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International Trade Model

 

Bekzod Makhmudov, Sarvar Ruzmatov

University of World Economy and Diplomacy

Tashkent, Uzbekistan

makhmudovb@gmail.com

 

How International Trade Occures

 

 

  In international trade we assume for simplicity that there are only two countries wanting to engage in it. Theoretically, a concept called comparative advantage determines which country will export and which one will import a particular product. In our case, since there are only two countries, the comparative advantage will be determined by national equilibrium prices in this particular product market in both countries.

 

In order to understand this process, we first assume that the two countries do not trade with each other. In this case, national equilibrium price in each country is determined by the intersecting points of their respective supply and demand curves. Since countries differ from each other in terms of available natural, production, and human resources, as well as purchasing power of consumers, the national equilibrium prices in both countries will be different.

 

Now assume that both countries want to open up their borders for trade. The difference in respective national equilibrium prices will determine the direction of trade, i.e. which country will export and which one will import a particular product. In this case, if one country's national equilibrium price is lower than that of the other country, then the first country will export and the second one will import a particular product. International equilibrium price will then be determined untill both countries' export and import capacities will be fullfilled.

 

Now, let us demonstrate how international trade between the two countries can be programmed and simulated with Maple application.

Country A.

 

Suppose that in country A manufacturers produce a particular product in the same national market.

The quantity of a product (q) that manufacturers can supply in the market at a particular price (p) is denoted by a supply function. In our case we can denote the supply function of country A by PSq1 (which is a function of p from q):

 

(1.1.1)

 

The quantity of a product (q) that consumers can purchase in the market at a particular price (p) is denoted by a demand function. In our case we can denote the demand function of country A by PDq1 (which is a function of p from q):

 

(1.1.2)

 

Since national supply and demand functions in country A are given as a function of price from quantity, it is also helpful to convert them to a function of quantity from price. To do so, we will solve equations for q for country A:

 

(1.1.3)

  where QSp1 - supply function as of quantity from price for country A, and

 

(1.1.4)

where QDp1 - demand function as of quantity from price for country A.

 

 

Since we know the functions of supply and demand for a particular product in country A, we can calculate national equilibrium price (EP1) and national equilibrium quantity (EQ1). This can be done by equalizing supply and demand functions (PSq1=PDq1) and solving this equation for EQ1:

 

(1.1.5)

 

After finding equilibrium quantity of a product, we can proceed to finding equilibrium price. This can be done by substituting the value of the equilibrium quantity (EQ1) to either national supply or demand function and solving for equilibrium price (EP1):

 

(1.1.6)

 

After we have calculated national equilibrium price and national equilibrium quantity for country A, we can proceed to summarize the procedures above in a single graph. For this we will plot the graph with the following procedure:

 

 

 



 

 

 

 

Where A - consumers' surplus (CS), B - producers' surplus (PS), A+B - national surplus (NS).

 

We can calculate these surpluses with the following procedure:

 

(1.1.7)

(1.1.8)

(1.1.9)

 

 

Country B

 

Now, suppose that in country B manufacturers also produce the same product as that in country A in their own national market.

The quantity of a product (q) that manufacturers can supply in the market at a particular price (p) is denoted by a supply function. In our case we can denote the supply function of country B by PSq2 (which is a function of p from q):

 

(1.2.1)

 

The quantity of a product (q) that consumers can purchase in the market at a particular price (p) is denoted by a demand function. In our case we can denote the demand function of country B by PDq2 (which is a function of p from q):

 

(1.2.2)

 

 

Since national supply and demand functions in country B are given as a function of price from quantity, it is also helpful to convert them to a function of quantity from price. To do so, we will solve equations for q for country B:

 

(1.2.3)

where QSp2 - supply function as of quantity from price for country B, and

 

(1.2.4)

where QDp1 - demand function as of quantity from price for country B.

