International Trade with
Partial Equilibrium Models
and Optimization
Strategies:
A basic Approach
Master Économie et Affaires Internationales
Paris Dauphine -October 2006
Dr. Ramón Mahía
Professor of Applied Economics Department
www.uam.es/ramon.mahia
International Trade
with Partial
Equilibrium Models
and Optimization
Strategies:
A basic Approach
STRUCTURE OF DOCUMENT AND EXPOSITION
Basic elements for understanding Partial
Equilibrium Models

 Closed economy
Do we need optimization?
A break for introducing Excel Solver
 Open Economy
Basic concepts
Tradable / Non tradable Goods definition
Impact of trade measures: example of tariffs
A real example: Banana Market
International Trade
with Partial
Equilibrium Models
and Optimization
Strategies:
A basic Approach
STARTING POINT: CLOSED ECONOMY
Equilibrium with linear demand & supply curves
can be mathematically derived easily

70
New D
D Initial
60
New S
S Initial
40
30
20
10
Quantity
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
0
Price
50
International Trade with
Partial Equilibrium
Models and Optimization
Strategies:
A basic Approach
But it runs out to be very complex if linearity is lost
300
Supply
250
Demand
200
Prices

STARTING POINT: CLOSED ECONOMY
150
100
50
0
0
5
10
15
20
Quantity
25
30
35
International Trade with
Partial Equilibrium
Models and Optimization
Strategies:
A basic Approach
EXCEL SOLVER COMPLEMENT
The optimization problem should be written in an
Excel worksheet as it could be solved “by hand”
The basic elements of an optimization problem are:

Optimization function to maximize, minimize or
achieve an exact value
Parameters to move to achieve optimization
function objective
Restrictions to be taken into account
Options
for changing optimization algorithm
definition

International Trade with
Partial Equilibrium
Models and Optimization
Strategies:
A basic Approach
OPEN ECONOMY: BASIC DEFINITIONS
We will use Partial Equilibrium Model with three
assumptions:

Single product: with no substitutive items
Small country: When an economy opens, new
international trade is small enough to not change
international prices
Perfect
competition:
Domestic
prices
automatically move to converge to international
prices = financial parity prices

International Trade with
Partial Equilibrium
Models and Optimization
Strategies:
A basic Approach
OPEN ECONOMY: BASIC DEFINITIONS
When an economy opens, an alternative market
with a different price appears inducing a price
competition with domestic market.

For a meaningful comparison between international
market price and the domestic price received by
farmers, we must adjust the price of the product in
the international market. International prices thus
adjusted are called financial parity prices.

International Trade with
Partial Equilibrium
Models and Optimization
Strategies:
A basic Approach
OPEN ECONOMY: BASIC DEFINITIONS
We calculate the financial export
parity price by deducting from the
border price (FOB in this case) all
transport and marketing costs from the
farm to the port, any export taxes or
subsidies, and all local port charges
including taxes, storage, loading
agents' fees, etc., so as to be left with
the farm-gate price.

International Trade with
Partial Equilibrium
Models and Optimization
Strategies:
A basic Approach
OPEN ECONOMY: BASIC DEFINITIONS
FOB stands for FREE ON BOARD. It
is the cost of an export good at the exit
point in the exporting country loaded in
the ship or other means of transport in
which it will be carried to the importing
country. It is equal to the CIF price at
the port of destination minus the cost of
international freight and insurance and
the unloading onto the destination
dock.

International Trade with
Partial Equilibrium
Models and Optimization
Strategies:
A basic Approach
OPEN ECONOMY: BASIC DEFINITIONS
We calculate the financial import parity price by
first choosing a domestic wholesale reference
market, for instance the wholesale market of the
capital city, where imported goods are supposed to
enter into competition with locally produced
equivalent goods.
We then add to the border price (CIF in this case)
all port charges after the import touches the dock,
any domestic tariffs and other taxes or fees, duties
or subsidies, and the transport and marketing costs
from the port to the market of reference. If we further
want to obtain the import parity price at the farmgate, we subtract the transport and marketing costs
that farmers have to pay to put their produce in the
market of reference

International Trade with
Partial Equilibrium
Models and Optimization
Strategies:
A basic Approach
OPEN ECONOMY: BASIC DEFINITIONS
CIF stands for COST, INSURANCE AND
FREIGHT. It is the landed cost of an import
good on the dock or other entry point in the
receiving country. It includes the cost of
international freight and insurance and
usually also the cost of unloading onto the
dock. It excludes any charge after the import
touches the dock such as port charges,
handling and storage and agents' fees. It
also excludes any domestic tariffs and other
taxes or fees, duties or subsidies.

