This is due to the order the program is run. First the global variables are set, then setup() once, then draw() continuously. At the time of setting the global variables x and y, the values for width and height have not yet been set. The width and height are set in setup() via the size call. So you can solve your problem by setting x and y in setup() after the width and height have been set.

Adapted Code

1. int x, y; // here width and height are not yet set
   
2. 
   
3. void setup() {
4.   size(800, 600); // here width and height are set
   
5.   x = width/2; // now you can use width and height
   
6.   y = height/2;
7. }
8. 
   
9. void draw() {
10.   ellipse(x, y, 50, 50); // here you could also use width and height
    
11. }