I do not have the time to research any numbers, but since you are inventing your world, you might have a general idea for numbers to use in your world. I'm also neither a historian nor an economist.
Here is how I would go about it:
We have a price for all the equipment they need to buy specifically for this expedition like ropes, traps, food, wine, rent for stuff, nails, permits perhaps, information about where orcs are and so on (let's say p_a).
You have stuff you can use multiple times like a weapon, tools or horses or so where you have to divide the price for buying them by the number of orc hunts they will be of use for (let's say amounting to p_b).
You might have to hire several people to do the job. You have to pay them according to the job they are doing. Just some kid fetching stuff for you or a veteran orc hunter spotting for you? You have to collect the entire pay for the operation (let's say p_c).
Hunting an orc takes time, practice and more. Count all the days you put into it and consider what one of those mercenaries gets per day and is willing to work for at the minimum which should be very close to the amount of money you need per day just to support your lifestyle. This could be the amount he would earn if he didn't go Orc hunting but do something else instead (like working on a farm) or just the bare minimum to stay alive (let's say it's minimum wage per day x days spend at this = p_d).
Now we can substract all your expenses from your bounty:
2 gold - \sum_{i=a,b,c,d} p_i = surplus.
Your surplus could be a measure for the effort it takes to take down an Orc because that's the amount (whoever) pays extra just so that people consider going Orc hunting.
Now I would do the following: Extract everything that makes it hard to go Orc hunting. For example a boy fetching you stuff isn't making killing an Orc easier, but an extra fighter will. So do traps or poison you might need, but the price for an Orc hunting permit (if it does exist, just an example) does have nothing to do with the difficulty. Be aware that an extra Orc killer will consume more food and maybe require an extra horse.
So now take everything in p_a b and c (not d) that makes hunting an Orc easier. In combination with your surplus for your own efforts, you have the money they give you just because it's a hard job. If you want to be fancy, you can also divide your time and you're hired mercenaries time and pay into administration duties (and other stuff like traveling and more) and actual fighting and so on and adjust your surplus and p_c accordingly. At the end you will get some amount.
Now you have to compare the money that remains to let's say a bounty for a wolf or a criminal and you might be able to say: "killing an orc is worth twice as much gold as killing a particular criminal and assuming a linear relationship, that means killing an Orc is twice as hard".
Yes, this is a very primitive model, but I believe one would have to know a lot more about your world to actually find some equilibrium price, starting from the sanity of the guy making up the bounty (if he really hates Orcs, he might overpay) to how many people offer those services and Orc density and much much more. I can't do that stuff without spending some time refreshing my memory. I hope my answer refresehd yours, this is actually very doable, you just have to remember some basic economic stuff you might have heared in school or college.