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Price Taking Firms Concept

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I'm having a little trouble fully grasping the price-taker firm concept. I understand that there are two features of the demand facing a firm will ensure that the firm must act as a price taker:
a. That other firms be willing to provide all that is demanded at the current price, and
b. That consumers of the firm's output regard it as identical to that of its competitors.

Is it that all firms produce a good that is similar that it makes little difference where or from whom the consumer purchases these goods? Why are both of these conditions required if the firm is to treat the price of its output as fixed?
Is it possible for one of the conditions held but not the other? What would happen if this were the case?

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Price taking firms concept is discussed in the solution.

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First, let me rephrase your two conditions to make them more accurate,

a) No firm can impact the market price, that is, there are infinitely many little firms and the individual market share is too little (if you raise your prices, there are always other firms that are willing to make up your share of the market at the present price).

b) Products are indistinguishable by consumers.

Now we answer the questions,

Is it that all firms produce a good that is similar that it makes little difference where or from whom the consumer purchases these goods?

Yes, in fact, we assume that goods have virtually no ...

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