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The Leontief Input-Output Method, Part 1

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The Leontief Input-Output Method, Part 1

The Leontief Input-Output Method was developed by Wassily Leontief (1906-1999).

The Leontief Input-Output Method, Part 1

The Leontief Input-Output Method was developed by Wassily Leontief (1906-1999).

He used this method to study the interactions between different sectors of the U.S. economy. His examples studied the interactions of about 70 different sectors, but our examples will be simpler than that.

The Leontief Input-Output Method, Part 1

The Leontief Input-Output Method can take advantage of two strategies we have previously studied:

Graph Theory and Matrices

The Leontief Input-Output Method, Part 1

Example 1: Sunny Summer Beverages produces and bottles a variety of fruit juices. For every dollar worth of juice it produces, it keeps $.04 worth of juice in house to help keep the workers hydrated and happy.

If the company produces $200 worth of juice, how much will be available for sale?

The Leontief Input-Output Method, Part 1

Example 1: Sunny Summer Beverages produces and bottles a variety of fruit juices. For every dollar worth of juice it produces, it keeps $.04 worth of juice in house to help keep the workers hydrated and happy.

P - .04P = D

.96P = D

.96(200) = $192 = D

D: Demand

P: Total Production

The Leontief Input-Output Method, Part 1

Example 1: Sunny Summer Beverages produces and bottles a variety of fruit juices. For every dollar worth of juice it produces, it keeps $.04 worth of juice in house to help keep the workers hydrated and happy.

How much juice must the company produce in order to sell $300 worth?

The Leontief Input-Output Method, Part 1

P - .04 P = D

.96P = 300

P = $312.50

The Leontief Input-Output Method, Part 1

Example 2: ABC Furniture manufactures a variety of office furniture. It also manufactures bolts, some of which are used in its furniture. Every dollar worth of bolts produced requires an input of $.03 worth of bolts and $.02 worth of office furniture. Each dollar worth of office furniture requires an input of $.04 worth of bolts and $.05 worth of office furniture.

The Leontief Input-Output Method, Part 1

Example 2: $1 of bolts requires: $.03 bolts, $.02 office furniture. $1 of office furniture requires: $.04 of bolts, $.05 of office furniture.

Draw a weighted digraph that represents this situation.

The Leontief Input-Output Method, Part 1

Example 2: $1 of bolts requires: $.03 bolts, $.02 office furniture. $1 of office furniture requires: $.04 of bolts, $.05 of office furniture.

Draw a weighted digraph that represents this situation.

.03

F

B

The Leontief Input-Output Method, Part 1

Example 2: $1 of bolts requires: $.03 bolts, $.02 office furniture. $1 of office furniture requires: $.04 of bolts, $.05 of office furniture.

Draw a weighted digraph that represents this situation.

.03

F

B

.02

The Leontief Input-Output Method, Part 1

Draw a weighted digraph that represents this situation.

.04

.05

.03

F

B

.02

The Leontief Input-Output Method, Part 1

Construct a consumption matrix for this company.

(Pay careful attention to the To and From labels.)

The Leontief Input-Output Method, Part 1

Construct a consumption matrix for this company.

To

B F

B F

From

The Leontief Input-Output Method, Part 1

Example 2: If the company produces $300 worth of bolts, what input of bolts and office furniture does it require?

To

B F

B F

From

The Leontief Input-Output Method, Part 1

Example 2: If the company produces $300 worth of bolts, what input of bolts and office furniture does it require?

Bolts: 300(.03) = $9

Office Furniture: 300(.02) = $6

To

B F

B F

From

The Leontief Input-Output Method, Part 1

Example 2: If the company receives an order for $400 worth of bolts, what value of bolts must it produce to fill the order?

To

B F

B F

From

The Leontief Input-Output Method, Part 1

Example 2: If the company receives an order for $400 worth of bolts, what value of bolts must it produce to fill the order?

400 = P - .03P = .97P

P = $412.37

To

B F

B F

From

The Leontief Input-Output Method, Part 1

Exercise 1: