“The recent global economic crisis is now evident in the declining demand worldwide and across many markets. Discuss the short-run and long-run equilibrium effects and the efficiency implications of this decline in demand on firms operating in perfectly competitive markets and firms in monopoly markets. Support your verbal discussion with graphs for both the perfectly competitive and monopoly markets.”

If someone can help about this question I'll apprecieate it because I'm stuck...

With a drop in demand across all prices, the demand curve shifts left in the short run. Now think about what that means with respect to the equilibrium point. (Drawing simple graphs will help you get a 'visual'.)

Now follow that with some thinking about how producers would be expected to respond in the long run. The word 'efficiency' in your question is a clue.

As producers figure out ways to squeeze more efficiency out of their production processes, what does that mean in terms of profit-dollars per every revenue-dollar? And hence, what does that do to the supply curve?