Hellow my fellow evil narrators...COF COF*, sorry, DM's.

First of all, good evening, good morning and good night, wharever fits your place the best. Thank you so much in advance for taking the time to read, comprehend and type a response to this issue i have, i really appreciate any help you can bring me. 

That said, this is the situation;

-We have started to play the introductory module "lost mine of phandelver". I've been narrating pathfinder for a while now and i felt prepared to avoid using the premade characters, so we jumped in with a group of new characters (1 warrior, 1 barbarian, 1 wizard and a paladin). This last boi is the one making me feel a bit worried. This player took the noble background, and i told him that his family is far from beign a royal one, or even a high noble family. His family made it climbing from the ground to the top, and for now, they have little influence as nobles, but they are good merchants. 

The "problem" comes when my group defeat the cragmaw goblins in the cave and then they decide that the problem of the redbrands in phandulin is not that big of a deal...in one evening. So, they leave phandulin the day after they arrive in the town, heading for the cragmaw castle.

Hey, DM bro, we cant see any problem here...yeah, i know, let me get to the point. The paladin player has a plan, they pretend to defeat the cragmaws and, then, head to phandulin to ask his family a favor: "we want you to hire like 30 mercenaries and kill all the redbrands in phandulin, we will make you a favor in exchange for this". 

My problem here is...how should i handle this plan? I mean, its not like his family can not hire this mercenaries, they can, of course, and that baddas warriors can rip off the redbrands of phandulin, yeah but...should i give the players PX for this even if it may be a good idea? should i add another mission to the module so then they can compensate the loss of PX taking this path of action? should i let them see what happens when other handles YOUR problem and you have to face stronger enemys with less PX and equipment? How can i reward good ideas and thinking out of the box without making it feel too easy? 

And also, if i let him do this...how can i avoid the feeling that they can just surpass any challenge just exploiting the noble background?

Thanks in advance my fellow evil...forget it, i love you all.

take care!

Critical thinking and problem solving, as well as creativity, of your players is the foundation for a fun campaign.

You should let them know that if they use wealth to solve their problems then they might solve the immediate issues, but they won't become more powerful themselves. 

The Noble (MM, 348): Ac of 15, 9 hit points.  Charismatic but not strong or particularly dexterous or intelligent.  This can represent the player that exploits the noble background.  It's a cushy lifestyle, but in a world of dangers, it doesn't adequately prepare an individual for combat.

From the name "experience points", we can come to the conclusion that by not getting actual experience, you can't get XP.

So with that in mind, let them get a small amount of loot depending on the context, but no XP. 

Redbrands are bandits and brigands, right? Interesting thing about mercenaries is that a lot of times they, too, are bandits and brigands. In fact, what's to say some of the mercenaries aren't redbrands themselves? Or at least buddies with them? If you want to play this up, let the player make it known his family wants to hire some mercenaries to deal with these brigands. In short order, a group of 30 mercenaries shows up to take the job. They assure the players that the situation is well in hand and as soon as the money changes hands, you can start showing some cracks in the veneer and making the players wonder if this was really the right way to go. The mercenary leader seems a little too confident in his skills. Maybe a lot of them are drunks. Maybe the players catch them exchanging not-too-subtle winks and nudges as they promise to handle the problem.

The players just got took. The mercenaries (redbrands) may settle down and lay low for a few days or a week while they drink and party it up on the paladin's family's money, but as soon as the funds run out, they will be back to their bandit ways. Even worse, they now know the paladin's family is loaded. They could start hassling him for more money, or worse yet, they could try to ambush and rob the party. You already have a stat block for this. Just use the redbrands :)

I'm not suggesting you change the story fundamentally to punish the players, but maybe a little danger sets the mood and definitely let the paladin know he got taken and there's more to adventuring than buying your way out of your problems. Oh, and daddy wants to know what his son has to show for the considerably sum of money he just fronted him. When it's all said and done, don't give them the full exp for the work they didn't do, but you should throw a little exp their way as "reward" for the lesson they just got... once they finish clearing out the redbrands themselves.

let them implement their cunning plan 
they get neither xp nor loot for doing so, make them write down the exact instruction that they give to the mercenaries even. then pick out every loop hole in their wording and make it go as horribly wrong as you possibly can.  though i might ask, what benefit would their merchant family derive from getting rid of the red bands,  are they directly affecting their business?, in that case i may let them resolve it that way, but they still would recieve neither loot nor experience.
this will be good preparation for the day you go mad and give them a wish spell without having accidentally disintegrated someone first.

option: the family doesn't want to hire mercs because they have a perfectly capable family member who can do the job for free

the nobles father could send a mere 5 unblooded mercenaries, saying "son, if you can manage the task with these you will have earned honour for our house" or some such line. these mercs are more of a liability but allow the story to unfold as intended, and certainly rewards the player. allowing their ideas to be in the game without actually eliminating the challenge. it might be prudent to remind the player that mercenaries don't take work from nobles that got the last mercs killed.

Just because the character came from a noble family doesn't mean they can or will hire a band of mercenaries on a whim. There were already a number of suggestions which were quite good. Another thing to consider is that there is a huge range of quality regarding mercenaries. If the family does decide to send the mercs, they might be lvl 0 and get their asses kicked by the bandits.

Backgrounds are for flavor, not content.

Thank you all so much!!!

Overall i can see that the main course of action you all suggest in common is "punish this way of action while you also reward it". I guess you are right, mercenaries are not the best kind of soldiers and they may fail, retreat, bluff or steal if they got the chance (for example, if the characters decide to let the fortune soldiers go on their own under the mannor). But i also have to reward the players for trying to solve something using their backgrounds and personal stories...it's hard, i will try to keep the balance so we all have fun and also this idea does not turn in a common way to solve the character's problems. 

Again, thank you so much, i've learned a lot from you guys, i think i may be a little soft when it comes to punish my players, maybe it's because all the games i've played are very dense in punishments and i think that can ruin a game...but i guess a little bit of punishment balanced with rewards helps to enhance the campaign!

Take care! i'll keep on watching this thread so i can take more ideas, feel free to keep writing hints and tips!

if words matter; I would suggest that you are "guiding" players that are meant to make heroic choices. rather than "punishing" players in any particular way.

also time is of the essence here, if the characters are going to wait for reinforcements... the bad guys could get away. no spoilers, but the rebrands are not the main antagonist and somebody... has a lead on the race.... to the lost mine

What an interesting idea you just gave me....

You could have the family refuse to help, but be all suspicious about why. When pressed for details you can reveal that the father/mother is being blackmailed by the Redbrands and cannot risk bringing in mercenaries or the leader of the Redbrands will release some secret that will completely ruin the family. This must be handled subtly, perhaps some convenient team of heroes could sneak into their hideout and deal with the leader once and for all? Just put a dossier of documents in the leader's office stamped with the family crest as the quest item. After that is retrieved then the family will finally give their blessing for the son to become a travelling adventurer.

Reward the plan with story, and drag the party back onto the path.