Question

2. Consider an international trade model consisting of three countries, A, B, and C. Suppose that: A spends 1/4 of its income on domestic goods, 1/2 of its income on imports from B, and 1/4 of its income on imports from C. B spends 2/5 of its income on imports from A, 1/5 of its income on domestic goods, and 2/5 of its income on imports from C. C spends 1/4 of its income on imports from A, 1/2 of its income on imports from B and 1/4 of its income on domestic goods. Find the ratio of the incomes of the three countries.

Answer 1

By given conditions, (A/2)+(C/2) = B

(A/4)+(2B/5) = C

(2B/5)+(C/4) = A

i.e., A+C = 2B.......(i)

5A+8B = 20C.......(ii)

8B+5C = 20A..........(iii)

Now, multiplying (i) by 5 and then subtracting from (ii) we get, 8B-5C = 20C-10B

i.e., 18B = 25C

i.e., B/25 = C/18........(iv)

Again, subtracting (ii) from (iii) we get, 5C-5A = 20A-20C

i.e., 25C = 25A

i.e., C = A......(v)

From (iv) and (v) we have, A/18 = B/25 = C/18

Therefore, A:B:C = 18:25:18

Hence, ratio of their income is 18:25:18.