Question

HW11: Problem 5 Previous Problem Problem List Next Problem 1 point Consider an international trade model consisting of three countries XX and Z. Suppose X uses of its production domestically, sends 횰 of its production toY and sends ¼ of its production to Z Suppose Y uses of its production domestically, sends of its production to X, and sends 3 of its production to Z. Suppose Z uses of its domestic goods, sends of its production to X and sends 측 of its production to Y. Assume this is a closed Leontief model. If we know country Z produced 256 thousand units of goods, then country X produces thousand units of goods, and country Y produces thousand units of goods.

Answer 1

Let us consider A = [1/4 2/5 1/4 1/2 1/5 1/2 1/4 2/5 1/4] let X = [x y z] here, x, y, z represents the units of goods produced by 3 countries respectively. we know, AX = X [1/4 2/5 1/4 1/2 1/5 1/2 1/4 2/5 1/4] [x y z] = [x y z] [x/4 + 2y/5 + z/4 x/2 + y/5 + z/2 x/4 + 2y/5 + z/4] = [x y z] In Q from, x/4 + 2y/5 + z/4 = x rightarrow (1) x/2 + y/5 + z/2 = y rightarrow (2) x/4 + 2/5 y + z/4 = z rightarrow (3) \r\n It is given that, can try z produced 256 thousand units i.e., z = 256 from equation (2) and (3) we get., equation (1) = equation (3)