In fact the demand curve for a P-Competitive Firm is a horizontal line corresponding to the going price.
And that makes sense, because the price in a P-Competitive market is determined by supply and demand -- not by the seller or the buyer. Conversely, so far as the seller or the buyer is concerned, the price must be a given, since it is determined by supply and demand. The seller has no control over the price, and to say that the seller has no control control over the price is to say that the price is given -- a constant, a horizontal line -- from the point of view of the seller.
Economists sometimes express this by saying that the price is "parametric," meaning that while it may change from time to time, it does not change in response to the firm's output decision.

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