Leontief Input-Output Analysis

1. 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

2. 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.

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

4. 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:

5. Solving the demand equations • Solve for X: • In our example:

6. 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