Wow - anyone charging $200 a day must be doing this work on the side..
And in regards to competition - who cares? No matter how cheap you do it, someone else who's hungrier will do it for less, so do not compete on price and do not set your price with mind to the competition. Who knows if the other guys have any true idea of what it takes to run a business, or whether they are licensed or have insurance, etc..
So figure out how much you need for the time and charge that. If you get the old line "I don't even make that much!!", then followup with " I'm sorry, Mr. client, you are obviously confusing an hourly rate with the cost of doing business - they are not one in the same.
And if you get the "The other guy will do it for this much!" then followup with a summary of what exactly makes you better: higher quality, cleaner work, better communication, guarantee of satisfaction, training, insurance, methods, etc.
And if you ever get asked to do free work, tell them you've found in the past that working for free results in you not being paid for your hard work.
Your value is the quality and commitment you bring to the work, NOT your great deal pricing. I barely would even want to be thought of as affordable - that'd drive me nuts.
In specific regards to the baseboard, linear foot pricing is the way to go, and $1.50 to $2.00 is a good reference, but overall job size, such as a 8x10 room would dictate that a minimum price is gonna add up to more than what the one room's linear measurements add up to.
Bottom line is that, like tile backsplashes, you have to have the charge the minimum amount necessary so that you can even begin to setup shop and start laying trim. In the case of tile backsplashes, often times it's simply a 20" x 6' wall, that if done by square foot pricing alone would not even begin to make it worth setting up the wet saw, etc.
Back to baseboard - other considerations are: moving furniture?, stain or paint?, obstructions to work around?, carpet or (possibly warped) hard surface floors?, doors, inside corners, outside corners, angled walls?
With some trim work, like crown molding, you'll have a basic linear foot price with an additional fixed amount per cut or splice or corner, etc. For instance, same room with crown molding. 72 linear feet molding install at $4.00 per foot + 4 corner cuts at $25 each = $388.00 not too bad for a few hours work.
No one's helping me pay my bills, and most of my clients are driving nicer cars than I am, so if it's not my girlfriend, best friend or mom, I'm not doing it for free.
Same with brother inlaws and the like. Minute you give outside family a great price, not only will they usually still think it cost too much, but then because they come out of it thinking that AFTER you did it cheaper than normal, you'll resent them!
So charge what you're worth, and never apologize for what it costs. Get good at saying "This is what it would cost for me to do the work well. After you present your numbers, never lower the price, ONLY change the scope of the work to make it more cost efficient.
I could go on, but it's getting a bit long-winded.
Julian