# Input - a 12 = 2 200 = 1000 a 21 ⇒ a 21 = 2 50 = 500 a 22...

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1 1 Question Last year, 1000 tons of grain and 500 tons of steel were produced. The steel industry used 200 tons of grain and 50 tons of steel, and the grain industry used 50 tons of grain and 100 tons of steel. (INFO 1) This year, the government wants 50 tons of grain and 300 tons of steel, foreigners want 200 tons of grain and no steel, and consumers want 800 tons of grain and 100 tons of steel. There are no other sources of demand. (INFO 2) In addition, the country is importing 100 tons of steel this year. It is not importing grain. 200 tons of grain and 0 tons of steel are left over from last year. (INFO 3)) Use input-output analysis to determine much steel and grain will be produced this year. 2 Solution Let good 1 be grain and good 2 steel. In the notation of http://www.econ.umn.edu/ evdok003/planning.pdf , you need to solve the following system of equations. V 1 + M 1 + X 1 = X 11 + X 12 + Y 1 V 2 + M 2 + X 2 = X 12 + X 22 + Y 2 Assuming Leontief production, V 1 + M 1 + X 1 = X 1 * a 11 + X 2 * a 12 + Y 1 V 2 + M 2 + X 2 = X 1 * a 12 + X 2 * a 22 + Y 2 Using INFO1, 50 = 1000 * a 11 a 11 = . 05 100 = 500 * a 12

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Unformatted text preview: a 12 = . 2 200 = 1000 * a 21 ⇒ a 21 = . 2 50 = 500 * a 22 ⇒ a 22 = . 1 Using INFO2, Y 1 = 1050 and Y 2 = 400. (Remember that the Y s are demands for steel and grain as ﬁnal goods. Total demand = Govt. demand + Consumer demand + Foreigners’ demand.) 2 Using INFO3, M 1 = ,M 2 = 100 ,V 1 = 200 ,M 2 = 0. Plugging everything into the two equations you need to solve, get 200 + X 1 = . 05 X 1 + . 2 X 2 + 1050 100 + X 2 = . 2 X 1 + . 1 X 2 + 400 Solve for X 1 in the ﬁrst equation: X 1 = 1 . 95 ( . 2 X 2 + 850 ) Plug this expression for X 1 into the second equation, 100 + X 2 = . 2 1 . 95 ( . 2 X 2 + 850 ) + . 1 X 2 + 400 You can use simple algebra to solve this for X 2 . If you round the solution to the integer, you should get X 2 = 554 . Plug this back into the expression for X 1 (and round) to get X 1 = 1011. Therefore, the state should produce 1011 tons of grain and 554 tons of steel....
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## This note was uploaded on 12/29/2010 for the course ECON 4313 taught by Professor Staff during the Fall '08 term at Minnesota.

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Input - a 12 = 2 200 = 1000 a 21 ⇒ a 21 = 2 50 = 500 a 22...

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