Three countries — Pumpland (P), Xiland (X) and Cheeseland (C) — trade among themselves and with the (other countries in) Rest of World (ROW). All trade volumes are given in IC (international currency). The following terminology is used:

• Trade balance = Exports - Imports

• Total trade = Exports + Imports

• Normalized trade balance = Trade balance / Total trade, expressed in percentage terms

The following information is known.

1. The normalized trade balances of P, X and C are 0%, 10%, and -20%, respectively.

2. 40% of exports of X are to P. 22% of imports of P are from X.

3. 90% of exports of C are to P; 4% are to ROW.

4. 12% of exports of ROW are to X, 40% are to P.

5. The export volumes of P, in IC, to X and C are 600 and 1200, respectively. P is the only country that exports to C.

How much is exported from P to ROW, in IC?

The correct answer is 200.

Let us break down the problem step-by-step using the given trade definitions and relationships.

1. Definitions and Setup
Let $E$ represent exports and $I$ represent imports. For Pumpland (P), Xiland (X), and Cheeseland (C), we define their total exports and imports as:
• $E_P,I_P$
• $E_X,I_X$
��� $E_C,I_C$
Let $E_{\mathrm{ROW}}$ be the total exports of the Rest of World (ROW).

2. Establishing Country-Specific Trade Ratios
From Statement 1, the normalized trade balances are:
• For Pumpland (P), the normalized trade balance is 0%:

$\frac{E_P-I_P}{E_P+I_P}=0\Rightarrow E_P=I_P$

• For Cheeseland (C), the normalized trade balance is -20%:

$\frac{E_C-I_C}{E_C+I_C}=-0.20\Rightarrow I_C=1.5E_C$

• For Xiland (X), the normalized trade balance is 10%:

$\frac{E_X-I_X}{E_X+I_X}=0.10\Rightarrow I_X=\frac{9}{11}$

3. Calculating Cheeseland's (C) Trade
From Statement 5, Pumpland is the only country that exports to C, and P's export to C is 1200. This means Cheeseland's total imports are:
$I_C=1200$
Using our relation $I_C=1.5E_C$, we find C's total exports:

$E_C=\frac{1200}{1.5}=800$

From Statement 3, C's exports are distributed as follows:
• To P: $90\%of{E}_C=0.90\times 800=720$
• To ROW: $4\%of{E}_C=0.04\times 800=32$
• To X: $(100\%-90\%-4\%)=6\%of{E}_C=0.06\times 800=48$

4. Setting up Xiland's (X) Trade Relations
From Statement 2:
• 40% of X's exports go to P: $E_{X\to P}=0.40E_X$
• 22% of P's imports come from X: $I_{P\leftarrow X}=0.22I_P$
Since $E_{X\to P}=I_{P\leftarrow X}$:

$0.40E_X=0.22I_P\Rightarrow E_X=0.55I_P$

Substituting this into the import equation for X:

$I_X=\frac{9}{11}$

5. Using Import Equations to Solve for Pumpland's Total Imports ($I_P$)
Pumpland's imports come from X, C, and ROW:
$I_P=I_{P\leftarrow X}+I_{P\leftarrow C}+I_{P\leftarrow \mathrm{ROW}}$
Using Statement 4 (40% of ROW exports go to P) and the calculated values:
• $I_{P\leftarrow X}=0.22I_P$
• $I_{P\leftarrow C}=720$
• $I_{P\leftarrow \mathrm{ROW}}=0.40E_{\mathrm{ROW}}$

So, we obtain the first equation:

$I_P=0.22I_P+720+0.40E_{\mathrm{ROW}}\Rightarrow 0.78I_P-0.40E_{\mathrm{ROW}}=720$   — (Equation 1)

Similarly, Xiland's imports come from P, C, and ROW:
$I_X=I_{X\leftarrow P}+I_{X\leftarrow C}+I_{X\leftarrow \mathrm{ROW}}$
Using Statements 4 and 5:
• $I_{X\leftarrow P}=600$
• $I_{X\leftarrow C}=48$
• $I_{X\leftarrow \mathrm{ROW}}=0.12E_{\mathrm{ROW}}$
And we know $I_X=0.45I_P$.

So, we obtain the second equation:

$0.45I_P=600+48+0.12E_{\mathrm{ROW}}\Rightarrow 0.45I_P-0.12E_{\mathrm{ROW}}=648$   — (Equation 2)

Now, let's solve Equations 1 and 2. Multiplying Equation 2 by $\frac{0.40}{0.12}=\frac{10}{3}$:

$1.50I_P-0.40E_{\mathrm{ROW}}=2160$   — (Equation 3)

Subtracting Equation 1 from Equation 3:

$(1.50-0.78)I_P=2160-720$

$0.72I_P=1440\Rightarrow I_P=2000$

6. Finding Pumpland's exports to ROW
Since P's trade balance is normalized to 0%, its exports equal its imports:
$E_P=I_P=2000$

P's total exports are distributed to X, C, and ROW:
$E_P=E_{P\to X}+E_{P\to C}+E_{P\to \mathrm{ROW}}$

Substituting the known values:
$2000=600+1200+E_{P\to \mathrm{ROW}}$
$E_{P\to \mathrm{ROW}}=2000-1800=200$

Thus, Pumpland exports 200 IC to the Rest of the World.