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A seller who will sell more by setting a lower price for its product, and indeed, must lower price to increase the quantity it can sell is called a...
Price searcher
What does the demand curve faced by an individual seller who is a price searcher look like?

What do we call the additional revenue a seller gets when one more of an item is sold?
Marginal Revenue

For a price taker, the marginal revenue is the same as the price (since the seller has no effect on the price). However, for a price searcher, the effect that making and selling more output will have on the price is important. To sell any additional units, the price taker has to lower the price, and this will affect its marginal revenue.
Marginal Revenue = ^{change in revenue}/_{change in quantity}

Here's a table showing how marginal revenue works for a price searcher:

Marginal revenue for a straight-line downward sloping demand curve will be below the demand curve, and will be twice as steep as the demand curve.


How does a price searcher with a downward sloping demand curve make output decisions?
Actually it’s quite similar to the way a price taker makes them. Both kinds of sellers are trying to maximize profit, and will make decisions based on cost.

For a price taker, the decisions are similar, except for the choice of how much output to make.


For a price searcher,
1. produce if P≥AVC (if any part of the demand curve is above minimum AVC)

2a. produce an amount up to where MR=MC

2b. price comes from demand curve and is the price that will sell the amount produced (although the seller actually probably finds 2a and 2b simultaneously).

3. profit if P>ATC (profit is [P minus ATC] times output).


Even though a price searcher is no more greedy than a price taker (and may not even make any greater profit), society has a reason to prefer production by a price taker over production by a price searcher...

For a price taker, 1. produce if P≥AVC 2. produce an amount up to where P=MC A price taker produces every unit that someone values more than its cost, an efficient use of resources (resources get used to make each unit of the good if, and only if, it is valued more than other things that could be made instead with the same resources) 3. profit if P>ATC (profit is (P minus ATC) times output.

For a price searcher, 1. produce if P≥AVC (demand above AVC) 2. produce an amount up to where MR=MC; since P>MR, P>MR=MC; so P> MC A price searcher will refuse to make some of the output for which P>MC; it doesn’t make an efficient amount. A price searcher produces too little output!! Resources that could be used to make this good will be used to make something less valuable to society. 2a. price comes from demand curve and is the price that will sell the amount produced 3. profit if P>ATC (profit is [P minus ATC] times output).