We build a spatial equilibrium trade model for apples using demand and supply relations for each importing and exporting country. The model maximizes welfare subject to demand and production constraints. A trade barrier (free trade) scenario which incorporates (removes) import quotas and tariffs is run. Comparison of the solutions of the two scenarios quantifies the impacts of trade barriers on US apple exports.apples, spatial equilibrium model, trade barriers, International Relations/Trade, F10,

Devadoss, Stephen

Sreedharan, Prasanna

Stodick, Leroy

Wahl, Thomas I.

English

Research Papers in Economics

 
Effects of Trade Barriers on U.S. Apple Exports 
 
 
 
 
 
Prasanna Sreedharan 
Department of Agricultural and Resource Economics 
Washington State University 
 
 
 
Stephen Devadoss 
Department of Agricultural Economics 
University of Idaho 
 
 
Leroy Stodick 
Department of Agricultural Economics 
University of Idaho 
 
 
Thomas Wahl 
Department of Agricultural and Resource Economics 
Washington State University 
 
 
 
 
 
 
 
 
This paper is prepared for presentation at the annual meeting of the American Agricultural Economics 
Association, Montreal, Canada, July 27-30, 2003 
 
 
 
 
 
 
Copyright. By [authors] Authors reserve all copyrights of this paper. No part or a section of this paper can 
be reported without proper credit given to authors.   1
Effects of Trade Barriers on U.S. Apple Exports 
Prasanna Sreedharan 
Stephen Devodoss 
Leroy Stodick 
Thomas Wahl 
 
Abstract 
We build a spatial equilibrium trade model for apples using demand and supply relations for each 
importing and exporting country. The model maximizes welfare subject to demand and production 
constraints.  A trade barrier (free trade) scenario which incorporates (removes) import quotas and tariffs 
is run.  Comparison of the solutions of the two scenarios quantifies the impacts of trade barriers on US 
apple exports. 
 
Key Words: apples, spatial equilibrium model, trade barriers. 
JEL Classification: F10 
 
I. Introduction  
The United States is a major apple producing country. Owing to an oversupply in 
the domestic market, US apple growers have not been receiving remunerative prices. 
Exporting apples to other countries can solve this resulting market saturation. However, 
apple exports are far below the consumption potential in importing countries mainly due 
to high trade barriers. Tariffs range from a low of 15% in Venezuela to as high as 54% in 
Egypt and India. This implies that US apples cost about 1.5 times more in some countries 
even without accounting for transportation costs. Thus, US apple prices compare 
unfavorably with the locally grown apples. The dismantling or phasing out of these trade 
barriers will enable US apples to be competitive in foreign markets and thereby greatly  
increase US apple exports. In this paper we develop a trade model for the world apple 
market and quantify the impact of trade barriers on US apple exports. 
II. World Apple Trade and the Impediments to free Trade 
     2
World apple trade has steadily grown over the years with total value of world 
exports being over US$ 2.3 billion in 2000. The United States is an important player in 
the world apple market accounting for over 15% of world exports in value. US domestic 
apple consumption has been relatively stagnant compared to its production therefore 
making exports very crucial to the apple industry. High levels of tariff prevalence in 
many countries have severely impeded the trade of apples. There is a huge market for 
apples in countries like India where imports have increased from practically nothing to 
around 17000 tones in 2000. The important importing regions worldwide are Mexico, 
Africa, Middle Eastern countries and the Far East. Countries like Egypt, Korea, Thailand, 
Vietnam and India, all potential markets for US apple exports, impose very high import 
tariffs thereby effectively limiting domestic apple consumption in these countries way 
below potential demand. The elimination of trade barriers results in increase in net social 
welfare. It brings down prices in importing countries thereby making the product more 
affordable. It will also increase export price for US apple growers relieving them of the 
present price slump. Therefore, tariff reduction in apples is very consequential to US 
apple growers.  
III. Methodology 
            The method used in the paper is a spatial equilibrium trade model proposed by 
Takayama and Judge (1971). The model assumes perfect competition in all markets and 
involves maximizing the net social monetary gain function subject to a set of linear 
constraints. The net social monetary function is defined as the total social revenue minus 
the total social production cost minus total transportation cost.  The model assumes the 
existence of linear regional demand and supply relations, which are used to construct the  3
objective function. Under perfect competition and using the market equilibrium and 
arbitrage conditions, we derive the optimal solution to the quadratic programming 
problem. 
We assume that there are two or more regions indexed  j i, where  . ,.... 1 , n j i =  
trading in a single product and separated by a positive transportation cost. The following 
form of demand and supply relations for each region is assumed: 
                Demand:   i i i i y p ω λ − =  for all i , 
                Supply:     i i i
i x p η υ + =  for all i, 
             Where, 
     = i y  Quantity demanded in region i, 
              = i x  Quantity supplied in region i, 
              = i p  Demand price in region i, 
              =
i p  Supply price in region i, 
              &   i λ ,  i ω  and  i η  ≥  0  
We define  
             
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= Ω
n ω
ω
ω
.
.
2
1
           
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=
n
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η
η
η
.
.
2
1
 
                    
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=
n λ
λ
λ
λ
.
.
2
1
     and     
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=
n υ
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.
.
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  4
         Using these notations we have the set of demand and supply relations defined as 
  
Hx P
y P
x
y
+ =
Ω − =
υ
λ
 
Further we assume that the following two conditions are satisfied for each region: 
1.  The quantity demanded in each region is less than or equal to the quantity shipped 
into the region from all other regions I.e. 
                  i x y
n
j
ji i ∀ ≤ ∑
=1
 Where  ji x  represents a trade flow form  j to i  
      2.   The quantity supplied in each region is greater than or equal to the quantity    
            Shipped from the region to all other regions 
               i x x
n
j
ij i ∀ ≥ ∑
=1
 Where  ij x  represents a trade flow form i to  j  
                   These can be combined to be expressed as: 
                   
