Post on 20-Sep-2020
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Optimum Tariff and Finite Sequential Trade War Final Project of ECON 567
Xin Chen
Spring, 2014
Introduction This purpose of this project is to demonstrate the effect of unilateral optimum tariff and a
simulation of finite sequential tariff war under a two country two product HOS (Heckscher-Ohlin-
Samuelson) model using GAMS. The simulation of the tariff war evaluated symmetric and asymmetric
setting of trading countries. It also studied the existence of first mover advantage in such tariff war. This
model adapted from "two country version of the HOS model with trade taxes", as described in Chapter 19
of Gilbert and Tower: Introduction to Numerical Simulation for Trade Theory and Policy.
Outlines
Part I 1. Solve the initial model of two countries with no tariff
2. Solve the optimal US import tariff to maximize US utility, given no tariff of UK
3. Lerner Symmetry Theorem - Solve the optimal US export tax/subsidy to maximize US utility,
given no tariff of UK
4. Lerner Neutrality Theorem - US sets both import and export taxes at 10%, given no tariff of UK
5. Factor price equalization theorem
6. Stolper-Samuelson Theorem - Plot US Import Tariff on Beer(T) vs. Utility(U), Consumptions(C),
Export(X) and Production(Q), Given Zero Tax in UK
7. Sensitivity Analysis on
a. Beta ('Auto','US')
b. FBAR (‘K’,’US’) (US Capital Endowment).
Part II Simulate a retaliatory trade war between US and UK, with each country imposing optimal trade taxes in
turn.
8. Finite Sequential Trade War (US moves in odd periods, UK moves in even periods)
a. US starts first, set the optimal tariff, given UK tax fixed.
b. UK then sets its optimal tariff, given US tariff rate from previous step.
c. Repeat for 10 rounds
9. Finite Sequential Trade War (US moves in odd periods, UK moves in even periods, adjustment of
share parameters in utility of US)
2
10. Finite Sequential Trade War (US moves in odd periods, UK moves in even periods, adjustment of
share parameters in utility of US)
11. Finite Sequential Trade War (UK moves in odd periods, US moves in even periods, adjustment of
share parameters in utility of US)
Model The model employed in this paper is the two country version of the HOS (Heckscher-Ohlin-
Samuelson) model with trade taxes.
In this model, we have two countries, US and UK. Each produces two goods, auto and beer, using
identical CES production function. Auto is capital intensive and beer is labor intensive. US has relatively
higher ratio of capital to labor.
Assumptions
1. Endowment factors
2. Flexible factor prices
3. Flexible exchange rate
4. Production function with constant elasticity of technological substitution(CES)
Sets J = {K, L}
I = {Auto, Beer}
D = {US, UK}
3
Table 1. Parameters
Description Notation Initial Value
Shift parameter in utility 𝜶𝒅 US = 2
UK = 2
Share parameter in utility
𝜷𝒊𝒅 Auto.US = 0.5
Auto.UK = 0.5
Beer.US = 0.5
Beer.UK = 0.5
Initial domestic prices 𝑷𝑶𝒊𝒅 1
Initial world prices 𝑷𝑾𝑶𝒊 1
Initial trade
𝑿𝑶𝒊𝒅∗ (𝑋𝑂𝑖𝑑 = 𝑄𝑂𝑖𝑑 − 𝐶𝑂𝑖𝑑)
Auto.US = 62.5
Auto.UK = -62.5
Beer.US = -62.5
Beer.UK = 62.5
Initial utility levels 𝑼𝑶𝒊𝒅 US = 275
UK = 275
Initial consumption levels 𝑪𝒊𝒅 137.5
Shift parameters in production
𝜸𝒊𝒅 Auto.US = 1.676
Auto.UK = 1.676
Beer.US = 1.676
Beer.UK = 1.676
Share parameters in production
𝜹𝒋𝒊𝒅 K.Auto.US = 0.777
K.Auto.UK = 0.777
K.Beer.US = 0.223
K.Beer.UK = 0.223
L.Auto.US = 0.223
L.Auto.UK = 0.223
L.Beer.US = 0.777
L.Beer.UK = 0.777
Elasticity parameters in production 𝝆𝒊𝒅 0.1
Factor Endowments
�̅�𝒋𝒅 K.US = 175
K.UK = 100
L.US = 100
L.UK = 175
Initial output levels
𝑸𝑶𝒊𝒅 Auto.US = 200
Auto.UK = 75
Beer.US = 75
Beer.UK = 200
Initial factor prices 𝑹𝑶𝒊𝒅 1
Initial factor use levels
𝑭𝑶𝒋𝒊𝒅 K.Auto.US = 160
K.Auto.UK = 60
K.Beer.US = 15
K.Beer.UK = 40
L.Auto.US = 40
L.Auto.UK = 15
L.Beer.US = 60
L.Beer.UK = 160
Initial GDP 𝑮𝑫𝑷𝑶𝒅 US = 275
UK = 275
4
Table 2. Variables
Description Notation Numbers
Utility Indices 𝑼𝒊 2
Tax on import/export 𝑻𝒊𝒅 3+1
Prices 𝑷𝒊𝒅 4
Consumption Levels 𝑪𝒊𝒅 4
Output Levels 𝑸𝒊𝒅 4
Factor Prices 𝑹𝒋𝒅 4
Factor Use Level 𝑭𝒋𝒊𝒅 8
World Prices 𝑷𝑾𝒊 2
Trade Levels 𝑿𝒊𝒅 4
Gross Domestic Product 𝑮𝑫𝑷𝒅 2
Note: Variables in red are endogenous.
