Leontief Input-Output Analysis A way to analyze economics of interdependent sectors Case study: Oil and Transportation –Transportation requires gasoline from the oil industry transportation of equipment from the transportation industry –Oil production requires transportation of gasoline from the transportation industry oil-based fuels for processing from the oil industry –We will look at a single oil company and a single transportation company as a closed system

Some basic calculations Oil Industry Cost of producing $1 worth of gas: –$.32 in oil costs –$.12 in transportation costs Transportation industry Cost of producing $1 worth of transportation: –$.50 in gas costs –$.20 in transportation costs Suppose that the demand from the outside sector of the economy (all consumers outside of oil and transportation) is: –$15 billion for oil –$1.2 billion for transportation If the companies produce exactly this amount, then the amount used in production is: –.32(15) +.50(1.2) = $5.4 billion in oil –.12(15) +.20(1.2) = $2.0 billion in transportation This leaves only $9.6 billion of oil and $1.0 billion of transportation to meet the demand.

Leontief analysis allows us to calculate how much each company should produce to meet a given demand Let x = the total output from oil company Let y = the total output from transportation company The internal demand for each is the combined demand from the oil industry and from the transportation industry

Setting up the demand equations The total output of each company will equal the sum of the internal and external demands: Expressed as a matrix equation:

Solving the demand equations Solve for X: In our example:

The solution Putting it all together: In order to meet the demand the companies need to produce –$20.8 billion of oil –$4.4 billion of transportation