Unit 3 Lesson 5 - Leontief_Model_Presentation.pptx

This is a comprehensive discussion on Leontief Model. It describes how different sectors of an economy depend on one another — how the output of one industry is used as an input by another. The basic idea of this concept Every industry (or sector) in an economy produces goods or services.
Some of this output:vis used internally by other industries (to produce more goods), and
the rest is sold externally (to satisfy final demand — consumers, exports, etc.).
The Leontief model expresses this relationship mathematically.

1. The Leontief Input-Output Model

2. Introduction The Leontief Input-Output Model models interdependence of economic sectors. Developed by Wassily Leontief. Assesses how changes in final demand impact production.

3. Objectives Understand the theory behind the model. Derive production equations. Solve Leontief systems. Apply to real-world and community problems.

4. Assumptions Fixed number of sectors. Each sector produces and consumes outputs. Relationships are linear and technology is constant.

5. Principle of Leontief Model “ Total Output = Internal Consumption + Final Demand "

6. Leontief Production Equation X = total output vector A = matrix of input coefficients D = final demand vector A * x = Internal Consumption X = AX + D “Total Output = Internal Consumption + Final Demand"

7. The Matrix of Input Coefficient The input-output matrix A records the input requirements per unit of output. Entry aij ​ represents the amount of output from sector i required to produce one unit of output in sector j.

8. Applications in Community Contexts Farming and Food Processing Utilities and Services Retail and Logistics Forestry and Paper Mining, Construction, Power Urban Water and Waste

9. Example 1 In a rural province, the economy is composed of two key sectors: Agriculture and Food Processing . To produce 1 unit of agricultural output, 0.4 units of agriculture and 0.1 units of processed goods are consumed. To produce 1 unit of processed goods, 0.2 units of agriculture and 0.3 units of processed goods are needed. Local demand (consumers and exports) requires: 80 units of agricultural output 100 units of processed goods Question: How much total output must each sector produce to meet both internal inter-industry demand and final demand?

10. Example 2 A metropolitan area has three main sectors: Energy , Transportation , and Communication . These services rely on each other for operation: Energy depends on 20% of its own output, 10% from transport, and 20% from communication. Transportation consumes 30% of energy, 20% of itself, and 10% from communication. Communication uses 10% of energy, 20% of transportation, and 20% of its own output. To meet household and commercial demand, the city requires: 60 units of energy 80 units of transportation 90 units of communication services Question: How much must each sector produce to meet the final demand while sustaining internal dependencies?

11. Example 3 A small business ecosystem includes Retail and Logistics services. Retail needs 0.5 units of retail services and 0.3 units of logistics per unit of output. Logistics depends on 0.4 units of retail and 0.2 units of its own services. Final demand from customers and external clients is: 50 units of retail goods 70 units of logistics services Question: How much total production must both sectors generate to fulfill demand and maintain internal operations?