the same and constant returns to scale production technology
and produce the food of quality q

according to profit maximization. Then, assuming cAAtobe the constant marginal cost of the firms in country A, the profit each firm of the foodindustry in country A can be described as p x  c x , where xAfood produced in country A and pAAAAA

is the total amount ofis the price of food of country A. Hereafter, we call thefood produced in country A as food A.
Similarly, all firms in country B have the same and constant returns to scale
production technology and produce the food of quality qB

according to the profit

maximization. Hereafter, we call the food produced in country B as food B. Firms in country B
may mix false food into food B so as to reduce the production cost. Let the ratio of the amountof false food to the total amount of food be  . We assume that the marginal cost to produce
food B can be expressed as the function

c B  c B ( ) ,2

where c   0 and c   0 . Thus, the larger the mixed rate of the false food the lower theBBmarginal cost.
We turn our attention to the behavior of consumers in country A. Each consumer will buy
one unit of food when he wants to buy it. Each consumer’s preference to food is characterized
by a parameter  , where   [0,1] . We suppose that consumers are uniformly distributed
in [0,1] . A consumer of type  can obtain utility q by consuming one unit of food i , whereii  A, B . Thus the consumer surplus can be exhibited by

CS i ( )  q i  p i ,where CS ( ) is the consumer surplus of type  consuming one unit of food i . Notice that,
iif CS ( )  q  p  0 , the consumer does not buy food i .
iii

Now we place the following assumption.
Assumption 1.

qA  qB .

This assumption implies that food A is better in quality than food B. We also assume that eachconsumer can distinguish the country in which country the food is produced but no one canrecognize which food among food B is false. A consumer who consumed false food does nothave health damage in the short-run but does in the long-run. The consumer is assumed totake a myopic behavior by disregarding the long-run effect of false food.
Then, the conditions for the consumer of type  to purchase food A are

q A  p A  q B  p B andq A  p A  0 ,whose first inequality is rewritten aspA  pB.
qA  qB

We make another assumption.

Assumption 2.

pB pA
.
qB qAAssumption 2, together with Assumption 1, implies that the better the quality of food thehigher the price of its quality unit. Then we can illustrate a typical consumer distribution asin Figure 1, where consumers whose preference  are in [0, p / q ] do not demand for anyBBfood, consumers whose  are in ( p / q , ( p  p ) /( q  q )) demand for food B, andB

BA

3BAB

consumers whose  are in [( p  p ) /( q  q ),1] demand for food A.
ABA

BFigure 1

Finally, we consider the government behavior in country A. The government of country A
cares consumers’ health affected by the false food in the long-run. Therefore, the government
inspects the food imported from country B by taking some samples for examination. Let G
be an average cost for examination and  be a probability to detect the false food. Weassume  to be expressed by a function of G , that is    (G) where  G  0 and GG  0 .
Once the false food is detected, the government charges a fine Z to per unit of the false
food to the firms of country B. We assume that the aim of government A is to maximize thewelfare of country A. The welfare function of country A is written as1AAp / qBSW   (q A  p A )d   B

where A (q B  p B )d  (1   (G))x B B  x B G   (G) x B Z , (1)pB
1pA  pBBx
(A)
and.
BAB
q 1   (G) q q

The first and second terms of the RHS of the above welfare function mean the consumer
surplus obtained from the consumption of food A and food B, respectively. The third term isthe long-term health damage by the consumption of the false food, the forth term is the total
cost incurred by the inspection of false food and the last term is the government revenue fromthe fine imposed on the detected false food.
3. GameNow we are in a position to explain the game between the firms of country B and thegovernment of country A. The game is played by three stages. At first stage, the governmentof country A determines the budget for inspection on the false food in the imported food. At thesecond stage, under the circumstances where the budget scale G
4for inspection is given,

the firms of country B determine the mixed rate of the false food  and the government ofcountry A determines the level of fine Z . At the second stage, all players are assumed to movesimultaneously. At the third stage, the amounts of food A and food B are determined so as tosatisfy the demand condition. We solve this game by backward induction.

4. Results
At the second stage, we establish
Theorem 1
As the health damage by taking the false food is heavier, the mixed rate of the false food islower, the price of food B is higher and the level of fine imposed on the detected false food ishigher.
andTheorem 2As the budget for searching the false food increases, the mixed rate of the false food andthe price of food B becomes lower(higher) and higher(lower), respectively, under the condition
that the health damage caused by the false food is sufficiently small(large).
As for the full equilibrium, we have
Theorem 3

dp B d 0.
dG dG
Theorem 4
Suppose that the health damage by taking the false food becomes heavier. Then the mixed
rate of the false food is lower and the price of food B is higher. Moreover, the level of fine
imposed on the detected false food is lower if  is small enough or B is large enough.

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