Table 3. Equations
Description Equation #
Utility functions 𝑈𝑑 = 𝛼 ∏ 𝐶𝑖
𝛽𝑖𝑑
∀𝑖∈𝑰
∀𝑑 ∈ 𝑫 2
Demand functions 𝐶𝑖𝑑 =
𝛽𝑖𝑑 𝐺𝐷𝑃𝑑
𝑝𝑖,𝑑 ∀ 𝑖 ∈ 𝑰, ∀ 𝑑 ∈ 𝑫 4
Open economy
material balance
𝑋𝑖𝑑 = 𝑄𝑖𝑑 − 𝐶𝑖𝑑 ∀ 𝑖 ∈ 𝑰, ∀ 𝑑 ∈ 𝑫 4
International market
clearing
∑ 𝑋𝑖𝑑 = 0
∀𝑑∈𝑫
∀ 𝑖 ∈ 𝑰 2
International price
arbitrage
𝑃𝑖𝑑 = (1 + 𝑇𝑖𝑑) 𝑃𝑊𝑖 ∀ 𝑖 ∈ 𝑰, ∀ 𝑑 ∈ 𝑫 4
Production functions
𝑄𝑖𝑑 = 𝛾𝑖𝑑 [ ∑ 𝛿𝑗𝑖𝑑𝐹𝑗𝑖𝑑𝜌𝑖𝑑
∀𝑗∈𝑱
]
1𝜌𝑖𝑑
∀ 𝑖 ∈ 𝑰, ∀ 𝑑 ∈ 𝑫
(e.g. 𝑄 = 𝛾[𝛿𝐾𝜌 + (1 − 𝛿)𝐿𝜌]1
𝜌)
4
Resource constraints
𝐹𝑗𝑑̅̅ ̅̅ = ∑ 𝐹𝑗𝑖𝑑
∀𝑖∈𝑰
∀ 𝑗 ∈ 𝑱, ∀ 𝑑 ∈ 𝑫
(e.g. 𝐾𝑈𝑆 = 𝐾𝐴𝑢𝑡𝑜,𝑈𝑆 + 𝐾𝐵𝑒𝑒𝑟,𝑈𝑆)
4
5
Factor demand
functions
𝑅𝑗𝑖𝑑 = 𝑃𝑖𝑑𝑄𝑖𝑑 [ ∑ 𝛿𝑗𝑖𝑑𝐹𝑗𝑖𝑑𝜌𝑖𝑑
∀𝑗∈𝑱
]
−1
𝛿𝑗𝑖𝑑𝐹𝑗𝑖𝑑𝜌𝑖𝑑−1
∀ 𝑗 ∈ 𝑱, ∀ 𝑖 ∈ 𝑰, ∀ 𝑑 ∈ 𝑫
8
Gross domestic
products
𝐺𝐷𝑃𝑑 = ∑ 𝑃𝑖𝑑𝑄𝑖𝑑
∀𝑖∈𝑰
− ∑ 𝑃𝑊𝑖 𝑇𝑖𝑑 𝑋𝑖𝑑
∀𝑖∈𝑰
∀ 𝑑 ∈ 𝑫 2
Given our equations of open economy material balance, X(I) is defined such that exports are
positive and imports are negative. Consumer and firm behavior in response to domestic prices is reflected
by demand and consumption functions.
In the original model, both countries share the identical production function and utility function.
The utility function is in Cobb-Douglas form with sum of exponents equaling to one. The share
parameters in utility functions are all equal to 0.5, which means that autos and beers each take half of the
total expenditure for both countries. The production function has constant elasticity of substitution. The
CES function has a elasticity parameter 𝜌 equals 0.1, while the elasticity of substitution equals 1/(1 − 𝜌).
The function converges to the Cobb-Douglas case as 𝜌 → 0, is linear when 𝜌 = 1 and approaches the
Leontief (min) function as 𝜌 → −∞. So the initial value of 𝜌 = 0.1 is more close to a Cobb-Douglas
form.
The only difference between the two countries is their factor endowments. The ratio of capital to
labor for US is reciprocal of that for UK. The sums of K and L for both countries are the same. In other
words, this is a symmetric model of two countries with same size. Later on in this paper, we will modify
some parameters and the size of the countries to conduct sensitivity analysis and simulation of sequential
tariff war.
Results
Part I
The results of scenario 1-5 are shown in table 4 and 5. Table 4 shows the results of optimal tariffs
and demonstration of Lerner Symmetry Theorem. Table 5 illustrates factor price equalization theorem.
Each scenario is shown in a column highlighted with different color. Rows correspond to specific
variables. Variables, such as T, have more than one dimension (country and good). So the values are
6
shown in a matrix with country labeled horizontally and other dimension vertically. Cells with missing
value in T section represent zero tariff.
In scenario 1, we can see a symmetry results with identical utility and consumption level under
free trade. The utility is 275 for both countries. US exports autos and UK exports beers. In our model, US
endows relatively more capital and UK endows more labor. Auto is capital intensive and beer is labor
intensive. This is consistent with Heckscher-Ohlin Theorem which states that if tastes are identical and
homothetic in the two countries, each country will export the commodity which uses intensively the factor
with which it is relatively well endowed.
Scenario 2 and 3 evaluates the optimal tariff and export tax for US to maximize its utility, given
free trade in UK. We can see that both import tariff and export tax can achieve same level of utility for
US. US has higher utility level (from 275 to 278.24) after it imposing optimal tariff/subsidy at the
expense of UK’s welfare (from 275 to 269.58). This demonstrates the Lerner Symmetry Theorem which
says that an across-the-board import tariff is identical to an across-the-board export tariff assuming that
the exchange rate always adjusts to maintain balance of payments equilibrium, and no individual holds
any assets in the other country. The joint utility of both countries, however, drops after the tariff (from
550 to 547.82). This shows that a unilateral optimal tariff is not the best way to transfer wealth.
Transferring purchasing power by cash while maintain free trade is a better way in such transfer problem.
Scenario 4 simply shows that Lerner Neutrality Theorem holds in such two country general
equilibrium model. In this scenario, US imposes 10% import tariff and 10% export tax. Comparing
scenario 1, we can see that the only differences are the values in red. Notice domestic good prices and
factor prices in US increase 10% while all real variables hold constant. This is consistent with Lerner
Neutrality Theorem which states that a tariff on all imports combined with an identical subsidy on all
exports will have no economic impact. The increasing in prices are due to the exchange rate adjustment.
Relative prices, however, do not change. GDPs are calculated based on domestic prices, so US’s GDP
increases 10% while UK’s remains constant.
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Table 4. Results of Evaluation of Optimal Tariff
Variables
1. No Tariff 2. US Opt.
Tariff
3. US Opt.
Export Tax
4.Lerner
Neutrality
US UK US UK US UK US UK
U 275 275 278.24 269.58 278.24 269.58 275 275
US UK US UK US UK US UK
T Auto -0.19 0.1
Beer 0.23 0.1
US UK US UK US UK US UK
P Auto 1 1 1.00 1.00 0.81 1.00 1.1 1
Beer 1 1 1.11 0.90 0.90 0.90 1.1 1
US UK US UK US UK US UK
C Auto 137.5 137.5 146.49 127.94 146.49 127.94 137.5 137.5
Beer 137.5 137.5 132.12 142.01 132.12 142.01 137.5 137.5
US UK US UK US UK US UK
Q Auto 200 75 185.79 88.64 185.79 88.64 200 75
Beer 75 200 88.50 185.63 88.50 185.63 75 200
US UK US UK US UK US UK
R K 1 1 0.97 1.04 0.79 1.04 1.1 1
L 1 1 1.15 0.87 0.93 0.87 1.1 1
US UK US UK US UK US UK
F
K Auto 160 60 154.38 68.20 154.38 68.20 160 60
K Beer 15 40 20.62 31.80 20.62 31.80 15 40
L Auto 40 15 31.88 20.69 31.88 20.69 40 15
L Beer 60 160 68.12 154.31 68.12 154.31 60 160
Auto Beer Auto Beer Auto Beer Auto Beer
PW 1 1 1.00 0.90 1.00 0.90 1 1
US UK US UK US UK US UK
X Auto 62.5 -62.5 39.29 -39.29 39.29 -39.29 62.5 -62.5
Beer -62.5 62.5 -43.62 43.62 -43.62 43.62 -62.5 62.5
US UK US UK US UK US UK
GDP 275 275 292.99 255.87 238.04 255.87 302.5 275
Table 5 shows that the factor price equalization theorem holds in such model setting. Scenario 1
is listed here for comparison. The theorem relies on the assumption that there exists free international
trade, 2 factors of production, 2 goods, identical production functions in both countries, only one
diversification cone at equilibrium prices, and neither country is specialized. If these assumptions hold,
then factor prices will be equalized absolutely worldwide.
