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Let's take a simpler approach here.

Consider an economy with just one good in production: Cars.

THe economy only produces cars and only employs people to produce cars.

The demand for the car in that economy is 10.000 cars/year.

And in order to produce 10.000 cars/ year, the economy has to employ 1000 people so 10 cars/person.

For some weird reason, the demand for the cars decrease to 8000 cars/ year.

Now, to produce 8000 cars, the economy only needs 800 people. Therefore, those 200 people are fired, creating unemployment.

Aggregate demand works the same with the only different that it's the total demand of every single goods in an economy (cars,oils,house.... and thousands more). And so, if it falls, it needs less people to produce enough good to satisfy the demand => unemployment.

Supply works in the same way if not simpler.

Back to the car example, if for suddenly a factory blows up and forces the production to go down from 10.000 cars to 5.000 cars. Therefore, the economy employs 500 more employees than it needs to produce those cars. Thus, it creates unemployment where those 500 people are fired.

In aggregate world, if the total (aggregate) supply falls, all those people who are on the "excess" level would be fired and become unemployed, thus generating unemployment rate.

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