Mark Duplicate Values :: Insert Word Duplicate Next To Row

I am using the following macro to insert the word "Duplicate" in the first blank column next to a duplicate row. My data is sorted by the first column. Data Example:

12345 a
12345 a DUPLICATE
11111 b
23123 b

Here is the macro I am using and it does not work. It marks the first duplicate it finds then goes into an infinite loop. Any Idea where I went wrong?

Sub MarkDupes()
x = ActiveCell.Row
y = x + 1
Do While Cells(x, 1).Value <> ""
Do While Cells(y, 1).Value <> ""
If (Cells(x, 1).Value = Cells(y, 1).Value) Then
Cells(y, 3).Formula = "Duplicate"
Else
y = y + 1
End If
Loop
x = x + 1
y = x + 1
Loop
End Sub