Um, you can buy 8GB of ram for ~$80. NOT EXPENSIVE AT ALL!!!!. 4GB costs about $40. It will be the apple tax that makes it expensive.
You need to do a bit more research about what components and how many will actually fit in the MacBook Air since the MacBook Air is not using SO-DIMM modules. The integrated circuits are soldered directly to the logic board so throwing extra IC chips at it like you are suggesting will not work since logic board real estate is limited. The only way to solve this is to increase the capacity of the few IC chips already present on the board.
The Apple tax on RAM is much more reasonable these days than it used to be.