How much does a pink heart shaped 14 carat diamond cost?

The diamond you want will be an extremely rare diamond, based on the desired weight.

Here's an example of a sizable pink diamond: The Graff Pink, purchased at auction in November 2010 weighs 24.78 carats, a little larger than the one you want to buy. The buyer paid "... US $46 million (£29 million), making it the most expensive single jewel ever sold at auction."*

You would pay less, given that you want to buy a less weighty stone. As well, you could compromise on clarity, and colour and save money.

You can read more about the Graff Pink, below.

*Wikipedia