Schmitz, Andrew

Schmitz, Troy G.

Seale, James L., Jr.

English

Research Papers in Economics

PBTC 02-6
TPTC 04-01 
 
THE OPTIMAL PROCESSOR TARIFF UNDER THE BYRD 
AMENDMENT 
 
By 
 
Andrew Schmitz, Troy Schmitz, and James Seale 
 
 
TPTC 04-01                        June 2004 
TECHNICAL PAPER SERIES 
 
 
 
 
 INTERNATIONAL AGRICULTURAL TRADE AND POLICY CENTER 
 
The International Agricultural Trade and Policy Center (IATPC) was established in 1990 
in the Food & Resource Economics Department (FRED) of the Institute of Food and 
Agricultural Sciences (IFAS) at the University of Florida. Its mission is to provide 
information, education, and research directed to immediate and long-term enhancement 
and sustainability of international trade and natural resource use. Its scope includes not 
only trade and related policy issues, but also agricultural, rural, resource, environmental, 
food, state, national and international policies, regulations, and issues that influence trade 
and development.  
 
The Center’s objectives are to: 
 
-  Support initiatives that enable a better understanding of U.S. and international 
trade policy issues impacting the competitiveness of Florida agriculture and all 
specialty crops and livestock nationwide; 
-  Serve as a nationwide resource base for research on international agricultural 
trade policy issues on all specialty crops and livestock; 
-  Disseminate agricultural trade related research results and publications; 
-  Interact with researchers, business and industry groups, state and federal agencies, 
and policymakers to examine and discuss agricultural trade policy questions. 
 
Programs in the IATPC have been organized around five key program areas. 
 
-  Risk Management and Capital Markets 
- Agricultural  Labor 
-  Regulatory Policy and Competitiveness 
-  Demand Systems and International Trade 
-  State and Local Government Policy and Agricultural Competitiveness. 
 
There are 10 faculty from the Food & Resource Economics Department who conduct 
research in these program areas for the IATPC. Each of these program areas has a set of 
projects that have been undertaken to address these critical areas of need. Faculty have 
acquired additional grant funds of more than one million dollars over the last three years 
to augment these programs. 
  
 
 
 
 
 
 
 
 
 The Optimal Processor Tariff Under the Byrd Amendment 
Andrew Schmitz, Troy Schmitz, and James Seale
*
I. Introduction 
The  Continued Dumping and Subsidy Offset Act (CDSOA) of 2000 allows 
producers and processors who successfully petition the U.S. government to impose 
antidumping (AD) or countervailing (CV) tariffs on competing imports to keep the 
proceeds of those tariffs.  This is referred to as the Byrd Amendment.  This paper 
develops the theory of the optimal processor tariff where processors gain as a result of 
keeping the revenue generated from tariffs, which is permissible under the Byrd 
Amendment. 
In this paper we draw on trade theory to develop an optimal AD tariff that 
maximizes profit from a processor’s point of view.
1  This optimal AD tariff represents the 
first-best situation for processors who successfully lobby for AD and CV tariffs against 
competing products from other countries under the CDSOA.  In this paper we show that a 
processor tariff not only enhances processor welfare, but also improves the welfare of the 
import competing producers. 
II. Model 
  The processor tariff is discussed with reference to Figure 1.  The excess supply 
curve for the exporter is given by ES.  The importer domestic supply schedule is Sd and 
demand is Dd.  The free trade price (absent of transport costs) is Pf.  Exports are given by 
                                                 
* Andrew Schmitz, Professor, University of Florida; Troy Schmitz, Associate Professor, Arizona State 
University; and James Seale, Professor, University of Florida. 
1 The optimal revenue tariff and optimal welfare tariff are well-known results from trade theory.  A detailed 
discussion of each tariff instrument can be found in Just, Hueth, and Schmitz (1982) and Schmitz and 
Schmitz (1994). 
 Q1.  (These are exports of the raw products since Dd is the derived demand schedule 
facing producers.) 
Now we impose processors who are involved in processing the raw product.   
Under free trade, they buy product Q1 from abroad at price Pf and, in addition, buy an 
amount q1 domestically at price Pf.  The total outlay for the raw product thus becomes 
  ( ) ( ) 1 1 q P Q P f f • + •   
 
