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I understand that workers in a competitive labor market will take the market rate as given. Firms can hire as many workers as they want at the market rate. Why doesn't this apply to monopsonies? If there's only one employer, then if the workers need jobs they would be forced to work for the monopsony employer, which would mean they would have to take the existing wage rate for that employer, right?

Also, since there are many buyers in a competitive labor market, shouldn't companies need to raise their wages to attract more workers? Workers have more options for employment, and so need to be convinced to work for the company.

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You seem to misunderstand the terms you are using.

Taking the market wage as given means the market wage is exogenously (from the point of view of employee, since from the market POV it’s still endogenous) determined by supply and demand forces outside the employer’s or employee’s control. It does not mean that the wage will be low or or even lower than in case where the wage is not exogenously given. Depending on parameters you would typically find higher wage in competitive labor markets, but that does not mean the wage is not exogenously given.

When it comes to monopsony, the wage is chosen endogenously by the monopsony employer to maximize its profit. This is what is meant when people say the wage is not treated as given.

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