What causes eggs to be brown or white?

According to the experts of the UC Davis Animal Science Department, the short answer is simply genetics. Here is an excerpt from their "Poultry Fact Sheet", by Francine Bradley, Extension Poultry Specialist and Annit King, Professor, UC Davis:

A brown or pigmented egg shell is the result of the hen depositing pigments on the shell during egg formation. Ultimately this is determined by the genetic background of the bird. Our typical commercial egg layer, the Single Comb White Leghorn, is one of the Mediterranean breeds. Developed in Leghorn (Livorno, It.), Italy, hens of this breed always lay white-shelled eggs. Our American breeds, such as the Rhode Island Red, New Hampshire, and Plymouth Rock, lay brown-shelled eggs. The brown pigment is ooporphyrin, a break-down product of hemoglobin. The Araucana, or Easter egg chicken, from South America lays green or bluish-green eggs. This pigmentation is due to oocyanin, a by-product of bile formation. The color of the egg shell is not determined by the diet of the bird and is in no way related to the quality or nutritional value of the egg.

It has been suggested to me that egg coloring can be influenced by an additive to their feed. The above fact sheet does not specifically adress this. I will dig deeper for evidence of this possibility.