 
Now, suppose processors are effective in lobbying for a tariff on the raw product 
of size T.  The processor now only imports Q2 at a price of pt.  The amount of tariff 
revenue collected by the government is p
thgpf*.  If the processor collects the tariff 
revenues under the Byrd Amendment, then the effective outlay on imports is ( ) 2
* Q Pf • .  
But note that due to the tariff, expenditures on the raw product by processors actually go 
up from ( ) 1 q Pf •  to  .  However, total expenditures by processors for both  ( 2 q P t • )
  2imports and domestic production actually decrease due to the tariff after the tariff revenue 
is rebated to the processors. 
  Note that rent seeking, on the part of processors to have tariffs imposed, also 
benefits domestic producers; hence they will not oppose tariffs.  Domestic producers 
receive the benefits of both high prices and expanded output.  From the processor tariff, 
producers of the raw product receive added rents of  .  c b p p f
t
  In the above discussion, we assume that processors are able to lobby the 
government to impose the optimal welfare tariff T.  This tariff is determined where Sd 
plus the marginal outlay curve Mo to ES crosses Dd.  But unlike standard analyses, the 
processors, rather than the government, collect the tariff revenue.  However, this is not 
the profit maximizing solution for the processor where the processing sector can exert 
both monopsony and monopoly power.  To incorporate monopoly power into the model, 
we construct the excess demand schedule ED and the corresponding marginal revenue 
schedule MR.  For a tariff of T
0, the processing sector reduces imports below Q2.  The 
tariff revenue rebated processors becomes  ⎟
⎠
⎞ ⎜
⎝
⎛ • ′
m f t q p P
* * .  Domestic producers become 
better off than under the optimal welfare tariff by an amount  ⎟
⎠
⎞ ⎜
⎝
⎛ ′ d c p P t t .  The optimal 
tariff for processors leads to a welfare improvement for domestic producers of the raw 
product over free trade.  As a result, lobbying efforts by processors for tariffs is 
strengthened by support from domestic producers of the raw product. 
  With international trade and the imposition of tariffs, the profit maximizing 
solution discussed above for the processor is different than in the case where tariffs do 
not exist.  In the extreme case, the processor would behave as a monopsonist in buying 
  3both from abroad and from the internal market.  Thus in equilibrium, the profit 
maximizing solution for the processor results in a single price being paid for the input 
(excluding transportation and handling costs), regardless of whether it is imported or 
produced domestically.  Note that this profit maximizing solution leads to greater profits 
and, in the case above, that tariffs are imposed on the importation of inputs. 
  Interestingly, in the optimal processor tariff case, the market power by the 
processor comes about through lobbying for tariffs.  With the Byrd Amendment, where 
the processor received the tariff revenue, the mechanism is put into place whereby the 
processor can behave noncompetitively through government tariff policy. 
  What is the optimal processor tariff?  The optimal processor tariff is given in 
Figure 2.  The exporter’s excess supply is Es and the importer’s demand and supply are 
Dd and Sd.  The free trade price is Pf. 
 
 
  4  Under imperfect competition, a “pure” multinational processor would behave as 
both a monopsonist and a monopolist in order to maximize profits.  The profit 
maximizing imports for the processor is qt for which the processor pays producers in the 
exporting country price Pp.  Producers in the importing country now receive a higher 
price of Pt, but consumers are also charged this higher price.  Export producers lose 
PpPf b´b, import consumers lose PtPf gh, domestic producers gain PtPf ec, and processors 
gain abPpPt. 
  In terms of the welfare of producers in the importing country, as the analysis 
shows, they clearly gain from a processor tariff.  However, their gains are less than the 
case where the producers negotiate an optimal Byrd Amendment tariff.  Using the 
analysis by Schmitz and Seale (2004), one can show that the optimal antidumping duty 
where producers receive the tariff revenue is higher than the optimal processor tariff 
derived in this paper.  As a result, producer prices are lower with the processor tariff, 
resulting in a smaller gain in producer surplus than under a producer tariff.  In addition, 
with the processor tariff, the producers do not get to keep the tariff revenue. 
 
