Gasoline and beer are monopolistic competition. But why the prices of gasoline always changes while beer's price is constant?

Answer 1

First of all, they are not monopolistic. There are plenty of companies making and selling both, and price fixing is illegal. The prices of beer periodically drop a bit just before holidays (and the price of gasoline goes up).

The answer they probably want to your question, for gasoline, is mainly that the raw material (crude oil) price fluctuates a lot. There is also a somewhat seasonal fluctuation of demand for gasoline, and periods when refineries shut down to change their formula to meet air pollution standards. This is, in California at least, always used as an excuse to raise prices.