Competition drives down the price - with many producers in the market they undercut each other in price to sell more, until (in the ideal/ extreme case) everybody's selling at cost price.

However, in paradoxical opposition to everyday intuition, a lowest price / price-matching guarantee can actually help producers to keep prices high! This follows from two considerations:

i) Explicit collusion on prices is forbidden by law (under anti-trust / anti-monopoly laws); and so . .
ii) a price-matching guarantee can be used as a subtle signal to other producers to coordinate implicitly

the analysis follows from game theory;
a Nash equilibrium is a stable status quo such that no participant can gain by (and thus has no incentive to adopt) a unilateral change of strategy if the strategies of the others remain unchanged;

in a competitive market with no signals the nash equilibrium is producers charging cost price - given that other players are charging cost price, charging anything above cost price would result in no business so it's best to also charge cost price; and everybody else is charging higher than cost price, then it definitely makes sense to charge just slightly above it to steal all their business. In other words, on an individual level there's always the risk of being undercut and the incentive to undercut others - the nature of competition - and so the default would be everybody charging cost price.

but with a price matching guarantee if the prices are high to start out with . . .

let's take two shops, shop A and shop B. shop A charges $10 for a lipstick and has a price matching guarantee; shop B has just entered the market.

Never mind the theory, think in business terms: why in the world would shop B choose to undercut shop A AT ALL? (in this artificially oversimplified world, though the intuition is same for larger number of shops) If shop B charges $8, shop A would immediately lower their own price to $8. In other words there is no point charging anything less than $10 since A would always price match and they'd always end up with half the market - but with lower profits, a sadder outcome for both.

So why bother? Share the market at $10 each, more profits for both. I'll put up a price matching guarantee in my shop too.

-----

2)

They would set Marginal Revenue = Marginal Cost to decide optimal profit-maximizing quantity Q*;

then charge maximum price P(Q*) - plugging Q* into the inverse demand function
- so that quantity demanded at that price is exactly the optimal quantity of sales Q*.
----
3) Cartels are a special kind of monopolies, or firms practicing non-competitive behavior.

We say that a firm has monopolistic power if the firm can influence the market price of the product by restricting it's own output. The monopolistic firm recognizes this power, and restricts quantity to sub-competitive level to derive maximum profit.

This monopolistic power arises from barriers to entry; these barriers prevent new firms from entering the market, thus preventing the market from becoming competitive. Examples of entry barriers are:

i) Technological barrier (e.g. inefficient production technology)
ii) First mover advantage with increasing returns to scale
iii) Legal barriers
iv) Customer/brand loyalty
v) Geographic barrier
vi) Incomplete information about the market (e.g. many sellers on the Internet, but trying to find the cheapest one is like going for a needle in an ocean)