III. Processor  Costs 
  Under standard tariff analysis where the government collects the tariff revenue, 
processors lose from tariffs.  In this case, the total value of imports purchased by the 
processor decreases under the tariff while the total value of the input purchased from 
domestic sources increases.  However, in aggregate, the per-unit cost of the input 
increases for the processor.  This is very different than in the case where the tariff 
revenue resides with the processor.  In this case, even though the total expenditures on 
  5imports decrease and expenditures on purchases from domestic producers increase, the 
per-unit cost for the processor falls.  The implications are discussed below.  
The cost structure assumed for the processing sector is given in Figure 3.  The 
demand for the processed product is given by D*.  Under free trade, the raw product price 
is p0 , and (  of the product is processed, given the cost curves ATC and MC.  
Under the processor tariff, the cost structure becomes 
) 1 1 q Q +
C AT ′and  because the price 
of its major input has fallen due to the tariff.  The amount processed now becomes 
.  The processors earn profits of the amount 
C M ′
( 2 2 q Q + ) ( ) ab c p 0 1 .  Consumers lose abe.   
 
The net gain or loss is  .  There would be a net gain if the processors 
lobbied for tariffs that were of the optimal welfare tariff nature. 
()( af c p bfe 0 0 − )
  From the previous analysis, processors and domestic import competing producers 
benefit from tariffs under the Byrd Amendment when the tariff revenue remains in the 
hands of the processors.  This is not the case, however, when tariff revenue is collected 
  6and becomes part of government revenue.  In this case, domestic producers prefer tariffs 
to free trade, but processors prefer free trade to tariffs.  With reference to Figure 3, if the 
tariff revenue remains in the hands of the government, the processor’s average total cost 
curve becomes ATC*, which above the free trade average total cost curve ATC.  When 
the tariff remains with the processor, the average total cost curve ATC´ lies below the 
free trade cost curve ATC. 
  Under the Byrd Amendment, there are incentives for processors and producers in 
the import competing country to form coalitions in favor of tariffs.  Even though in the 
case where the tariff revenue goes to processors, producers in the importing country are 
made better off than under free trade.  However, the incentive for coalitions would not 
exist where tariff proceeds go to governments, since processors lose from tariffs and 
primary producers win.  This is clearly illustrated in Figure 4.  Producer gains increase as 
the level of tariff increases regardless of whether or not the Byrd Amendment applies to 
processors.  Note that if the Byrd Amendment does apply, processors, after some tariff 
level, lose from heightening the tariff.  In the case where the tariff revenue goes to the 
government, processors prefer free trade, but producers do not. 
 
  7 
 
IV. Conclusion 
The above analysis assumes that processors and producers are separate entities.  
However, there are many real world cases where producers also own their own 
processing facilities.  In this case, not only do producers become better off from tariffs 
under the Byrd Amendment, but they also gain from the processing part of their 
businesses.  In this case, joint rent seeking for tariffs would be done by the industry 
where processors and producers are vertically and horizontally integrated.  Even if 
producers are separate from processors, our paper shows that rent-seeking, by processors 
for tariffs, would be supported by the import-competing producers of the raw product. 
 
  8References 
Just, R.E., D.L. Hueth, and A. Schmitz. (1982). Applied Welfare Economics and Public 
Policy. Ingle Cliffs, NJ: Prentice-Hall, Inc. 
Schmitz, A. and T.G. Schmitz. (1994). “Tariffs and Trade.” Chapter 6, in the 
Encyclopaedia of Agricultural Sciences, volume 4. San Diego, CA: Academic 
Press, Inc. 
Schmitz, T.G. and A. Schmitz. (2003). “Food Supply Management and Tariffication: A 
Game Theoretic Approach.” Journal of Agriculture and Food Industrial 
Organization 1(1): 1–19. 
Schmitz, Troy G. and James L. Seale, Jr. (2004) “Antidumping Duties and The Byrd 
Amendment.”  Working Paper, School of Agribusiness, Arizona State University, 
Tempe, AZ. 
WTO (World Trade Organization). (2002). “United States - Continued Dumping and 
Subsidy Offset Act of 2000” Second Panel Hearing: Oral Statement by Australia 
(WT/DS217 and WT/DS234). Geneva, Switzerland (March). 
 
 
  9

The Optimal Processor Tariff Under the Byrd Amendment

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