 

Since we know the functions of supply and demand for a particular product in country B as well, we can calculate national equilibrium price (EP2) and national equilibrium quantity (EQ2). This can be done by equalizing supply and demand functions (PSq2=PDq2) and solving this equation for EQ2:

 

(1.2.5)

 

After finding equilibrium quantity of a product, we can proceed to finding equilibrium price. As in the case of country A, this can be done by substituting the value of the equilibrium quantity (EQ2) to either national supply or demand function and solving for equilibrium price (EP2):

 

(1.2.6)

 

After we have calculated national equilibrium price and national equilibrium quantity for country B, we can proceed to summarize the procedures above in a single graph. For this we will plot the graph with the following procedure:

 

 

 


 

 

 

 

 

 

 

Where A - consumers' surplus (CS), B - producers' surplus (PS), A+B - national surplus (NS).

 

We can calculate these surpluses with the following procedure:

 

(1.2.7)

(1.2.8)

(1.2.9)

 

 

International Trade

 

 

If we assume that both countries want to open up their borders for trade, the difference in respective national equilibrium prices EP1 and EP2 will determine the direction of trade. In this case, country B's national equilibrium price is lower than that of country A (EP1>EP2). Therefore, country B will export and country A will import the product at a world price (or international equilibrium price) that will be determined between the two national equilibrium prices EP1 and EP2.

 

But in order to determine international equilibrium price, we will have to identify international supply and international demand functions.

 

In general, international supply of a particular product is identified by the exporting country's ability and willingness to supply to the world market (in our case, it is country B), while international demand of the same particular product is identified by the importing country's ability and willingness to purchase from the world market (in our case, it is country A).

 

Now, to find international supply function, we will subtract national supply from national demand of country B (exporting country):

 

(1.3.1)

 

Then, to find international demand function, we will subtract national demand from national supply of country A (importing country):

 

(1.3.2)

 

Since we know the functions of international supply and international demand for a particular product in world market, we can calculate international equilibrium price (EPIT) and international equilibrium quantity (EQIT). This can be done by equalizing supply and demand functions (QSIT=QDIT) and solving this equation for EPIT:

 

(1.3.3)

After finding international equilibrium price of a product, we can proceed to finding international equilibrium price. This can be done by substituting the value of the equilibrium price (EPIT) to either international supply or demand function and solving for equilibrium quantity (EQIT):

 

(1.3.4)

 

After we have calculated international equilibrium price and international equilibrium quantity, we can proceed to summarize the procedures above in a single graph. For this we will plot the graph with the following procedure:

 

 

 


 
 

 

 

 

 

 

This graph shows that international trade will be balanced at a price of 1000 when country B exports 50000 pcs of products and country A imports the same quantity.

 

International trade provides net gains for both countries. In this case, area A represents a net gain of country A (GA), and area B represents a net gain of coutry B (GB) from international trade. We can calculate them by applying the following procedure:

 

(1.3.5)

GB:=

(1.3.6)

Welfare Effects of International Trade

 

In order to see how international trade between country A and country B effects welfares of their economic agents, i.g. consumers, producers, and the country as a whole, we need to evaluate their gains and/or losses incurred after they have opened their borders for trade. To do so, we should depict the price changes in a single graph for each country and then calculate welfare effects for each agent.

 

Country A

 

For country A, which is an importing country, the graphical representation of price changes is as follows:

 

 

 

 

 

 

 

 

 

 

 

 

where A - producers' loss, A+B+C - consumers' surplus, B+C - national surplus.

 

This graph shows that when country A opens up for international trade, the national price is affected by international market price, which creates competition for the national producers. A lower international price increases consumption from 40 000 unit of products to 65 000 units, while on the other hand it decrease national production from 40 000 units to 15 000 units. The difference, 50000, is imported from country B.Clearly, in the case of an importing country, consumers gain from international trade, which is represented by area A+B+C, whereas producers lose from international trade as they face competition and their loss is represented by area A. The country as a whole wins from international trade as its net gain is calculated as a difference between consumer surplus and producer loss, which will give us area B+C.