Given the assumptions hold, the first case in scenario 5 has the results which are consistent with
factor price equalization theorem. In this case, the US endowment of capital changes from 175 to 100.
8
Other settings are the same as initial. The results indicate that the capital prices rise in both countries from
1 to 1.06, and labor prices drops from 1 to 0.79. The relative prices change is due to the decrease of
aggregate capital endowment so that the relative scarcity of capital raise its price. Also notice that US
now becomes smaller in terms of the endowment size, so its optimal utility under free trade becomes
smaller. UK, on the other hand, also suffers because the relative price of beer drops as a consequence of
the capital shrink. Notice that although the relative factor price changes, the factor prices are equal
between two countries. So the factor equalization theorem is preserved in this case.
In the second case of scenario 5, the factor of elasticity of substitution in production become
0.00001 in both countries, which means the production function is almost Cobb-Douglas. The US capital
endowment becomes 9999 and US labor endowment becomes 10. Under such setting, the factor price
equalization theorem no longer holds. The factor prices between two countries are no longer equal. A
speculation is that this setting has more than one diversification cone at equilibrium prices, so that the
assumptions of the theorem are no longer supported.
9
Table 5. Demonstration of factor price equalization theorem
Variables 1. No Tariff 5. Factor Price Equalization Theorem
US UK US UK US UK
U 275 275 202.37 267.06 701.26 568.02
US UK US UK US UK
T Auto
Beer
US UK US UK US UK
P Auto 1 1 1.00 1.00 1.00 1.00
Beer 1 1 0.84 0.84 1.34 1.34
US UK US UK US UK
C Auto 137.5 137.5 92.55 122.14 237.52 171.46
Beer 137.5 137.5 110.63 145.99 191.24 125.18
US UK US UK US UK
Q Auto 200 75 116.95 97.74 375.33 33.66
Beer 75 200 81.46 175.15 74.47 241.95
US UK US UK US UK
R K 1 1 1.06 1.06 0.45 0.89
L 1 1 0.79 0.79 4.05 1.45
US UK US UK US UK
F
K Auto 160 60 87.50 73.13 387.58 33.66
K Beer 15 40 12.50 26.87 28.13 66.34
L Auto 40 15 30.44 25.44 11.33
L Beer 60 160 69.56 149.56 8.42 175.61
Auto Beer Auto Beer Auto Beer
PW 1 1 1.00 0.84 1.00 1.34
US UK US UK US UK
X Auto 62.5 -62.5 24.40 -24.40 137.81 -137.81
Beer -62.5 62.5 -29.16 29.16 -116.77 116.77
US UK US UK US UK
GDP 275 275 185.11 244.28 475.05 342.93
Initial Factor
Endowment:
K.US = 175
K.UK = 100
L.US = 100
L.UK = 175
Factor Endowment:
K.US = 100
K.UK = 100
L.US = 100
L.UK = 175
RHO(I,D)=0.00001
Factor
Endowment:
K.US = 9999
K.UK = 100
L.US = 10
L.UK = 200
In the following five graphs, we plot US utility, consumptions, productions and trade volumes to
see the effect of US tariff rate on these variables, given free trade in UK. We can see that the utility curve
is concave and the optimal tariff rate which maximize utility is around 0.23, which is consistent with the
10
value in scenario 1 of table 4. As US tariff of beer become higher, the US relative prices of beer to autos
rises. As a result, the US beer consumptions drops and auto consumptions rises. We also notice that the
US price of K drops and price of L rises. This result is consistent with Stopler-Samuelson Theorem which
predicts that assuming a country is not specialized, an increase in the relative price of a good
unambiguously raises the real reward of the factor used intensively in producing that commodity and
lowers the real reward of the other factor. In our case, rising beer price rewards the labor as price of L
rises and punish the capitalist.
260
265
270
275
280
0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1
US IMPORT TARIFF ON BEER
US UTILITY
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1
US IMPORT TARIFF ON BEER
US GOOD AND FACTOR PRICES
US Auto Price US Beer Price US Price of K US Price of L
11
Sensitivity Analysis
We conducted two sensitivity analysis on auto share parameter of US utility Beta('Auto','US') and
US capital endowment FBAR(‘K’, ‘US’). In both studies, US sets optimal tariff to maximize its utility
while UK is under free trade.
50
70
90
110
130
150
170
190
0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1
US PRODUCTIONS AND CONSUMPTIONS
US Auto Consumption US Beer Consumption
US Auto Production US Beer Production
-80
-60
-40
-20
0
20
40
60
80
0 0 . 2 0 . 4 0 . 6 0 . 8 1 1 . 2
US IMPORT TARIFF ON BEER
TRADE VOLUMN
US Beer Import US Auto Import
12
The following four graphs are results of sensitivity analysis on auto share parameter of US utility,
Beta('Auto','US'). The utility function is in Cobb-Douglas form, so higher Beta('Auto','US') represents
higher proportion of the expenditure on auto consumption. We plot the endogenous variables with
Beta('Auto','US') from 0.3 to 1. Keep in mind that the initial value of Beta('Auto','US') in our original
model is 0.5.
Notice that US utility is a convex function of Beta('Auto','US'). The minimum is at around
Beta('Auto','US') = 0.45. As US has larger share of expenditure on autos, it consumes more autos and less
beers, so both its import and export decrease. Beer relative price decreases as a respond to the lower
demand, and US produces more auto and less beer accordingly. UK’s utility slightly goes down with the
increasing of Beta('Auto','US').
