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Let’s assume that when the labor markets are in equilibrium, there are 165 million workers working....

Let’s assume that when the labor markets are in equilibrium, there are 165 million workers working. Does this mean that everyone in the labor force (100%) is working and that the unemployment rate is zero? (A labor supply and demand diagram might be helpful in your explanation.)

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NO, even when the labor market is in equilibrium that means that the demand and supply of the labor are equal in the market, but even at this point the unemployment rate will not be zero, it will be at the natural rate of the unemployment that is around 5% for the US economy, this unemployment is due to people changing jobs and structural unemployment in the market.

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