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Since the marginal cost of hiring workers will rise when the producers hire more and more workers, what is the advantage of having monopsony power (while in a competitive market, labour buyers can hire workers at a fixed wage rate)?

Furthermore, what are the disadvantages to have monopsony power?

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Having monopsony power means that all suppliers of labour have to come to you to sell their labour. This gives the monopolist the possibility to extract more surplus from the market than in the case of was a competitive labour market.

More rigourously, in a competitive market, labour supply for the individual firm is perfectly wage elastic. The height of this wage (w*, the fixed wage you refer to) is determined at the labour market, where aggregated labour supply meets labour demand, and will equal the value of its marginal product (vmpl, represented by the demand curve). When the firm has monopsony power in the labour market, it can pay wages lower than the vmpl. That's the benefit of the monopsonist. To the monopsonist, having monopsony power is never disadvantageous.

A graph or some algebra will certainly prove this point. http://econpage.com/301/handouts/labormkts/monopsony.GIF

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The advantage of having monopsony power is that producers can decrease the wage when they want to cut down their employment, due to some negative demand shocks or technological shocks. In the perfect-competitive market, the producers cannot cut wage as otherwise they would loose all their employment.

The disadvantage of having monopsony power is, as you said, higher marginal cost of labor than perfect-competitive market. In the real world, I doubt that any firms who want to expand and earn more profits would like to obtain some monopsony power, i.e. an upward-slopping labor supply curve.

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