250
300
350
400
450
500
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
BETA('BEER','US')
UTILITY
US Utility UK Utility
-0.2
0.3
0.8
1.3
0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1BETA('BEER','US')
TARIFF AND PRICES
T* US Auto Price US Beer Price
13
The second sensitivity analysis is on US capital endowment FBAR(‘K’, ‘US’). We plot the effect
of US capital endowment growth on endogenous variables. The results show that both US and UK benefit
from such capital expansion, but US is significantly better off. US beer production remains relatively
constant while its production of auto booms. The US relative price of beer grows significantly, which is
due to the expansion on auto production. It is not a surprise that US price of K drops while US price of
labor increases due to the relative scarcity of labor. An interesting result is that the US optimal tariff
0
50
100
150
200
250
300
0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1
BETA('BEER','US')
CONSUMPTION AND PRODUCTION
US Auto Consumption US Beer Consumption
US Auto Production US Beer Production
-80
-60
-40
-20
0
20
40
60
80
0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1
BETA('BEER','US')
TRADE VOLUMN
US Beer Import US Auto Import
14
revenue does not rise as fast as its utility increases, because most of its gain on utility comes from the
increasing consumption on autos rather than tariff revenue and growth of consumption on beer.
250
270
290
310
330
350
370
390
1 7 0 1 9 0 2 1 0 2 3 0 2 5 0 2 7 0 2 9 0 3 1 0
US K ENDOWMENT
UTILITY
US Utility UK Utility
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1 7 0 1 9 0 2 1 0 2 3 0 2 5 0 2 7 0 2 9 0 3 1 0
US K ENDOWMENT
PRICES OF GOODS AND FACTORS
US Auto Price US Beer Price US Price of K US Price of L
15
0
50
100
150
200
250
300
350
1 7 0 1 9 0 2 1 0 2 3 0 2 5 0 2 7 0 2 9 0 3 1 0
US K ENDOWMENT
US PRODUCTION AND CONSUMPTION
US Auto Consumption US Beer Consumption
US Auto Production US Beer Production
-80
-60
-40
-20
0
20
40
60
80
1 7 0 1 9 0 2 1 0 2 3 0 2 5 0 2 7 0 2 9 0 3 1 0
US K ENDOWMENT
US IMPORTS
US Beer Import US Auto Import
16
Part II Finite Sequential Tariff War
Traditional textbook theory follows the work of Johnson (1953), considering the case of two
countries that attempt to maximize some form of social welfare by imposing a tariff to shif t the offer
curves. A Cournot behavioral assumption is typically used to explain the reaction to a change in a tariff.
The well-known result is a tariff war, resulting in either an equilibrium point, or a tariff cycle (Johnson,
1953). Another way of modeling the tariff war was proposed by Tower who treated retaliation as a
Stackelberg leader/follower situation which country one perceived itself as a leader which country two as
a follower (Tower, 1976). In our simulation, we followed a similar setting as Johnson’s Cournot game.
The difference was that in each round only one player moved based on the action of another player from
previous round. So player set his best respond (optimal tariff) at each round considering another player’s
best respond from last round. If the best responses converges, then the result should be the same as that in
a Cournot behavioral game.
8
10
12
14
16
18
20
22
24
26
28
1 7 5 1 9 5 2 1 5 2 3 5 2 5 5 2 7 5 2 9 5
US TAX REVENUE
US Tax Revenue
17
Given the initial setting, we let US move first. So US moves in all odd periods and UK moves in
all even periods. Each one plays ten rounds so we have twenty rounds in total. The following graph plots
each player’s optimal tariff in each round. We can see that after 8 rounds, both of their optimal tariffs
converges to 0.17. Their utilities converges to 272.6. The joint utility under such tariff war is 272.6 * 2 =
545.2. Comparing to previous scenarios, it is lower than those under free trade (550) and unilateral
optimal tariff (547.82). Such result is similar as duopoly price war under collusion and Cournot game.
0
0.05
0.1
0.15
0.2
0.25
0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0
OPTIMAL TARIFF
US Optimal Beer Tariff UK Optimal Auto Tariff
18
In the above tariff war, the convergent optimal tariffs and utilities are equal. This is due to the
symmetric setting of our model. Next, we simulate a tariff war using unsymmetric setting of countries. In
the following simulation, we set Beta('auto','US')=0.7; Beta('beer','US')=0.3. So US has a higher share of
expenditure on auto than beer. On the other hand, UK maintain its betas equaling to 0.5 for both auto and
beer.
In the following set of graphs, the left side shows the results which US moves first, and those on
the right side represent the result which UK moves first. It turns out that the convergent optimal tariffs
and utilities are independent of who starts first. In other words, in terms of the end value, the first mover
does not have anvantage. The unsymmetric settings of country generate unsymmetirc convergent values.
In this case, US has higher end value of utility but lower value of opimal import tariff.
269
270
271
272
273
274
275
276
277
278
279
0 1 2 3 4 5 6 7 8 9 1 0
UTILITY
US Utility UK Utility
19
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 2 4 6 8 1 0
OPTIMAL TARIFF
US Optimal Beer Tariff
UK Optimal Auto Tariff
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 2 4 6 8 1 0
OPTIMAL TARIFF
US Optimal Beer Tariff
UK Optimal Auto Tariff
265
270
275
280
285
290
295
300
305
0 2 4 6 8 1 0
UTILITY
US Utility UK Utility
265
270
275
280
285
290
295
300
305
0 2 4 6 8 1 0
UTILITY
US Utility UK Utility
20
Reference Johnson, H. G. (1953). Optimum Tariffs and Retaliation. The Review of Economic Studies, 21(2), 142–
153. doi:10.2307/2296006
Tower, E. (1976). The Optimum Tariff, Retaliation and Autarky. Eastern Economic Journal, 3(2), 72–75.
21
Appendix * Adapted from "two country version of the HOS model with trade
taxes", as described in Chapter 19 of
* Gilbert and Tower: Introduction to Numerical Simulation for Trade
Theory and Policy.
