A shofar can be quite small and still be kosher. The minimum size requirement, according to halacha is one tefach, or four thumb breadths, i.e. big enough so that when held in one hand, a bit of shofar is visible extended from the person’s grasp on both sides.
Interestingly, this means someone with a very large hand may need to use a slightly larger shofar, i.e. the same shofar would be kosher for one shofar sounder, but not for another (see Orech Chaim, 686, 19).
In the laws of the Four Species we find that when you buy an esrog you should add up to one-third of the price you paid in order to upgrade to a bigger esrog. The Magen Avraham holds that this rule applies to all mitzvahs, citing shofar as an example. However, he also holds that this rule requiring you to spend an additional amount to upgrade to a bigger esrog or a bigger shofar only applies if the buyer can go back to the seller and exchange the one he bought for a larger one.
In practical terms, larger shofars are more expensive because large horns are harder to obtain and because the production process is more complicated. Also, it should be kept in mind that a jumbo ram’s horn shofar can be harder to blow than a medium-size ram’s horn shofar, whereas a large kudu shofar is generally easier to blow than a small or medium kudu horn.