Final answer:
The Leontief input-output model for an economy with two sectors - goods and services - can be represented by a system of linear equations based on the input requirements for each sector. Solving the equations provides the total output needed for each sector to meet the final demand, while accounting for the interdependencies.
Step-by-step explanation:
To set up the Leontief input-output model for an economy with two sectors, goods and services, we must consider the input requirements for producing one unit of output in each sector. For goods, it requires 0.2 units from goods and 0.5 units from services. Conversely, for services, it requires 0.4 units from goods and 0.3 units from services.
Given the final demand of 20 units of goods and 30 units of services, the system of linear equations representing this model can be written as follows:
- x = 0.2x + 0.4y + 20
- y = 0.5x + 0.3y + 30
Where x represents the total output of goods and y represents the total output of services. Solving this system gives us the total output needed in each sector to meet the final demand while considering the interdependencies of each sector.
The input-output analysis is a fundamental tool in understanding the complex interrelations in an economy, helping to determine the ripple effects of changes in demand in one sector on the production in others. It is pivotal for effective economic planning and analysis.