Question Details

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 C to X, in IC?

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Correct Answer :

Solution :

The correct answer is 48.

Here is the step-by-step derivation to find the export volume from Cheeseland (C) to Xiland (X):

Step 1: Understand the trade equations for Cheeseland (C)
Let $E_{C}$ be the total exports of Cheeseland and $I_{C}$ be the total imports of Cheeseland.
We are given that the normalized trade balance of C is -20% (or -0.2). Using the definition of normalized trade balance:

$\frac{E_{C} - I_{C}}{E_{C} + I_{C}} = - 0.2$

By cross-multiplying and solving for $I_{C}$ :

$E_{C} - I_{C} = - 0.2 (E_{C} + I_{C})$

$E_{C} - I_{C} = - 0.2 E_{C} - 0.2 I_{C}$

$1.2 E_{C} = 0.8 I_{C}$

$I_{C} = 1.5 E_{C}$

Step 2: Calculate Cheeseland's total imports ( $I_{C}$ )
According to statement 5, the export volume of Pumpland (P) to C is 1200 IC, and P is the only country that exports to C. Therefore, all imports of C come exclusively from P:

$I_{C} = 1200$

Step 3: Calculate Cheeseland's total exports ( $E_{C}$ )
Substitute the value of $I_{C}$ into the relation derived in Step 1:

$1200 = 1.5 E_{C}$

$E_{C} = \frac{1200}{1.5} = 800$

Step 4: Determine exports from Cheeseland to Xiland
According to statement 3, the distribution of C's exports is as follows:
• 90% of C's exports are to P.
• 4% of C's exports are to ROW.
Since C only trades among P, X, C, and ROW, the remainder of C's exports must go to Xiland (X):

$Percentage exported to X = 100 % - 90 % - 4 % = 6 %$