*Setting of the model
* Define the indexes for the problem
SET I Goods /Auto,Beer/;
SET J Factors /K,L/;
SET D Countries /US,UK/;
ALIAS (J, JJ);
* Create names for parameters
PARAMETERS
ALPHA(D) Shift parameter in utility
BETA(I,D) Share parameter in utility
PO(I,D) Initial domestic prices
PWO(I) Initial world prices
XO(I,D) Initial trade
UO(D) Initial utility levels
CO(I,D) Initial consumption levels
GAMMA(I,D) Shift parameters in production
DELTA(J,I,D) Share parameters in production
RHO(I,D) Elasticity parameters in production
FBAR(J,D) Factor Endowments
QO(I,D) Initial output levels
RO(J,D) Initial factor prices
FO(J,I,D) Initial factor use levels
GDPO(D) Initial gross domestic product;
* Assign values to the parameters
PWO(I)=1;
PO(I,D)=1;
RO(J,D)=1;
PARAMETER QO(I,D) Initial output levels /
Auto.US 200
Auto.UK 75
Beer.US 75
Beer.UK 200 /;
CO(I,D)=137.5;
XO(I,D)=QO(I,D)-CO(I,D);
PARAMETER FO(J,I,D) Initial factor use levels /
22
K.Auto.US 160
K.Auto.UK 60
K.Beer.US 15
K.Beer.UK 40
L.Auto.US 40
L.Auto.UK 15
L.Beer.US 60
L.Beer.UK 160 /;
FBAR(J,D)=SUM(I, FO(J,I,D));
GDPO(D)=SUM(I, PO(I,D)*QO(I,D));
RHO(I,D)=0.1;
DELTA(J,I,D)=(RO(J,D)/FO(J,I,D)**(RHO(I,D)-1))/(SUM(JJ,
RO(JJ,D)/FO(JJ,I,D)**(RHO(I,D)-1)));
GAMMA(I,D)=QO(I,D)/(SUM(J,
DELTA(J,I,D)*FO(J,I,D)**RHO(I,D)))**(1/RHO(I,D));
UO(D)=GDPO(D);
BETA(I,D)=CO(I,D)/GDPO(D);
ALPHA(D)=UO(D)/PROD(I, CO(I,D)**BETA(I,D));
* Create names for variables
VARIABLES
U(D) Utility indices
T(I,D)
P(I,D) Prices
C(I,D) Consumption levels
Q(I,D) Output levels
R(J,D) Factor prices
F(J,I,D) Factor use levels
PW(I) World prices
X(I,D) Trade levels
GDP(D) Gross domestic products
OBJ Objective;
* Assign initial values to variables, and set lower bounds
U.L(D)=UO(D);
P.L(I,D)=PO(I,D);
C.L(I,D)=CO(I,D);
Q.L(I,D)=QO(I,D);
R.L(J,D)=RO(J,D);
F.L(J,I,D)=FO(J,I,D);
PW.L(I)=PWO(I);
X.L(I,D)=XO(I,D);
GDP.L(D)=GDPO(D);
OBJ.L=SUM(D, UO(D));
P.LO(I,D)=0;
C.LO(I,D)=0;
Q.LO(I,D)=0;
R.LO(J,D)=0;
F.LO(J,I,D)=0;
23
GDP.LO(D)=0;
PW.LO(I)=0;
* Fix the value of one price to serve as a numeraire
PW.FX('Auto')=1;
* Create names for equations
EQUATIONS
UTILITY(D) Utility functions
DEMAND(I,D) Demand functions
PRODUCTION(I,D) Production functions
RESOURCE(J,D) Resource constraints
FDEMAND(J,I,D) Factor demand functions
INCOME(D) Gross domestic products
MAT_BAL(I,D) Open economy material balance
INT_CLEAR(I) International market clearing
ARBITRAGE(I,D) International price arbitrage
OBJECTIVE_SUM Objective function
OBJECTIVE_US Objective function
OBJECTIVE_UK Objective function;
* Assign the expressions to the equation names
UTILITY(D)..U(D)=E=ALPHA(D)*PROD(I, C(I,D)**BETA(I,D));
DEMAND(I,D)..C(I,D)=E=BETA(I,D)*GDP(D)/P(I,D);
MAT_BAL(I,D)..X(I,D)=E=Q(I,D)-C(I,D);
INT_CLEAR(I)..SUM(D, X(I,D))=E=0;
ARBITRAGE(I,D)..P(I,D)=E=(1+T(I,D))*PW(I);
PRODUCTION(I,D)..Q(I,D)=E=GAMMA(I,D)*SUM(J,
DELTA(J,I,D)*F(J,I,D)**RHO(I,D))**(1/RHO(I,D));
RESOURCE(J,D)..FBAR(J,D)=E=SUM(I, F(J,I,D));
FDEMAND(J,I,D)..R(J,D)=E=P(I,D)*Q(I,D)*SUM(JJ,
DELTA(JJ,I,D)*F(JJ,I,D)**RHO(I,D))**(-
1)*DELTA(J,I,D)*F(J,I,D)**(RHO(I,D)-1);
INCOME(D)..GDP(D)=E=SUM(I, P(I,D)*Q(I,D))-SUM(I, PW(I)*T(I,D)*X(I,D));
OBJECTIVE_US..OBJ=E=U('US');
OBJECTIVE_UK..OBJ=E=U('UK');
OBJECTIVE_SUM..OBJ=E=SUM(D,U(D));
MODEL TRADE / UTILITY, DEMAND, MAT_BAL, INT_CLEAR, ARBITRAGE,
PRODUCTION, RESOURCE, FDEMAND, INCOME, OBJECTIVE_SUM /;
MODEL TRADE_US / UTILITY, DEMAND, MAT_BAL, INT_CLEAR, ARBITRAGE,
PRODUCTION, RESOURCE, FDEMAND, INCOME, OBJECTIVE_US /;
MODEL TRADE_UK / UTILITY, DEMAND, MAT_BAL, INT_CLEAR, ARBITRAGE,
PRODUCTION, RESOURCE, FDEMAND, INCOME, OBJECTIVE_UK /;
*1.solve the model of two countries with no tariff
FBAR(J,D)=SUM(I, FO(J,I,D));
24
T.FX(I,D)=0;
Solve TRADE USING NLP MAXIMIZING OBJ;
execute_unload"results.GDX" U T P C Q R F PW X GDP
execute'gdxxrw.exe results.GDX var=U rng=s1!D1:E2'
execute'gdxxrw.exe results.GDX var=T rng=s1!C3:E5'
execute'gdxxrw.exe results.GDX var=P rng=s1!C6:E8'
execute'gdxxrw.exe results.GDX var=C rng=s1!C9:E11'
execute'gdxxrw.exe results.GDX var=Q rng=s1!C12:E14'
execute'gdxxrw.exe results.GDX var=R rng=s1!C15:E17'
execute'gdxxrw.exe results.GDX var=F rng=s1!B18:G22'
execute'gdxxrw.exe results.GDX var=PW rng=s1!D23:E24'
execute'gdxxrw.exe results.GDX var=X rng=s1!C25:E27'
execute'gdxxrw.exe results.GDX var=GDP rng=s1!D28:E29';
*2. US sets import tariff to maximize US utility, given no
tax in UK
FBAR(J,D)=SUM(I, FO(J,I,D));
T.FX(I,'UK')=0;
T.FX('Auto','US')=0;
T.LO('beer','US')=-INF;
T.UP('beer','US')=INF;
Solve TRADE_US USING NLP MAXIMIZING OBJ;
