I agree with Enno Shioji that the use of the expression あなた安いな for “You are so cheap (= You are so easily satisfied)” is uncommon in Japanese. I do not think that it has been used in Japanese for a long time. However, this usage definitely exists; we can see several webpages which contain this usage of 安い (I searched “安い人だ” in Google and chose suitable usages from the search results).
(The third example above may or may not be in the same category because it may be regarded as a metaphor which describes a person as a commercial product.)
It may be the case that this usage of 安い was derived from the usual meaning “costing little” of the word 安い by the metaphor, independently of English, just in the same way as the English word “cheap” acquired its “easily satisfied” meaning. Or it may be the case that the expression in Japanese originates from the literal translation of the English expression “You are cheap.” I do not know how to tell which is true.
安い has a different but perhaps related usage: Daijisen (sense 2) lists the meaning “insignificant” with an example 安く見られる (considered insignificant, underestimated), and Daijirin has a separate entry for 安く見られる. My impression is that 安く見られたものだ (literally “I am considered insignificant”) is a common expression in Japanese to express dissatisfaction or anger of the speaker. This is similar to your example in that 安い is used to describe a person, but different because your example does not mean “You are insignificant.”