Yes, public school teachers should get merit pay to encourage them.
Firstly, there are many different kinds of teachers. Some teach for the money. Some for the experience. Some for the prestige, and some because they enjoy teaching. Teachers who work harder because they sincerely care for the education of their pupils should be rewarded more than the others who just go through the motion daily, teaching, but not understanding.
A good teacher must not only teach, but respond to the individual needs of his/her students. It is getting very difficult to find teachers like this in public schools these days. The sincere teachers who you find in public school are there not so much for the meagre pay but out of duty and care. These teachers should be rewarded. Otherwise, why should any good teacher want to teach in the public school? No incentives, no motivation or encouragement whatsoever. Even the most caring teacher will quit from the lack of encouragement; public school students can be very difficult to teach. Most good teachers will be employed by the better private schools.
But of course, private schools cost more to run, because the teachers fees are higher! So only the well-off students have the benefit of private school education. The poorer students are at a disadvantage. Are they not to get the benefit of having a good education from a caring and sensitive teacher because they are poor, and cannot afford private school education? Of course, one may argue that that's what scholarships are for: for the promising by economically disadvantaged students. But I put to you: how can these poorer students show any promise if they have no one to assist and encourage them? To a teacher who teaches for money, investing their time for these students is not worth it. They are busy! Why should they give away their valuable time for students who may not even prove to become anyone special?
Merit pay then, encourages teachers to invest their time in students, not just the quality ones, but even those who are struggling in their study. Don't forget: students are our future leaders. What we put into their education is what will come back to us.