execute_unload"results.GDX" U T P C Q R F PW X GDP
execute'gdxxrw.exe results.GDX var=U rng=s2!D1:E2'
execute'gdxxrw.exe results.GDX var=T rng=s2!C3:E5'
execute'gdxxrw.exe results.GDX var=P rng=s2!C6:E8'
execute'gdxxrw.exe results.GDX var=C rng=s2!C9:E11'
execute'gdxxrw.exe results.GDX var=Q rng=s2!C12:E14'
execute'gdxxrw.exe results.GDX var=R rng=s2!C15:E17'
execute'gdxxrw.exe results.GDX var=F rng=s2!B18:G22'
execute'gdxxrw.exe results.GDX var=PW rng=s2!D23:E24'
execute'gdxxrw.exe results.GDX var=X rng=s2!C25:E27'
execute'gdxxrw.exe results.GDX var=GDP rng=s2!D28:E29';
*3. US sets export tax/subsidy to maximize US utility,
given no tax in UK
FBAR(J,D)=SUM(I, FO(J,I,D));
T.FX(I,'UK')=0;
T.FX('beer','US')=0;
T.LO('auto','US')=-INF;
T.UP('auto','US')=INF;
Solve TRADE_US USING NLP MAXIMIZING OBJ;
25
execute_unload"results.GDX" U T P C Q R F PW X GDP
execute'gdxxrw.exe results.GDX var=U rng=s3!D1:E2'
execute'gdxxrw.exe results.GDX var=T rng=s3!C3:E5'
execute'gdxxrw.exe results.GDX var=P rng=s3!C6:E8'
execute'gdxxrw.exe results.GDX var=C rng=s3!C9:E11'
execute'gdxxrw.exe results.GDX var=Q rng=s3!C12:E14'
execute'gdxxrw.exe results.GDX var=R rng=s3!C15:E17'
execute'gdxxrw.exe results.GDX var=F rng=s3!B18:G22'
execute'gdxxrw.exe results.GDX var=PW rng=s3!D23:E24'
execute'gdxxrw.exe results.GDX var=X rng=s3!C25:E27'
execute'gdxxrw.exe results.GDX var=GDP rng=s3!D28:E29';
*4. US sets both import and export taxes at 10%, given no
tariff of UK (Lerner Symmetry Theorem).
FBAR(J,D)=SUM(I, FO(J,I,D));
T.FX(I,'UK')=0;
T.FX('beer','US')=0.1;
T.FX('auto','US')=0.1;
Solve TRADE_US USING NLP MAXIMIZING OBJ;
execute_unload"results.GDX" U T P C Q R F PW X GDP
execute'gdxxrw.exe results.GDX var=U rng=s3!D1:E2'
execute'gdxxrw.exe results.GDX var=T rng=s3!C3:E5'
execute'gdxxrw.exe results.GDX var=P rng=s3!C6:E8'
execute'gdxxrw.exe results.GDX var=C rng=s3!C9:E11'
execute'gdxxrw.exe results.GDX var=Q rng=s3!C12:E14'
execute'gdxxrw.exe results.GDX var=R rng=s3!C15:E17'
execute'gdxxrw.exe results.GDX var=F rng=s3!B18:G22'
execute'gdxxrw.exe results.GDX var=PW rng=s3!D23:E24'
execute'gdxxrw.exe results.GDX var=X rng=s3!C25:E27'
execute'gdxxrw.exe results.GDX var=GDP rng=s3!D28:E29';
*5.Demonstration of Factor equalization theorem
*assumptions hold, change the relative K/L ratio
RHO(I,D)=0.1;
T.FX(I,D)=0;
PARAMETER FBAR(J,D)/
K.US = 100
K.UK = 100
L.US = 100
L.UK = 175/;
Solve TRADE USING NLP MAXIMIZING OBJ;
26
execute_unload"results.GDX" U T P C Q R F PW X GDP
execute'gdxxrw.exe results.GDX var=U rng=s1!D1:E2'
execute'gdxxrw.exe results.GDX var=T rng=s1!C3:E5'
execute'gdxxrw.exe results.GDX var=P rng=s1!C6:E8'
execute'gdxxrw.exe results.GDX var=C rng=s1!C9:E11'
execute'gdxxrw.exe results.GDX var=Q rng=s1!C12:E14'
execute'gdxxrw.exe results.GDX var=R rng=s1!C15:E17'
execute'gdxxrw.exe results.GDX var=F rng=s1!B18:G22'
execute'gdxxrw.exe results.GDX var=PW rng=s1!D23:E24'
execute'gdxxrw.exe results.GDX var=X rng=s1!C25:E27'
execute'gdxxrw.exe results.GDX var=GDP rng=s1!D28:E29';
*assumptions fail (factor intensity reversal) and change the relative
K/L ratio
RHO(I,D)=0.00001;
T.FX(I,D)=0;
PARAMETER FBAR(J,D)/
K.US = 9999
K.UK = 100
L.US = 10
L.UK = 200/;
Solve TRADE USING NLP MAXIMIZING OBJ;
execute_unload"results.GDX" U T P C Q R F PW X GDP
execute'gdxxrw.exe results.GDX var=U rng=s5!D1:E2'
execute'gdxxrw.exe results.GDX var=T rng=s5!C3:E5'
execute'gdxxrw.exe results.GDX var=P rng=s5!C6:E8'
execute'gdxxrw.exe results.GDX var=C rng=s5!C9:E11'
execute'gdxxrw.exe results.GDX var=Q rng=s5!C12:E14'
execute'gdxxrw.exe results.GDX var=R rng=s5!C15:E17'
execute'gdxxrw.exe results.GDX var=F rng=s5!B18:G22'
execute'gdxxrw.exe results.GDX var=PW rng=s5!D23:E24'
execute'gdxxrw.exe results.GDX var=X rng=s5!C25:E27'
execute'gdxxrw.exe results.GDX var=GDP rng=s5!D28:E29';
*6. Plot US Import Tariff vs. U, C, X and Q, given no tax
in UK
FBAR(J,D)=SUM(I, FO(J,I,D));
T.FX(I,D)=0;
SET ITERR /1*99/;
PARAMETER
Us(ITERR)
27
Ts(ITERR)
PAs(ITERR)
PBs(ITERR)
CAs(ITERR)
CBs(ITERR)
QAs(ITERR)
QBs(ITERR)
RKs(ITERR)
RLs(ITERR)
XAss(ITERR)
XBss(ITERR)
;
LOOP(ITERR,
SOLVE TRADE_US USING NLP MAXIMIZING OBJ;
Us(ITERR)=U.L('US');
Ts(ITERR)=T.L('Beer','US');
PAs(ITERR)=P.L('Auto','US');
PBs(ITERR)=P.L('Beer','US');
CAs(ITERR)=C.L('Auto','US');
CBs(ITERR)=C.L('Beer','US');
QAs(ITERR)=Q.L('Auto','US');
QBs(ITERR)=Q.L('Beer','US');
RKs(ITERR)=R.L('K','US');
RLs(ITERR)=R.L('L','US');
XAss(ITERR)=X.L('Auto','US');
XBss(ITERR)=X.L('Beer','US');
T.FX('Beer','US')=T.L('Beer','US')+0.05;
);
