If we witness events taking place on the moon, where gravitation is weaker than on Earth, would we expect to see a gravitational red shift or a gravitational blue shift? and Explain please

Question

a)blue shift
b)red shift
c)no shift

Answer 1

The moon is hardly moving toward/away from an observer on the Earth.

Answer 2

So is there no shift? and if so why is that the case?

Answer 3

We expect to see a gravitational blue shift. Events on the moon run a bit faster and also because Earth's gravitational field is stronger than moon's.