MAT 122 Lecture 16: Input Output Models
Document Summary
Input output models: also known as- leontief input-output model, using and producing some products, example, an energy company produces electricity, natural gas and oil. To produce one unit of electricity- 1/2 unit of electricity, 1/3 unit of gas, 1/4 unit of oil. One unit of gas- 1/4 unit of electricity, 1/4 unit of gas, 1/3 unit of oil. Question a: make the problem into equations e= electricity = 1/2x + 1/4y + 1/3z g= gas = 1/3x + 1/4y + 1/3z o= oil = 1/4x + 1/3y + 1/4z, make the equations into a matrix. 1/4 1/3 1/4 x y z e g. Amount for sale (d) = amount produced (x) - amount used in production (ax) D = (i-a)x x = (i-a)-1d: solve for the equation x = (i-a)-1d. *note that 74, 37, 111 are all multiples of 37. 1 unit of agriculture = 1/4 manufacturing & 1/2 transportation. 1 unit of manufacture = 1/2 agriculture & 1/4 transportation.