International Trade with
Partial Equilibrium
Models and Optimization
Strategies:
A basic Approach
OPEN ECONOMY: NON TRADABLE GOODS
Non tradable good: (1) the domestic price (Pd) is
higher than the financial export parity price (Pep), so
that exporting the good is not justified

Domestic wholesale reference market price
Transport farm - reference market
Domestic wholesale reference market price (at farm-gate)
$32,00
$1,50
$30,50
EXPORTS (for crops with NO industrial transformation)
Exporter-Border Price (FOB)
Transport Farmer-Port
Export Taxes
Export Subsidies to exporter (not to producer)
Exporter Port charges (taxes, storage, loading)
$34,00
$2,00
$1,00
$2,00
$1,00
Financial export parity price (at the farm-gate)
$28,00
International Trade with
Partial Equilibrium
Models and Optimization
Strategies:
A basic Approach
OPEN ECONOMY: NON TRADABLE GOODS
Non tradable good: (2) in addition the financial
import parity price of the good (pip) is higher than
the domestic price (Pd), and hence importing the
good is not justified

Domestic wholesale reference market price
Transport farm - reference market
Domestic wholesale reference market price (at farm-gate)
$32,00
$1,50
$30,50
IMPORTS (for crops with NO industrial transformation)
Border Price (CIF - €)
Nominal Exchange rate $/€
Border Price (CIF - $)
Domestic Tariff (ad valorem)
Other Taxes+Fees
Transport from Port to Reference Market
28,00 €
1,26
$35,28
5%
1%
$2,00
Financial import parity price (at the reference market)
Financial import parity price (at the farm-gate)
$39,40
$37,90
International Trade with
Partial Equilibrium
Models and Optimization
Strategies:
A basic Approach
OPEN ECONOMY: NON TRADABLE GOODS
Non tradable good: (1) the domestic price (Pd) is
higher than the financial export parity price (Pep)
and lower than financial export parity price (Pip)

70
60
D Initial
S Initial
Pep
Pip
40
30
20
10
Quantity
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
0
Price
50
International Trade with
Partial Equilibrium
Models and Optimization
Strategies:
A basic Approach
OPEN ECONOMY: EXPORTABLE GOODS
Exportable goods: The financial export parity price
"pep" is higher than the domestic price in the
absence of trade, and hence there is an incentive
for the good to be exported

Domestic wholesale reference market price
Transport farm - reference market
Domestic wholesale reference market price (at farm-gate)
$32,00
$1,50
$30,50
EXPORTS (for crops with NO industrial transformation)
Exporter-Border Price (FOB)
Transport Farmer-Port
Export Taxes
Export Subsidies to exporter (not to producer)
Exporter Port charges (taxes, storage, loading)
$45,00
$2,00
$1,00
$2,00
$1,00
Financial export parity price (at the farm-gate)
$39,00
International Trade with
Partial Equilibrium
Models and Optimization
Strategies:
A basic Approach
OPEN ECONOMY: EXPORTABLE GOODS
Exportable goods: The financial export parity price
“Pep" is higher than the domestic price

70
S Initial
D Initial
60
Pep
40
30
20
10
Quantity
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
0
Price
50
International Trade with
Partial Equilibrium
Models and Optimization
Strategies:
A basic Approach
OPEN ECONOMY: EXPORTABLE GOODS
Main effects before opening economy for an
exportable good:

Domestic demand price tends to rise up
to Pep so domestic demand is lower at
this new price and consumer surplus
reduces
Supply is higher at this prices
….going now to domestic and export
markets
Producers
gain more money and
producers surplus grows

International Trade with
Partial Equilibrium
Models and Optimization
Strategies:
A basic Approach
OPEN ECONOMY: IMPORTABLE GOODS
Importable goods: The financial import parity price
of the good IS LOWER than the domestic price, so
there is an incentive to import the good

