Question

Page 10 of 10 Assume an open economy with two sectors, Food and Water. The production of $1,00 worth of Food needs S0.10 worth of Food and $0.30 worth of Water, and the production of $1,00 worth of Water needs $0.40 worth of Food and S0.20 worth of Water. a. Determine the consumption and Leontief matrices. (3 points) b. If the open sector has a demand of $12 worth of Food and $8 worth of Water, find the production vector that will meet this demand exactly. (7 points)

Answer 1

The given data is * Assume an open economy with two sectors food and water. rightarrow production of = $1.00 rightarrow worth of food needs = $0.10. & worth of food = $0.30 worth of water = $0.30 production = $1.00 worth water needs = $0.40 worth of water = $0.20 rightarrow Now, we have to determine the consumption of consumption matrix A = [0.10 0.10 0.20 0.20 0.10 0.30 0.40 0.30 0.10] Demand [60 40 50] Cl Ng T \r\n Leontief matrix I - A [1 0 0 0 1 0 0 0 1] - [0.10 0.10 0.20 0.20 0.10 0.30 0.40 0.30 0.10] = [-0.90 -0.10 -0.20 -0.20 0.90 -0.30 -0.40 -0.30 0.90] I - A = 0.90 (0.81 - 0.09) + 0.20 (-0.09 - 0.06) - 0.40(0.03) + 0.18 = 0.90 (0.72) + 0.20 (-0.84) - 0.40(0.21) = 0.648 - 0.64 - 0.084 I - A = 0.534 rightarrow (I - A) is positive and all diagonal element of A are less than 1. rightarrow Hence the system is variable.