There is no such thing as red, pink or rose gold!
There are however gold alloys which appear rose, red, or pink.
When jewellers speak of coloured gold, they mean coloured gold alloys.
It is very simple to produce a gold alloy with a reddish colouration. All that is needed is to increase the proportion of copper in the mixture. To maintain the correct proportion of gold in the alloy, this usually means decreasing the silver content. In the past, many goldsmiths have reduced the silver content and increased the copper content to save cost, as copper is less expensive than silver.
We encounter many people who believe that red gold is old gold, and vice versa; also that old gold is better than new gold. Neither of these beliefs are accurate.
Most pure metals are grey or silvery in colour except for gold and copper. When carat gold contains large amounts of copper, compared to other alloying metals (like silver & zinc), a red or rose gold is produced. Many different rose golds have been alloyed and it is difficult to match an old rose gold with modern alloys.
18 kt red gold is a subtle warm rosy colour. Yellow gold usually contains gold, silver, zinc and other metals to enhance hardness. Alloyed with silver (Electrum), it is very soft and is greenish-gold in colour. 22kt gold is a very rich yellow colour and is soft.

