Question

suppose that the countries of finland, hungary, poland, and belgium are economically interdependent. the following table shows exports and imports between these countries, with all monetary values given in millions of euros.

country of origin	exporting to...	amount (€ x 1,000,000)
finland	poland	2,499
finland	belgium	3,913
hungary	finland	2,614
hungary	poland	3,970
hungary	belgium	2,380
poland	finland	3,496
poland	hungary	4,973
poland	belgium	2,971
belgium	finland	3,023
belgium	hungary	3,828
belgium	poland	4,656

if these four countries trade only with each other, what is the difference between the highest balance of trade and the lowest balance of trade within this group?

Explanation:

Step1: Calculate total exports for each country

- **Finland**:
- Exports to Hungary: 2,298
- Exports to Poland: 2,499
- Exports to Belgium: 3,913
- Exports to Finland? Wait, no, the table is about exports between the four countries. Wait, the "Country of Origin" and "Exporting to" are the two countries. So for each country of origin, we sum the amounts when exporting to others. Wait, actually, the trade balance for a country is (Total Exports - Total Imports). So first, we need to find for each country (Finland, Hungary, Poland, Belgium) the total exports (sum of all amounts where Country of Origin is that country) and total imports (sum of all amounts where Exporting to is that country).

Let's list all transactions:

Finland (Country of Origin):

- Exporting to Hungary: 2,614
- Exporting to Poland: 3,496
- Exporting to Belgium: 3,023
Wait, no, looking at the table:

Wait the table has columns: Country of Origin, Exporting to, Amount (€ x 1,000,000)

Let's list each row:

1. Country of Origin: Finland, Exporting to: Hungary, Amount: 2,298
2. Country of Origin: Finland, Exporting to: Poland, Amount: 2,499
3. Country of Origin: Finland, Exporting to: Belgium, Amount: 3,913
4. Country of Origin: Hungary, Exporting to: Finland, Amount: 2,614
5. Country of Origin: Hungary, Exporting to: Poland, Amount: 3,970
6. Country of Origin: Hungary, Exporting to: Belgium, Amount: 2,380
7. Country of Origin: Poland, Exporting to: Finland, Amount: 3,496
8. Country of Origin: Poland, Exporting to: Hungary, Amount: 4,973
9. Country of Origin: Poland, Exporting to: Belgium, Amount: 2,971
10. Country of Origin: Belgium, Exporting to: Finland, Amount: 3,023
11. Country of Origin: Belgium, Exporting to: Hungary, Amount: 3,828
12. Country of Origin: Belgium, Exporting to: Poland, Amount: 4,656

Now, for each country, calculate Total Exports (sum of Amount where Country of Origin is the country) and Total Imports (sum of Amount where Exporting to is the country).

Finland:

- Exports (Country of Origin = Finland):
- Row 1: 2,298 (to Hungary)
- Row 2: 2,499 (to Poland)
- Row 3: 3,913 (to Belgium)
Total Exports (Finland) = 2,298 + 2,499 + 3,913 = 8,710

- Imports (Exporting to = Finland):
- Row 4: Hungary to Finland: 2,614
- Row 7: Poland to Finland: 3,496
- Row 10: Belgium to Finland: 3,023
Total Imports (Finland) = 2,614 + 3,496 + 3,023 = 9,133
Trade Balance (Finland) = 8,710 - 9,133 = -423 (deficit)

Hungary:

- Exports (Country of Origin = Hungary):
- Row 4: 2,614 (to Finland)
- Row 5: 3,970 (to Poland)
- Row 6: 2,380 (to Belgium)
Wait no, looking at the table:

Wait the rows are:

Wait the original table rows (let's re-express correctly):

1. Country of Origin: Finland, Exporting to: Hungary, Amount: 2,298
2. Country of Origin: Finland, Exporting to: Poland, Amount: 2,499
3. Country of Origin: Finland, Exporting to: Belgium, Amount: 3,913
4. Country of Origin: Hungary, Exporting to: Finland, Amount: 2,614
5. Country of Origin: Hungary, Exporting to: Poland, Amount: 3,970
6. Country of Origin: Hungary, Exporting to: Belgium, Amount: 2,380
7. Country of Origin: Poland, Exporting to: Finland, Amount: 3,496
8. Country of Origin: Poland, Exporting to: Hungary, Amount: 4,973
9. Country of Origin: Poland, Exporting to: Belgium, Amount: 2,971
10. Country of Origin: Belgium, Exporting to: Finland, Amount: 3,023
11. Country of Origin: Belgium, Exporting to: Hungary, Amount: 3,828
12. Country of Origin: Belgium, Exporting to: Poland, Amount: 4,656

Ah, I see, I misread earlier. So each country of origin (Finland, Hungary, Poland, Belgium) has three exports (to the other three countries). So:

Finland (Country of Origin):

- To Hungary: 2,298
- To Poland: 2,499
- To Belgium: 3,913
Total Exports (Finland) = 2,298 + 2,499 + 3,913 = 8,710

Hungary (Country of Origin):

- To Finland: 2,614
- To Poland: 3,970
- To Belgium: 2,380
Total Exports (Hungary) = 2,614 + 3,970 + 2,380 = 8,964

Poland (Country of Origin):

- To Finland: 3,496
- To Hungary: 4,973
- To Belgium: 2,971
Total Exports (Poland) = 3,496 + 4,973 + 2,971 = 11,440

Belgium (Country of Origin):

- To Finland: 3,023
- To Hungary: 3,828
- To Poland: 4,656
Total Exports (Belgium) = 3,023 + 3,828 + 4,656 = 11,507

