Question

(1 point) We assume that in a village there are farmers, carpenters, and tailors, who provide the three essential goods: food, housing, and clothing. Suppose the farmers consume of the food (produced by farmers), of the housing (produced by carpenters) and 륵 of the clothes (produced by tailors) The carpenter consumes of the food of the housing, and of the clothes. The tailors consu me of the food of the housing, and no clothes. Assume this is a closed Leontief model. If we know that the tailors produce 200 units of clothes, then the farmers produce units of food, and the carpenters produce i units of housing.

Answer 1

"Let former produced units of food carpenter produces y units of house . Tailor produce z units of cloths Therefore 2/5 x + 1/ 3 y + 1/2 z = x 2/5 x + 1/3 y + 1/2 z = y 1/5 x + 1/ 3 y + 0.z = z the system of equation can be written as -3/5 x + 1/3 y + 1/2 z = 0.......1 2/5 x - 2/3 y + 1/ z = 0.........2 1/5 x + 1/3 y - z = 0............3 Now solve these three equation by Gauss method [-3/5 2/5 1/5 1/3 -2/3 1/3 1/2 1/2 -1][0 0 0] App 5R_1 rightarrow R_1 5R_2 rightarrow R_2 5R_3 rightarrow R_3 [-3 2 1 5/3 -10/3 5/3 5/2 5/2 -5