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I'm working on a practice problem where I'm giving the following:

Suppose a firm is a price-taker and can sell the good it produces at price $p$.

There is more to the problem, but it is not relevant for my question.

I am not given any more information about the market other than the firm is a price-taker. So it is therefore not a price-setter meaning the market is setting the price.

I can imagine two scenarios under which a firm would not be a price-setter.

(1) if there were perfect competition between sellers, the firm could not set a price.

(2) Also, if there were only one buyer, the firm would not be able to set a price either since the buyer could refuse to buy until the price went low enough.

My Question:

Is there something that distinguishes price-taking due to competition between sellers from price-taking due to monopsony? How do I tell which one it is?

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You may notice that the price would almost surely vary with the quantity the firm wants to sell if it were operating on a monopsonic market. (Exotic cases when this is not true may be ignored as then competitive and monopsonic markets are indistinguishable). As you are given price and not price schedule, it is a sure indication that market can be considered competitive for any practical purpose.

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