Platinum tends to be worth more than gold by weight, but as prices  fluctuate, sometimes the gold price does go higher than the  platinum price.
To substitute for 1 egg you can use ingredients you already have. 1 Egg = 2 tbsp. flour 1/2 tbsp. butter 1/2 tsp. baking powder 2 tsp. water. Two years ago my daughter (who was 9) did a science project about this very subject. Basically, the eggs were binders to keep the cake together (and they did add flavor...).
Flax Seed. To replace one egg, blend 1 tbsp. flax seed until it is finely ground. Add 1/4 cup cold water and blend until thick. It has a nutty flavor and provides a jelly-like texture to your baking that mimics the consistency of egg yolks. You can find flax seed in health food or grocery stores.