Find the production matrix for the following input-output...

Find the production matrix for the following input-output and demand matrices using the open model.
$$A=\left[\begin{array}{ll}{0.8} & {0.2} \\ {0.2} & {0.7}\end{array}\right], \quad D=\left[\begin{array}{l}{2} \\ {3}\end{array}\right]$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Input-Output Analysis

This concept studies how different sectors of an economy are interrelated. It uses matrices to capture the flow of goods and services between industries, allowing one to understand how the output of one sector serves as an input to another.

Demand Vector

The demand vector represents the final demand for goods by consumers, government, and exports, beyond what is required for inter-industry exchanges. It is a crucial component in the open model, as it drives the total production requirement.

Open Model in Input-Output Analysis

The open model distinguishes between internal inter-industry transactions and final demand. In this model, the economy's total output is determined by both the intermediate demands (captured by the input-output matrix) and the final demand, leading to the formulation X = (I - A)?¹ D.

Leontief Inverse

This is the inverse of the matrix (I - A), where I is the identity matrix and A is the technical coefficients matrix. The Leontief inverse quantifies the total production needed in each sector, including both direct and indirect requirements, to satisfy a given final demand.

Transcript

Please give Ace some feedback