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
−
≥ 


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

x
y
X
G
G
x
y  
      and  
            , 0 ≥ y , 0 ≥ x 0 ≥ X  
         where                      
                    
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=
n y
y
y
y
.
.
2
1
,  
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=
n x
x
x
x
.
.
2
1
         
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
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=
nn
n
n
x
x
x
x
X
.
.
.
.
1
1
11
        and    5
                 
         
G
G
G
x
y =
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− − −
− − −
− − −
− − −
= 


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

1 . 1 1
1 . 1 1
1 . 1 1
1 . 1 1
1 1 1 1
. . . .
1 1 1 1
1 1 1 1
 
                                                                   ) 2 (
2 n n×  
Given this notation we formulate the problem maximizing net social monetary gain 
as:     
Find     ) , , ( ρ X Y that maximizes 
           
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−
−
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

−
ρ ρ
δ X
Y
X
Y
G E
G
E Q
T
C
T
T
T
0
0 0
0
0
 
     subject to  
           0
0
0 0
0
0
≤

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

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


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

−
−
−

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


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

−
ρ
δ X
Y
G E
G
E Q
T
C
T
T
 
      and    
T T T T X Y 0 ) ( ≥ ρ  
      where 
     





−
=
υ
λ
C       





=
x
y
Y         




Ω
=
H
Q   Constituting elements defined earlier 
  6
and 
       





=
x
y
ρ
ρ
ρ   , 



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







=
n
y
ρ
ρ
ρ
ρ
.
2
1
, 














=
n
x
ρ
ρ
ρ
ρ
.
2
1
, where   
  
i
i ρ ρ ,   are respectively the shadow demand and supply prices in region i 
    

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











=
nn
n
n
t
t
t
t
T
.
.
.
1
1
11
    
        where     ij t  represents the unit transportation cost between region i and  j  
G E ≡  , and 
              = δ G         

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

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

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−
−
+
+ +
1 . . .
. . . .
. . . .
. . . 1
) 1 /( 1 . . .
. . . .
. . . .
) 1 /( 1 . . ) 1 /( 1 1 11
nn
n
δ
δ δ
    
                                                         ) 2 (
2 n n×  
 Where     ij δ  is the ad-valorem tariff imposed by region  j  for imports from region i. 
The solution to this maximization problem satisfies the market equilibrium 
condition and the locational price equilibrium with ad valorem tariff condition.  We use  7
this problem formulation to solve for equilibrium prices and quantities. This specification 
enabled us to compute the competitive equilibrium prices, the quantities supplied and 
demanded, and the level of imports and exports for each country. We then conducted a 
free trade simulation by removing all the trade restrictions imposed by the importing 
countries. The comparison of the volume of trade and level of prices under the free trade 
scenario and the tariff regime allowed us to quantify the adverse impacts of trade barriers 
on the apple market. 
 
IV.Empirical Results 
Production, Demand and Price Data for 1971-2000 extracted from the Food and 
Agricultural Organization Database was used to estimate the linear demand and supply 
relations for 24 countries/regions. Countries with very little production/consumption were 
aggregated and demand and supply relations were derived for these aggregated regions. 
Prices in these regions were derived as a weighted average of the individual prices with 
the ratio of production/demand serving as the weights. All prices were converted to US$. 
Most data series showed strong autocorrelation and Weighted Least Squares Estimation 
was then carried out by transforming the data. Transportation prices were calculated by 
using the data from the Ocean Freight Rate Bulletins.  
Total apple trade in the free trade model is significantly greater than the baseline 
model. Imports increase in India, Rest of Asia, Rest of North and Central America and in 
Rest of Africa. US exports increase by about 8%. In the case of free trade India, Rest of 
Asia, Rest of North and Central America and Rest of Africa would all import more. This 
is reasonable given that all these countries have high tariff regimes and have very low  8
domestic production. India is a very big market for apples in the case of tariff reduction. 
There is a price drop of more than 15% in the free trade scenario resulting in a spurge in 
demand.  
V. Concluding Remarks 
  We built a spatial equilibrium model to assess the effect of trade barriers on US 
apple exports. The model identifies 24 countries/regions and used data covering 1971-
2000 to calculate equilibrium quantities and prices under the tariff regime and compare it 
with the results in a free trade scenario. The important findings were that apple trade 
increases significantly with the removal of tarrifs and resulted in an increase in US apple 
exports. A significant price drop in India identifies it as a potential market for US apples. 
The major importing countries/regions are Developing Africa, Mexico, Rest of North and 
Central America, India, and Rest of Asia. Removal of trade barriers increases net world 
welfare and is also very beneficial to US apple exporters.  
 
References 
Cramer, G. L., E. J. Wailes, and S. Shui. ￿Impacts of Liberalizing Trade in the World 
Rice Market.￿ American Journal of Agricultural Economics. 75 (February 1993): 219-
226. 
 
Takayama, T. and G. G. Judge. ￿Spatial Equilibrium and Quadratic Programming.￿ 
Journal of Farm Economics. 46 (February 1964): 67-93. 
 
Takayama, T. and G.G. Judge. Spatial and Temporal Price and Allocation Models. 
Amsterdam: North Holland Publishing, 1971. 
 
United States Department of Agriculture. Ocean Freight Rate Bulletin March 2003 
 
 

EFFECTS OF TRADE BARRIERS ON U.S. APPLE EXPORTS

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