Leontief Input Output Part 1 Purpose Analyzes flow

Leontief Input Output Part 1

Purpose �Analyzes flow of goods and services among sectors in an economy. �Can be used for extremely complex economies with hundreds of production sectors, such as a country, or to a single company that produces one product.

Communicate Effectively �Sectors of the economy: A grouping of the economy by the type of activity or service performed. �Consumption Matrix: A simple way for a manufacturer to describe internal use of their product. �Demand (D): The amount of product or service a company can sell. �Total Production: The amount of product that a company can make. 1/22/2022 3

Math Term – you already know! �Digraph: A graph with directed edges. �Directed mean only traveling one direction: A to B and B to B A 1/22/2022 B A B 4

Best Battery Company �Produces a battery that is used to power electric motors �However, not all can be sold �For every 100 batteries, 3 are used by various departments in the company �Thus, if 500 batteries are produced, 15 are used internally, and 485 can be sold.

Demand �P – 0. 03 P = D �What if we need receive an order for 5, 000 batteries?

2 sector economy �Given � For the battery division to produce 100 batteries it must use 3. � For every 100 batteries produced 1 motor is required from the motor division � For a motor division to produce 100 motors, it must use 4 (4%) of its own motors. � For every 100 motors produced, 8 batteries are required from the battery division. 1/22/2022 7

Digraph 0. 08 0. 03 0. 04 B M 0. 01 1. The battery division will require 0. 03 b from its own division and 0. 01 b motors from the motor division. 2. The motor division will require 0. 04 m motors from its division and 0. 08 m batteries from the battery division 1/22/2022 8

Technology Matrix

Leontief Input-Output Day 2

Leontief can get tricky! �The model becomes tricky quickly, even when dealing with only 1 and 2 sector economies. �There is an easier way! What do you think it is?

Recall the Battery – Motor Problem To 1/22/2022 From Battery Motor Battery . 03 . 08 Motor. 01 . 04 12

Standard Equations 1 of 2 Total Production = P External Demand = D Consumption Matrix = T Total Production = internal consumption + external demand. or P = TP + D P = (I –T)-1 D (If we know T and D, we can find P) *I = identity matrix 1/22/2022 13

We want… � 400 batteries and 100 motors

Standard Equations 2 of 2 1/22/2022 15