Above shown is the improved red-yellow logo design incorporated as a sticker. 
Above is a little chart that shows the evolution of the Chairman Mao beer logo from the existing design. I decided that the overall design should reflect more of a raw, non-decorative ideal. Therefore, I've focused on the primal shapes like square, triangle and circle. The type of the logo has been derived from these shapes and the sticker of the beer bottle would be a rectangle shape.
Red and yellow/gold are good luck colors in Chinese culture.
Chairman Mao often symbolised in front of a rising sun in propaganda posters. Thus, I am using that form rather than the star of Communist Party because of it's stronger direct resemblance to Mao himself.
A.