 

We can calculate the amounts of consumer surplus, producer loss and the country's gain with the following procedure from component tools:

 

 

 

 

Country B

 

 

For country B, which is an exporting country, the graphical representation of price changes is as follows:

 

 

 

 

 

 

 



 

 

 

 

where A+B - consumers' loss, A+B+C - producers' surplus, C - national surplus.

 

This graph shows that when country B opens up for international trade, the national price is affected by international market price, which creates opportunity for the national producers. A higher international price increases production from 50 000 unit of products to 75 000 units, while on the other hand it decrease consumption from 50 000 units to 25 000 units. The difference, 50000, is exported to country A. Clearly, in the case of an exporting country, consumers lose from international trade, which is represented by area A+B, whereas producers gain from international trade as they face opportunity and their gain is represented by area A+B+C. The country as a whole wins from international trade as its net gain is calculated as a difference between producers' surplus and consumers' loss, which will give us area C.

 

We can calculate the amounts of consumer loss, producer surplus and the country's gain with the following procedure from component tools:

 

Applying Trade Policy Instruments: Import Tariffs and Import Quotas

 

As can be seen from the above welfare effects of international trade on country A, which is an importing country, the country as a whole gains from free trade, but consumers gain more than do domestic producers of competing products. Moreover, these producers even lose from free trade because the international equilibrium price is lower than its domestic equilibrium price, so the producers are forced to sell at a lower price and reduce their output. Of course, this may lead to problems, especially when import competing industry is not mature enough to compete foreign producers. Therefore, in such cases, the government of country A may use trade policy instruments, such as import tariffs and import quotas.

 

Imposing an Import Tariff

 

 

Country A may choose to apply an import tariff to restirct imports to its territory. Import tariff can be used in the form of percentage on total imported value, i.e. import price. After imposing an import tariff, the import price will increase by tariff amount.

 

To illustrate price changes after imposing import tariff in country A, we will use the following procedure:

 

 

 

 

 

After imposing a set tariff rate, we can calculate import price and the results of trade flows for country A:

 

The graph demonstrates that after imposing an import tariff as a trade restrictive measure, several welfare effects can be observed. Namely:

 

area A+B+C+D - consumers' loss, area A - producers' surplus, C - government surplus (budget revenue), B+D - national loss.

 

The values of these welfare effects are calculated below:

 

 

Imposing an Import Quota

 

Country A may choose to apply an import quota to restirct imports to its territory. Import quota can be used to fix the quantity of import. After imposing an import quota, the import price will increase.

 

To illustrate price changes after imposing import tariff in country A, we will use the following procedure:

 

 

 

 

 

After imposing a fixed quota, we can calculate import price and the results of trade flows for country A:

 

The graph demonstrates that after imposing an import quota as a trade restrictive measure, several welfare effects can be observed. Namely:

 

area A+B+C+D - consumers' loss, area A - producers' surplus, C - government surplus (budget revenue), B+D - national loss.

 

The values of these welfare effects are calculated below:

Conclusion

 

The developed model of international trade above has demonstrated how trade between two countries occures given their domestic supply and demand functions of a particular product. It has also shown how international trade affects economic agents, i.e. consumers, producers and governments, of both countries and calculated welfare effects occuring from it. Moreover, the model developed above interactively demonstrates how trade policy instruments, namely tariffs and quotas, can be applied to show how imports for an importing country are restricted, how domestic price changes as a result of an import tariff or an import quota, and what welfare gains and losses can be incured by the economic agents of that country. In general, it has been shown that countries as a whole gain from trading with each other, but the potential gains from free international trade can be reduced as a result of trade policy instruments applied in an importing country to favor its producers and discourage its consumers.

References

 

Thomas A. Pugal, Peter H. Lindert. International Economics. Mc-Graw Hill, 2000

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