OPTIMIZATION EXERCISE
Prof. Dr. Ramón Mahía
Paris Dauphine – Master EAI
November 2008
1. Introduction
The Excel file “Optimization Questions.xls” contains the information that you will need for your
homework. This Excel book contains just one worksheet, “Trade Instruments _Tariff”, with all
the numerical information that you need for understanding 3 different scenarios:

Scenario 1.- Equilibrium for a closed Economy.
Domestic products are not in competition with international tradable goods, so Demand
and Supply Curves (Range B5:H6) define a domestic equilibrium that is defined by a
simple Wholesale Reference Market Price (Pd) and an equal volume of demand and
supply (Range B8:I11).

Scenario 2.- Equilibrium in an opened economy for an importable good in the
absence of tariffs.
Economy opens, and the International Parity Prices (Pip) for a given importable good
turns out to be lower than the Domestic Price (Pd) (calculations for this “Pip” in this
scenario 2 can be found in column “J” of range B28:J46).
The graph in range B53:K73 illustrate this new situation. The consequences on prices
and demand or supply volumes in this new scenario are summarized in range K76:K85
and can be easily compared with the starting point of a closed economy (closed
economy equilibrium is defined in range J76:J85 and comparison with an open
economy without tariff can be observed in N76:N85)

Scenario 3.- Equilibrium for an opened economy for an importable good WITH an
import tariff.
An Open Economy with a given importable good (Pip < Pd) impose a tariff on imports.
This tariff increases the value of the international Parity Import Price (calculations for
this new “Pip” in this scenario 3 can be found in column “K” of range B28:K46).
The graph in range L53:R73 illustrate this new situation. The consequences in prices
and demand or supply volumes in this new scenario are summarized in range L76:L85
and can be easily compared with the starting point of an open economy without tariff
and versus a closed economy (comparison between this Scenario 3 Vs an open
economy without tariff can be observed in range O76:O85, and comparison with an
open economy are summarized in range P76:P85 ).
2. Questions
Considering the information given above, try to answer the next questions:
1. For a given economy, total welfare can be computed as the sum of Consumer Surplus,
Producers Surplus, and Sate Revenues. Try to measure these 4 values in the three
different scenarios and make a brief comment on the distributions and changes implied in
the different situations.
2. Sometimes, trade administrator decisions decide to impose such a high tariff that imports
turn out to be prohibitive. Simulate, using Solver, which is the Level of this prohibitive tariff
in the Scenario 3. For a proper simulation, be sure that you use an starting value of
the tariff of 0% (instead of the default 20%) before running solver1. Make a brief
comment on the results.
3. Simulate, using Solver, the Level of the tariff in the Scenario 3 that maximizes tariff
government revenues. (Once again, and for a proper simulation, be sure that you use an
starting value of the tariff of 0% before running solver). Make a brief comment of the results.
4. A Quota Import is a trade instrument of protection consisting in the imposition of a limit
(quota) in the quantity of imports allowed for a given product. Quota systems used to be
common, but WTO uses to force the countries to remove their existing quotas and convert
them to tariff only systems (this process is called “tariffication” of a quota).
4.1. Taking this definition into account, and starting from an open economy scenario
(Scenario 2), try to compute the tariff level that is equivalent to a quota volume of 3
units. Make a brief comment of the results.
4.2. Do you find any difference, in terms of the distribution and total level of the economic
welfare, between a given quota and its equivalent tariff.
5. An economy placed in Scenario 2 is usually called a “net importer” for the considered good;
that is, the imports of the good are higher than the domestic supply. Apart from tariffs, a
different “trade intervention” measure consists in policy measures to support domestic
producers. This kind of measures (input subsidies, for example) helps producers to supply
more at the same price inducing them to be more competitive with international trade.
Taking these definitions into account, and Starting in Scenario 2:
5.1. Try to simulate a production subsidy in a way that the country turns into a selfdependency country. According to the results of the simulation, try to compute the
subsidy per unit of production paid by the state. Make a brief comment on the results.
6. Explore and make a brief comment of the differences obtained in your simulations
comparing the three trade measures ((1) tariff, (2) quota and (3) supply subsidy).
7. Given the fact that a subsidy measure is completely paid by the state and NOT by the
consumers (they still consuming the same and paying the same price for consumption that
in Scenario (2)), try to arrange a cheaper policy measure for the government….. ok I will
give you a clue: what about increasing taxes on consumption in a way that permits the
government to obtain the money for paying the subsidy?.
3. Job to Do and Deadline




1
Every student must present an individual work.
Every student must write down a Word document containing the obtained results and
comments. No excel file is required if the Word document encloses the main results and
comments.
The documents should be sent to ramon.mahia@uam.es with a clear identification of
the author in the subject of the e-mail and in the first sheet of the document.
The documents must be sent BY the end of November.
The starting value can affect solver algorithm.