execute_unload"s5plot.GDX" Us Ts PAs PBs CAs CBs QAs QBs RKs RLs XAss
XBss
execute'gdxxrw.exe s5plot.GDX par=Ts rng=s5!B2:CX2'
execute'gdxxrw.exe s5plot.GDX par=Us rng=s5!B4:CX4'
execute'gdxxrw.exe s5plot.GDX par=PAs rng=s5!B6:CX6'
execute'gdxxrw.exe s5plot.GDX par=PBs rng=s5!B8:CX8'
execute'gdxxrw.exe s5plot.GDX par=CAs rng=s5!B10:CX10'
execute'gdxxrw.exe s5plot.GDX par=CBs rng=s5!B12:CX12'
execute'gdxxrw.exe s5plot.GDX par=QAs rng=s5!B14:CX14'
execute'gdxxrw.exe s5plot.GDX par=QBs rng=s5!B16:CX16'
execute'gdxxrw.exe s5plot.GDX par=RKs rng=s5!B18:CX18'
execute'gdxxrw.exe s5plot.GDX par=RLs rng=s5!B20:CX20'
execute'gdxxrw.exe s5plot.GDX par=XAss rng=s5!B22:CX22'
execute'gdxxrw.exe s5plot.GDX par=XBss rng=s5!B24:CX24';
*7a.Sensitivity Analysis on Beta('US')
FBAR(J,D)=SUM(I, FO(J,I,D));
T.FX(I,'UK')=0;
T.FX('Auto','US')=0;
T.LO('beer','US')=-INF;
T.UP('beer','US')=INF;
28
Beta('auto','US')=0.3;
Beta('beer','US')=0.7;
SET ITERRR /1*69/;
PARAMETER
Usa(ITERRR)
Usaa(ITERRR)
Tsa(ITERRR)
PAsa(ITERRR)
PBsa(ITERRR)
CAsa(ITERRR)
CBsa(ITERRR)
QAsa(ITERRR)
QBsa(ITERRR)
RKsa(ITERRR)
RLsa(ITERRR)
XAssa(ITERRR)
XBssa(ITERRR)
Betasa(ITERRR)
;
LOOP(ITERRR,
SOLVE TRADE_US USING NLP MAXIMIZING OBJ;
Usa(ITERRR)=U.L('US');
Usaa(ITERRR)=U.L('UK');
Tsa(ITERRR)=T.L('Beer','US');
PAsa(ITERRR)=P.L('Auto','US');
PBsa(ITERRR)=P.L('Beer','US');
CAsa(ITERRR)=C.L('Auto','US');
CBsa(ITERRR)=C.L('Beer','US');
QAsa(ITERRR)=Q.L('Auto','US');
QBsa(ITERRR)=Q.L('Beer','US');
RKsa(ITERRR)=R.L('K','US');
RLsa(ITERRR)=R.L('L','US');
XAssa(ITERRR)=X.L('Auto','US');
XBssa(ITERRR)=X.L('Beer','US');
BETAsa(ITERRR)=Beta('auto','US');
Beta('auto','US')=Beta('auto','US')+0.01;
Beta('beer','US')=Beta('beer','US')-0.01;
);
execute_unload"s7aplot.GDX" Betasa Usa Usaa Tsa PAsa PBsa CAsa CBsa
QAsa QBsa RKsa RLsa XAssa XBssa
execute'gdxxrw.exe s7aplot.GDX par=Betasa rng=s5!B2:CX2'
execute'gdxxrw.exe s7aplot.GDX par=Usa rng=s5!B4:CX4'
execute'gdxxrw.exe s7aplot.GDX par=PAsa rng=s5!B6:CX6'
execute'gdxxrw.exe s7aplot.GDX par=PBsa rng=s5!B8:CX8'
execute'gdxxrw.exe s7aplot.GDX par=CAsa rng=s5!B10:CX10'
execute'gdxxrw.exe s7aplot.GDX par=CBsa rng=s5!B12:CX12'
execute'gdxxrw.exe s7aplot.GDX par=QAsa rng=s5!B14:CX14'
execute'gdxxrw.exe s7aplot.GDX par=QBsa rng=s5!B16:CX16'
execute'gdxxrw.exe s7aplot.GDX par=RKsa rng=s5!B18:CX18'
execute'gdxxrw.exe s7aplot.GDX par=RLsa rng=s5!B20:CX20'
29
execute'gdxxrw.exe s7aplot.GDX par=XAssa rng=s5!B22:CX22'
execute'gdxxrw.exe s7aplot.GDX par=XBssa rng=s5!B24:CX24'
execute'gdxxrw.exe s7aplot.GDX par=Tsa rng=s5!B26:CX26';
execute'gdxxrw.exe s7aplot.GDX par=Usaa rng=s5!B28:CX28';
*7b.Sensitivity Analysis on US Capital
FBAR(J,D)=SUM(I, FO(J,I,D));
T.FX(I,'UK')=0;
T.FX('Auto','US')=0;
T.LO('beer','US')=-INF;
T.UP('beer','US')=INF;
SET ITERRR /1*100/;
PARAMETER
Usb(ITERRR)
Usbb(ITERRR)
Tsb(ITERRR)
PAsb(ITERRR)
PBsb(ITERRR)
CAsb(ITERRR)
CBsb(ITERRR)
QAsb(ITERRR)
QBsb(ITERRR)
RKsb(ITERRR)
RLsb(ITERRR)
XAssb(ITERRR)
XBssb(ITERRR)
Betasb(ITERRR)
Rsb(ITERRR)
;
LOOP(ITERRR,
SOLVE TRADE_US USING NLP MAXIMIZING OBJ;
Usb(ITERRR)=U.L('US');
Usbb(ITERRR)=U.L('UK');
Tsb(ITERRR)=T.L('Beer','US');
PAsb(ITERRR)=P.L('Auto','US');
PBsb(ITERRR)=P.L('Beer','US');
CAsb(ITERRR)=C.L('Auto','US');
CBsb(ITERRR)=C.L('Beer','US');
QAsb(ITERRR)=Q.L('Auto','US');
QBsb(ITERRR)=Q.L('Beer','US');
RKsb(ITERRR)=R.L('K','US');
RLsb(ITERRR)=R.L('L','US');
XAssb(ITERRR)=X.L('Auto','US');
XBssb(ITERRR)=X.L('Beer','US');
BETAsb(ITERRR)=Beta('auto','US');
Rsb(ITERRR)=T.L('Beer','US')*P.L('Beer','UK')*X.L('Beer','UK');
FBAR('K','US')=FBAR('K','US')+2;
);
30
execute_unload"s7bplot.GDX" Usb Usbb Rsb Tsb PAsb PBsb CAsb CBsb QAsb
QBsb RKsb RLsb XAssb XBssb
execute'gdxxrw.exe s7bplot.GDX par=Usbb rng=s5!B2:CW2'
execute'gdxxrw.exe s7bplot.GDX par=Usb rng=s5!B4:CW4'
execute'gdxxrw.exe s7bplot.GDX par=PAsb rng=s5!B6:CW6'
execute'gdxxrw.exe s7bplot.GDX par=PBsb rng=s5!B8:CW8'
execute'gdxxrw.exe s7bplot.GDX par=CAsb rng=s5!B10:CW10'
execute'gdxxrw.exe s7bplot.GDX par=CBsb rng=s5!B12:CW12'
execute'gdxxrw.exe s7bplot.GDX par=QAsb rng=s5!B14:CW14'
execute'gdxxrw.exe s7bplot.GDX par=QBsb rng=s5!B16:CW16'
execute'gdxxrw.exe s7bplot.GDX par=RKsb rng=s5!B18:CW18'
execute'gdxxrw.exe s7bplot.GDX par=RLsb rng=s5!B20:CW20'
execute'gdxxrw.exe s7bplot.GDX par=XAssb rng=s5!B22:CW22'
execute'gdxxrw.exe s7bplot.GDX par=XBssb rng=s5!B24:CW24'
execute'gdxxrw.exe s7bplot.GDX par=Tsb rng=s5!B26:CW26';
execute'gdxxrw.exe s7bplot.GDX par=Rsb rng=s5!B28:CW28';
*8. Trade War
*US starts first, set the optimal tariff, given UK tax fixed.
