Price Floor and Quality

I was walking with my wife and talking about price floors. She is reading Stiglitz book in Japanese. She asked me the following question: "What is wrong with price floor if it brings quality to the good?"
It took me awhile to figure out what she was talking about. It was with the help of the electronic dictionary that I understood she is talking about price floors.
She followed that with : "Is quantity everything?"
I tried to remind her that in Japan watermelon costs around 8000 yen (about $90).
She paused and said the following: "At first I liked cheap watermelon but now...."
I waited.
She continued: " I wonder Is cheap cheap everything? What about taste?"
This made me think too.
There were three questions on my mind:
1) What is wrong with a price floor which is set up to encourage high quality goods. (This is different from U.S. farm subsidies which encourages quantity)
2) Are we happier with more? I dont know if the fruit were truly better in Japan or not but it was a treat to have a piece of fruit. Scarcity made it tastier.
3) Why is my wife (a non-economist) reading Stiglitz economic textbook?
4) How do the Japanese subsidize their farms? Is it a quota or a price floor?