Less ISK about
People will be busy doing PI. PI does not generate raw isk for the economy. The time they spend doing PI instead of ratting or mission-running represents a loss of isk that would otherwise be generated. PI seems to be both fascinating and time-consuming (at least initially) so in the short term expect people do be spending a lot of time doing this.
PI also has some isk drains. The installations are (I believe) purchased from NPC vendors. Some ships will be lost as delighted pirates happen across people sitting in an industrial in low sec trying to figure out the intricacies of the PI interface. Most advanced PI products require Capital Construction Parts which will require substantial amounts of asteroid minerals to manufacture. New skill books will be introduced and will need to be purchased by players (or possibly may be given out free in the new PI tutorial). Exporting and importing materials has an isk fee.
Less isk production due to the distraction of PI means that everything in Eve will tend to become cheaper as a smaller amount of money chases goods. There are exceptions to this general deflation.
Mineral price drop
Currently insurance values of ships are based on a series of set notional values for each asteroid mineral. This effectively creates a bottom for the minerals market because if mineral prices drop below the floor people will make ships, platinum insure them, then blow them up. One player is alleged to have blown up 2000 Rokh battleships in a day at 10m isk profit each. The removal of the insurance fraud floor in Tyrannis means minerals can drop in price. Individual minerals may or may not drop as a result of this but overall minerals are going down. They've been trying to go down in price for months, it's only the floor that's kept prices at current levels.
This is separate from my first point describing a general deflation. In other words, almost everything is going down in price but minerals even more so.
Tech 1 module shortage
Missions produce a very large amount of tech 1 modules, the basic meta 0 modules like, for instance, Small Shield Booster I. The drop rate will be significantly reduced to reduce the flow of minerals from this source to the market. However while some modules like ECCM are almost invariably reprocessed some modules are popular and in high demand. When they stop dropping at current rates the prices of these modules and the low end named versions will rise in response to the new scarcity where the demand by players fitting ships exceeds the reduced supply.
This in turn creates an opportunity for new players interested in manufacturing. At the moment it's really not worth making these simply products - the minerals are worth more than you can sell them for. As the supply from loot is reduced prices will rise and it will be worth the while of newer industrialists to make simple modules. This is so evidently newbie friendly and healthy for Eve that I would expect future patches to further reduce and eventually eliminate the drop rate of meta 0 modules.
Plexes may drop sharply
The plex market has bullish for about 8 weeks. The general deflation I'm expecting should reduce the price of plex. Now there are large plex stockpiles and the players sitting on them may be hoping to sell at the peak of the current upward trend. I expect to see players flooding the plex market during the rest of May as cashing in for 320m isk per plex is pretty good (especially when they may have been bought for 250m). I predict that plex will go under 300m during June, probably down to about 280m.
The habit players have of stockpiling plexes and only selling during peaks will prevent this market going as low as 250m any time soon. Simply put if it drops down to about 280m players will be thinking about buying a few billion isk worth in the confidence that the price will rise soon. There are a lot of people paying for their subs in isk so there's really a captive market for this product.
More fighting in nullsec
It's possible that improvements to lag will increase participation rates in the nullsec wars. There's actually a big set of improvements scheduled for some time this summer after Tyrannis plus minor fixes going out with Tyrannis.
More intense nullsec pvp means more people buying plexes for cash and more ships, modules and structures destroyed. There is the potential for enormous strategic gains because of PI. Basically if you have the infrastructure in position quickly to make POSes, SBUs and TCUs and your opponent doesn't he could be in real trouble against a multi-pronged attack.