Now, Total Imports for each country is the sum of all amounts where "Exporting to" is that country:

Finland (Importing, i.e., Exporting to = Finland):

- From Hungary: 2,614 (row 4)
- From Poland: 3,496 (row 7)
- From Belgium: 3,023 (row 10)
Total Imports (Finland) = 2,614 + 3,496 + 3,023 = 9,133

Hungary (Importing, Exporting to = Hungary):

- From Finland: 2,298 (row 1)
- From Poland: 4,973 (row 8)
- From Belgium: 3,828 (row 11)
Total Imports (Hungary) = 2,298 + 4,973 + 3,828 = 11,099

Poland (Importing, Exporting to = Poland):

- From Finland: 2,499 (row 2)
- From Hungary: 3,970 (row 5)
- From Belgium: 4,656 (row 12)
Total Imports (Poland) = 2,499 + 3,970 + 4,656 = 11,125

Belgium (Importing, Exporting to = Belgium):

- From Finland: 3,913 (row 3)
- From Hungary: 2,380 (row 6)
- From Poland: 2,971 (row 9)
Total Imports (Belgium) = 3,913 + 2,380 + 2,971 = 9,264

Now, Trade Balance for each country:

- Finland: Exports (8,710) - Imports (9,133) = -423
- Hungary: Exports (8,964) - Imports (11,099) = -2,135
- Poland: Exports (11,440) - Imports (11,125) = 315
- Belgium: Exports (11,507) - Imports (9,264) = 2,243

Now, we need to find the highest and lowest trade balances.

Highest trade balance: Belgium (2,243)
Lowest trade balance: Hungary (-2,135)

Wait, but let's check the calculations again:

Finland Exports:

Rows where Country of Origin is Finland:
- Exporting to Hungary: 2,298 (row 1)
- Exporting to Poland: 2,499 (row 2)
- Exporting to Belgium: 3,913 (row 3)
Sum: 2,298 + 2,499 = 4,797; 4,797 + 3,913 = 8,710 ✔️

Finland Imports (Exporting to Finland):

- From Hungary: 2,614 (row 4)
- From Poland: 3,496 (row 7)
- From Belgium: 3,023 (row 10)
Sum: 2,614 + 3,496 = 6,110; 6,110 + 3,023 = 9,133 ✔️
Balance: 8,710 - 9,133 = -423 ✔️

Hungary Exports (Country of Origin = Hungary):

- Exporting to Finland: 2,614 (row 4)
- Exporting to Poland: 3,970 (row 5)
- Exporting to Belgium: 2,380 (row 6)
Sum: 2,614 + 3,970 = 6,584; 6,584 + 2,380 = 8,964 ✔️

Hungary Imports (Exporting to Hungary):

- From Finland: 2,298 (row 1)
- From Poland: 4,973 (row 8)
- From Belgium: 3,828 (row 11)
Sum: 2,298 + 4,973 = 7,271; 7,271 + 3,828 = 11,099 ✔️
Balance: 8,964 - 11,099 = -2,135 ✔️

Poland Exports (Country of Origin = Poland):

- Exporting to Finland: 3,496 (row 7)
- Exporting to Hungary: 4,973 (row 8)
- Exporting to Belgium: 2,971 (row 9)
Sum: 3,496 + 4,973 = 8,469; 8,469 + 2,971 = 11,440 ✔️

Poland Imports (Exporting to Poland):

- From Finland: 2,499 (row 2)
- From Hungary: 3,970 (row 5)
- From Belgium: 4,656 (row 12)
Sum: 2,499 + 3,970 = 6,469; 6,469 + 4,656 = 11,125 ✔️
Balance: 11,440 - 11,125 = 315 ✔️

Belgium Exports (Country of Origin = Belgium):

- Exporting to Finland: 3,023 (row 10)
- Exporting to Hungary: 3,828 (row 11)
- Exporting to Poland: 4,656 (row 12)
Sum: 3,023 + 3,828 = 6,851; 6,851 + 4,656 = 11,507 ✔️

Belgium Imports (Exporting to Belgium):

- From Finland: 3,913 (row 3)
- From Hungary: 2,380 (row 6)
- From Poland: 2,971 (row 9)
Sum: 3,913 + 2,380 = 6,293; 6,293 + 2,971 = 9,264 ✔️
Balance: 11,507 - 9,264 = 2,243 ✔️

Now, the trade balances are:
- Finland: -423
- Hungary: -2,135
- Poland: 315
- Belgium: 2,243

Highest balance: 2,243 (Belgium)
Lowest balance: -2,135 (Hungary)

Step2: Calculate the difference between highest and lowest

Difference = Highest - Lowest = 2,243 - (-2,135) = 2,243 + 2,135 = 4,378

Wait, but let's check the numbers again. Wait the problem says "the difference between the highest balance of trade and the lowest balance of trade within this group".

Highest balance: 2,243 (Belgium)
Lowest balance: -2,135 (Hungary)
Difference: 2,243 - (-2,135) = 2,243 + 2,135 = 4,378 (in millions of euros, since the amount is € x 1,000,000)

Wait, but let's confirm the calculations once more:

Belgium's balance: 11,507 - 9,264 = 2,243 ✔️

Hungary's balance: 8,964 - 11,099 = -2,135 ✔️

Difference: 2,243 - (-2,135) = 4,378 ✔️

Answer:

4378 (in millions of euros, so the difference is 4,378 million euros, which is €4,378,000,000)