Mindyard | 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 ROW to ROW, in IC?

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 ROW to ROW, in IC?

Correct Answer :

1008

Solution :

The correct answer is 1008.

To determine the export volume from the Rest of the World (ROW) to itself, we analyze the trade relations between Pumpland (P), Xiland (X), Cheeseland (C), and ROW. Let us define the variables for each country/entity:
Let _{E_P}, _{E_X}, _{E_C}, and _{E_ROW} be the total export volumes of P, X, C, and ROW, respectively.
Let _{I_P}, _{I_X}, _{I_C}, and _{I_ROW} be the total import volumes of P, X, C, and ROW, respectively.

Step 1: Relate total exports and total imports using normalized trade balances

The normalized trade balance is defined as:
$Normalized Trade Balance = \frac{Exports - Imports}{Exports + Imports}$

For Pumpland (P), the normalized trade balance is 0%:
$\frac{E_{P} - I_{P}}{E_{P} + I_{P}}$

For Xiland (X), the normalized trade balance is 10%:
$\frac{E_{X} - I_{X}}{E_{X} + I_{X}} = 0.10 \Rightarrow E_{X} - I_{X} = 0.10 (E_{X} + I_{X}) \Rightarrow 0.9 E_{X} = 1.1 I_{X} \Rightarrow I_{X} = \frac{9}{11}$

For Cheeseland (C), the normalized trade balance is -20%:
$\frac{E_{C} - I_{C}}{E_{C} + I_{C}} = - 0.20 \Rightarrow E_{C} - I_{C} = - 0.20 (E_{C} + I_{C}) \Rightarrow 1.2 E_{C} = 0.8 I_{C} \Rightarrow I_{C} = 1.5 E_{C}$

Step 2: Determine trade details for Cheeseland (C)

We are given that P is the only country that exports to C. Thus, all of C's imports come from P:
$I_{C} = Exports of P to C = 1200$
Using our relation for Cheeseland's trade:
$1200 = 1.5 E_{C} \Rightarrow E_{C} = 800$

Now we calculate C's exports to other regions using the given percentages:
• Exports of C to P: 90% of C's exports = 0.90 × 800 = 720
• Exports of C to ROW: 4% of C's exports = 0.04 × 800 = 32
• Exports of C to X: The remaining 6% of C's exports (since C only trades with P, X, and ROW) = 0.06 × 800 = 48

Step 3: Analyze Pumpland's imports and exports to relate E_X and E_P

From Point 2, 40% of the exports of X are to P:
$Exports from X to P = 0.40 E_{X}$
Also from Point 2, 22% of the imports of P are from X:
$Imports of P from X = 0.22 I_{P}$
Since the imports of P from X must equal the exports of X to P:
$0.40 E_{X} = 0.22 I_{P} \Rightarrow I_{P} = \frac{20}{11}$
Since _{E_P} = _{I_P}, we also have:
$E_{P} = \frac{20}{11}$

Step 4: Formulate the system of equations for E_X and E_ROW

First, let's look at the total imports of Pumpland (P). P imports from X, C, and ROW:
$I_{P} = (Imports from X) + (Imports from C) + (Imports from ROW)$
We know:
• Imports from X = 0.40 _{E_X}
• Imports from C = 720
• Imports from ROW = 40% of ROW exports = 0.40 _{E_ROW}
Thus:
$I_{P} = 0.40 E_{X} + 720 + 0.40 E_{ROW}$
Substitute _{I_P} = $\frac{20}{11}$ :
$\frac{20}{11}$
Subtracting 0.40 _{E_X} (which is 2/5 _{E_X}) from both sides:
$(\frac{20}{11}) E_{X} - 0.40 E_{ROW} = 720$
$\frac{78}{55}$

Next, let's write the equation for the total imports of Xiland (X). X imports from P, C, and ROW:
• Imports from P = 600
• Imports from C = 48
• Imports from ROW = 12% of ROW exports = 0.12 _{E_ROW}
Thus:
$I_{X} = 600 + 48 + 0.12 E_{ROW} = 648 + 0.12 E_{ROW}$
Since $I_{X} = \frac{9}{11}$ , we have:
$\frac{9}{11}$

Step 5: Solve the system of equations

From Equation 2, express _{E_X} in terms of _{E_ROW}:
$E_{X} = \frac{11}{9}$
Substitute this into Equation 1:
$\frac{78}{55}$
Expanding:
$1123.2 + 0.208 E_{ROW} - 0.40 E_{ROW} = 720$
$1123.2 - 0.192 E_{ROW} = 720$
$0.192 E_{ROW} = 403.2 \Rightarrow E_{ROW} = 2100$

Step 6: Compute exports from ROW to ROW

The total exports of ROW are distributed as follows:
• Exports to P: 40% of _{E_ROW}
• Exports to X: 12% of _{E_ROW}
• Exports to C: 0% (since Pumpland is the only country exporting to C)
• Exports to ROW (itself): The remaining portion, which is:
$100 % - 40 % - 12 % - 0 % = 48 %$

Therefore, the volume exported from ROW to ROW is:
$Exports from ROW to ROW = 0.48 \times 2100 = 1008$

Get 3 Months FREE trial

Create, conduct, and manage professional online assessments with Mindyard. Perfect for teachers and institutes.

Unlock Our Free Library

You may also like

Study Material

Clat 2019 UG Question Paper with Solution

Clat 2018 UG Question Paper with Solution

Mock Tests

Clat 2015 UG

Clat 2019 UG

Ask AI Tutor