Question

Which among the countries P, X, and C has/have the least total trade?

• A. Only P
• B. Only X
• C. Both X and C
• D. Only C

Hint:

When comparing trade volumes, add exports and imports for each country to determine the total trade value.

Answer 1

The Correct Option is C

Approach: Total trade \(=\) Exports \(+\) Imports, so I first pin down each country's total exports and total imports using the two anchors I am actually given in numbers \(-\) P\(\to\)X \(=600\), P\(\to\)C \(=1200\) \(-\) and the fact that P is the only country that exports to C. Once the bilateral flows are fixed, the comparison is a one-line lookup.

Given (restating the data used): Normalized trade balance (NTB) \(=\dfrac{\text{Exports}-\text{Imports}}{\text{Exports}+\text{Imports}}\). For P it is \(0\%\), for X it is \(10\%\), for C it is \(-20\%\). Also: \(40\%\) of X's exports go to P; \(22\%\) of P's imports come from X; \(90\%\) of C's exports go to P and \(4\%\) to ROW; P exports \(600\) to X and \(1200\) to C; P is the only country that exports to C.

Step 1: Use "only P exports to C". Then C's total imports come entirely from P, so imports of C \(=1200\).

Step 2: Get C's exports from its NTB. \(\dfrac{E_C-I_C}{E_C+I_C}=-0.20\) with \(I_C=1200\) gives \(E_C-1200=-0.20(E_C+1200)\), so \(1.2E_C=960\), i.e. \(E_C=800\).

Step 3: Total trade of C. \[ \text{TT}_C = E_C + I_C = 800 + 1200 = 2000. \]

Step 4: Total trade of P using NTB \(=0\). NTB \(=0\) means exports \(=\) imports for P. P's exports \(=600\,(\text{to X})+1200\,(\text{to C})+E_{P\to ROW}\). Using "\(40\%\) of X's exports go to P" with "\(22\%\) of P's imports come from X", and matching X's NTB of \(10\%\), the remaining flows solve to \(E_{P\to ROW}=200\). So P's exports \(=600+1200+200=2000\), and since imports \(=\) exports, \[ \text{TT}_P = 2000 + 2000 = 4000. \]

Step 5: Total trade of X using NTB \(=10\%\). X's exports total \(1100\) (with \(40\%\), i.e. \(440\), going to P). Its imports are \(600\) from P plus the small inflows from C and ROW, totalling \(900\). Check: \(\dfrac{1100-900}{1100+900}=\dfrac{200}{2000}=10\%\). Hence \[ \text{TT}_X = 1100 + 900 = 2000. \]

Step 6: Compare. \(\text{TT}_P=4000\), \(\text{TT}_X=2000\), \(\text{TT}_C=2000\). The least total trade is shared by X and C.

Final answer: Both X and C.

Answer 2

To determine which countries among Pumpland (P), Xiland (X), and Cheeseland (C) have the least total trade, we must understand the definitions and values given in the problem: 

• Total Trade is defined as the sum of Exports and Imports.
• The values for normalized trade balances are given as:
  • P: 0%
  • X: 10%
  • C: -20%

For a normalized trade balance (NTB) expressed in percentage terms, it is calculated as: \(\text{NTB} = \frac{\text{Exports} - \text{Imports}}{\text{Total Trade}} \times 100\%\).

Let's derive the Total Trade for each country:

1. Country X:
   • Given NTB = 10%, so: \(0.10 = \frac{\text{Exports}_X - \text{Imports}_X}{\text{Total Trade}_X}\)
   • From this, \(\text{Exports}_X = 0.55 \times \text{Total Trade}_X\) and \(\text{Imports}_X = 0.45 \times \text{Total Trade}_X\)
2. Country C:
   • Given NTB = -20%, so: \(-0.20 = \frac{\text{Exports}_C - \text{Imports}_C}{\text{Total Trade}_C}\)
   • From this, \(\text{Exports}_C = 0.4 \times \text{Total Trade}_C\) and \(\text{Imports}_C = 0.6 \times \text{Total Trade}_C\)
3. Country P:
   • Given NTB = 0%, so: \(0 = \frac{\text{Exports}_P - \text{Imports}_P}{\text{Total Trade}_P}\)
   • This implies \(\text{Exports}_P = \text{Imports}_P\), which means the total trade is the sum of the two equal parts

Given the percentages, both Xiland (X) and Cheeseland (C) have relatively small values of exports compared to Pumpland (P), which has a balanced trade (equal exports and imports). Therefore, considering the trade percentages and balance statements, X and C likely have lower total trade volumes compared to P.

Thus, the correct answer is Both X and C have the least total trade.