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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

This note was uploaded on 12/29/2010 for the course ECON 4313 taught by Professor Staff during the Fall '08 term at Minnesota.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online