One nit, there isn't one "price the market will bear." If you drop prices, you and the industry as a whole will typically sell more units as customers on the margin now find your product just barely worth buying, where at the old price, they did not. In fact, "price the market will bear" pretty much has it backwards. There's an amount the market wants to buy at certain price ("demand the price will bear") and an amount the producers will make at a certain price. In both cases, price is the independent variable, not supply or demand. But I don't think that's the dominant effect here.
Yes, you pick B. In the short term, customers run from your competitors to your door and the increased sales overwhelms the some of the potential profit per widget. You cackle with glee as you roll in your vast piles of (honestly earned) dollars. But from there our stories differs because virtually every market that's not a legally enforced monopoly is "extremely competitive".
Imagine I'm the competitor, watching my shrinking sales with dismay. I will go out of business if I do nothing so I respond any way I can. Simplest is I just cut my profit to zero to match your prices. I'm desperate to turn the tables so I look for any innovation I can. Practically speaking, I don't believe you can stop me from finding some new, creative idea. If I can't find anything, I don't really deserve to be in business and I fold up shop. But with enough elbow grease, I find a different way to cut production costs by 55%. Now I can lower prices below you and smirk.
This leads to a virtuous (to the consumer) race to the bottom with each company fighting and clawing to be the most efficient and produce the most value for the money to earn your business. In the long term, the companies left in business will be selling widgets for much closer to the 50% price. And this is why 50% reductions in cost are really, really rare. Competition has already squeezed out all the easy stuff so people sweat blood to get a percent here and there.
There are, of course, a many corner cases. Someone who actually took Econ 101 as opposed to just reading some econ books can explain cases where the price-supply, price-demand, and customer preference equivalence curves lead to different results. That person is not me. But in general, that's how it works.
Don't believe me? Look at one of Slashdot's favorite whipping boys, cell phone service. You used to pay by the minute. You used to pay for long distance. You used to pay for mobile-to-mobile calls. You used to pay for roaming. You used to pay for each text. You used to have unlimited dat...er, well let's just skip that one. But just in the last two years, all the major carriers have started bundling more and more stuff in plans while keeping prices with dimes of each other. I'm more familiar with family plans because what's what I buy and just in the last two years, they're including more stuff for basically the same price.