Domestic wholesale reference market price
Transport farm - reference market
Domestic wholesale reference market price (at farm-gate)
$32,00
$1,50
$30,50
IMPORTS (for crops with NO industrial transformation)
Border Price (CIF - €)
Nominal Exchange rate $/€
Border Price (CIF - $)
Domestic Tariff (ad valorem)
Other Taxes+Fees
Transport from Port to Reference Market
18,00 €
1,26
$22,68
5%
1%
$2,00
Financial import parity price (at the reference market)
Financial import parity price (at the farm-gate)
$26,04
$24,54
International Trade with
Partial Equilibrium
Models and Optimization
Strategies:
A basic Approach
OPEN ECONOMY: IMPORTABLE GOODS
Importable goods: The financial import parity price
“Pip" is lower than the domestic price

70
S Initial
D Initial
60
Pip
40
30
20
10
Quantity
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
0
Price
50
International Trade with
Partial Equilibrium
Models and Optimization
Strategies:
A basic Approach
OPEN ECONOMY: IMPORTABLE GOODS
Main effects before opening economy for an
exportable good:

Consumers have an incentive to import at this
new price
…..so domestic supply price tend to fall down to
"Pip“
Demand is higher at this new and lower prices
Coming from domestic producers but also from
abroad
Domestic supply is lower at this new price
Producers lose some money
..but public revenues are collected from imports

International Trade with
Partial Equilibrium
Models and Optimization
Strategies:
A basic Approach
OPEN ECONOMY: IMPACT OF TRADE MEASSURES
Which is the effects of a tariff measure in an open
economy for an importable good?

We assume that the product is an importable
and we start from the previous situation of
equilibrium with trade and no protection. The
domestic price will be equal to the international
price Pw. Then a tariff “t” is introduced as a
percentage of the import value (ad-valorem
tariff).
The tariff will generate a series of reactions over
time from producers, consumers and traders
until a new equilibrium is reached in the
domestic market. Comparing the initial and final
situations the effects of the tariff are as follows

International Trade with
Partial Equilibrium
Models and Optimization
Strategies:
A basic Approach

OPEN ECONOMY: IMPORTABLE GOODS
Main effects of a tariff in an open economy:

Domestic Prices Increases
…...and therefore, consumers expenditures reduces
….. and consumption reduces in volume

Higher prices encourages producers to increase
their production

…… that replaces imported supply
…… reducing dependency on imports
…… and generating a rise in revenues of producers
…... and goverment

International Trade with
Partial Equilibrium
Models and Optimization
Strategies:
A basic Approach

OPEN ECONOMY: OPTIMIZATION SCHEME
Now, I porpoise an optimization problem:
Are we able to rise the tariff to restore the
initial situation of a closed economy?
Objective function: reduce to 0% dependency
on imports
Parameters to move: tariff level
Restrictions: none

International Trade with
Partial Equilibrium
Models and Optimization
Strategies:
A basic Approach

OPEN ECONOMY: OPTIMIZATION SCHEME
Further complexity:
Non linearity for every relation in the scheme
Non small country assumption
Non perfect competition
Importable and exportable good at the same
time
Different trade measures for import and export
and even “non measurable measures”
Matrixes: different countries, different CIF and
Fob prices, different transport costs,…etc
Market distortions: market power, dumping
strategies, ….

International Trade with
Partial Equilibrium
Models and Optimization
Strategies:
A basic Approach
REFERENCES
•(***) José María Caballero. Geraldo Calegar and Carlo Cappi.
2000. Instruments of Protection and their economic Impact.
Multilateral trade negotiations on agriculture a resource manual. FAO
•de Janvry, A. & Sadoulet, E. 1995. Quantitative Development Policy
Analysis. Baltimore and London, The John Hopkins University Press
•FAO. 1998. The Implications of Uruguay Round Agreement on
Agriculture for Developing countries - a Training Manual. Training
Materials for Agricultural Planning, No. 41. Rome.
•Gittinger, P J. 1982. Economic Analysis of Agricultural Projects.
Second Edition. Baltimore and London, John Hopkins University
Press.
•Josling, T. E., Tangermann, S. & Warley, T. K. 1996. Agriculture in
the GATT. London, Macmillan Press.
•Just, R., Hueth, D.L. & Schmitz, A. 1982. Applied Welfare
Economics and Public Policy. Prentice-Hall, N.J.
•Tsakok, I. 1990. Agricultural Price Policy: a Practitioner's Guide to
Partial Equilibrium Analysis. Ithaca, New York, Cornell University
Press.