At e3 during the skyrim demo Todd Howard says you can effect the economy, he says you can sabotage a woodmill. How exactly? I can't find any other way besides killing the guy working there. He also says during another interview that Skyrim has a working economy that you can take part off. I just don't see how? Is this just to market the game? I was excited for this so called economy but besides buying and selling items there is nothing. It is no different than any other Bethesda game.
I also watched the Oblivion E3 demo and Todd said many things that were a little fabricated if you ask me. There huge selling point was that now Skyrim has all the hand crafted dungeons, well in the Oblivion video he says that they are hand crafted. He made it seem like they had never done that until now.
Killing the guy working at a lumber mill is sabotaging the lumber mill, so that may very well be "how exactly" you sabotage a lumber mill. An NPC once told me that he buys cheap in one place and sells high in another. Can we do that, and can it be profitable for us? I don't know, but I'm skeptical.
The game isn't going to set off fireworks or raise glowing "ECONOMY IS AFFECTED HERE" banners to show you the effects of your actions on the economy. If there is a working economy, then you will have to work just to notice it. If you want to know whether something is cheaper at Best Buy or at Newegg, you start by taking note of the price at one store. Then you visit the other store and take note of its price. Then you compare the prices you wrote down.
If you want to see how your actions affect the economy in Skyrim, it seems obvious that you yourself should start taking meticulous notes. First take note of the prices and availability of items in a shop. Then go do something you think might affect the economy. Use your common sense. Go kill the worker at the lumber yard that supplies the town where the shop resides. Buy or sell a bunch of something. Try depleting or stealing all of the ore in a mine. Finally, return to the shop and compare items and prices to your recorded values. If you don't see any difference, then try checking again a week later. If you still don't see a difference, then try doing something else to affect the economy. Through it all, be sure to account for any changes in your Speech skill, which affects prices.
You might find that you have no more influence over the Skyrim's economy than you do over Oblivion's. You might find that even if you can affect the economy in new ways, the returns on your efforts are disproportionately small and unsatisfying (a bit like marriage

).
I haven't done the necessary work to identify a working economy. I would bet that those saying we can't affect the economy in Skyrim, that Todd lied, haven't done the work either. They were expecting fireworks and the "ECONOMY AFFECTED HERE" banners.