*UK then sets its optimal tariff, given US tariff rate from previous
step.
*US moves...
*100 rounds.
BETA('Auto','US')=0.7;
BETA('Beer','US')=0.3;
T.FX(I,D)=0;
SET ITER /1*10/;
PARAMETER
UUSs(ITER)
UUKs(ITER)
TUSBs(ITER)
TUKAs(ITER)
CAUSs(ITER)
CBUSs(ITER)
CAUKs(ITER)
CBUKs(ITER)
XAs(ITER)
XBs(ITER)
;
Loop(ITER,
T.FX('Auto','UK')=T.L('Auto','UK');
T.LO('Beer','US')=-INF;
T.UP('Beer','US')=INF;
SOLVE TRADE_US USING NLP MAXIMIZING OBJ;
31
UUSs(ITER)=U.L('US');
UUKs(ITER)=U.L('UK');
TUSBs(ITER)=T.L('Beer','US');
TUKAs(ITER)=T.L('Auto','UK');
CAUSs(ITER)=C.L('Auto','US');
CBUSs(ITER)=C.L('Beer','US');
CAUKs(ITER)=C.L('Auto','UK');
CBUKs(ITER)=C.L('Beer','UK');
XAs(ITER)=X.L('Auto','US');
XBs(ITER)=X.L('Beer','UK');
T.FX('Beer','US')=T.L('Beer','US');
T.LO('Auto','UK')=-INF;
T.UP('Auto','UK')=INF;
SOLVE TRADE_UK USING NLP MAXIMIZING OBJ;
);
execute_unload"S8.GDX" UUSs UUKs TUSBs TUKAs CAUSs CBUSs CAUKs CBUKs
XAs XBs
execute'gdxxrw.exe S8.GDX par=TUSBs rng=US!B2:GT2'
execute'gdxxrw.exe S8.GDX par=TUKAs rng=US!B4:GT4'
execute'gdxxrw.exe S8.GDX par=UUSs rng=US!B6:GT6'
execute'gdxxrw.exe S8.GDX par=UUKs rng=US!B8:GT8'
execute'gdxxrw.exe S8.GDX par=CAUSs rng=US!B10:GT10'
execute'gdxxrw.exe S8.GDX par=CBUSs rng=US!B12:GT12'
execute'gdxxrw.exe S8.GDX par=CAUKs rng=US!B14:GT14'
execute'gdxxrw.exe S8.GDX par=CBUKs rng=US!B16:GT16'
execute'gdxxrw.exe S8.GDX par=XAs rng=US!B18:GT18'
execute'gdxxrw.exe S8.GDX par=XBs rng=US!B20:GT20';
T.FX(I,D)=0;
Loop(ITER,
T.FX('Auto','UK')=T.L('Auto','UK');
T.LO('Beer','US')=-INF;
T.UP('Beer','US')=INF;
SOLVE TRADE_US USING NLP MAXIMIZING OBJ;
T.FX('Beer','US')=T.L('Beer','US');
T.LO('Auto','UK')=-INF;
T.UP('Auto','UK')=INF;
SOLVE TRADE_UK USING NLP MAXIMIZING OBJ;
UUSs(ITER)=U.L('US');
UUKs(ITER)=U.L('UK');
TUSBs(ITER)=T.L('Beer','US');
TUKAs(ITER)=T.L('Auto','UK');
32
CAUSs(ITER)=C.L('Auto','US');
CBUSs(ITER)=C.L('Beer','US');
CAUKs(ITER)=C.L('Auto','UK');
CBUKs(ITER)=C.L('Beer','UK');
XAs(ITER)=X.L('Auto','US');
XBs(ITER)=X.L('Beer','UK');
);
execute_unload"S8.GDX" UUSs UUKs TUSBs TUKAs CAUSs CBUSs CAUKs CBUKs
XAs XBs
execute'gdxxrw.exe S8.GDX par=TUSBs rng=UK!B2:GT2'
execute'gdxxrw.exe S8.GDX par=TUKAs rng=UK!B4:GT4'
execute'gdxxrw.exe S8.GDX par=UUSs rng=UK!B6:GT6'
execute'gdxxrw.exe S8.GDX par=UUKs rng=UK!B8:GT8'
execute'gdxxrw.exe S8.GDX par=CAUSs rng=UK!B10:GT10'
execute'gdxxrw.exe S8.GDX par=CBUSs rng=UK!B12:GT12'
execute'gdxxrw.exe S8.GDX par=CAUKs rng=UK!B14:GT14'
execute'gdxxrw.exe S8.GDX par=CBUKs rng=UK!B16:GT16'
execute'gdxxrw.exe S8.GDX par=XAs rng=UK!B18:GT18'
execute'gdxxrw.exe S8.GDX par=XBs rng=UK!B20:GT20'