What would happen to nominal income and wages if the money supply were fixed (100% reserve banking). Would real wages increase, even though nominal wages would stay the same or even decrease?
As Mick explains in the first paragraph of his answer, real wages would gradually increase along with productivity.
However, the fear that this effect would destabilize the economy by causing everyone to stuff their matterses with money and never buy anything is unfounded. The thought is that if goods are constantly becoming cheaper and better, nobody would anyone spend any money now if they can get more in the future.
This overlooks the fact that people by default have a certain time preference - why would I care that bread becomes cheaper 1 year from now if I am hungry now? In cases of decreasing prices, people will save until the good is cheap enough to be more immediately valuable than whatever else could have been bought in the future.
A good example is personal computers/smartphones, which have become exponentially better with time. People who want the latest model for important work or personal prestige have a high time preference and buy even though a better version comes out next year. Students tend to wait for sales where they can buy last year's model at a discount.
An Austrian Taxonomy of Deflation - With Applications to the U.S., by Joseph T. Salerno (29 pages)
The four types of inflation, good or bad, are classified as: 1. growth deflation; 2. cash building deflation; 3. bank credit deflation; and 4. confiscatory deflation.
The possibility of downward flexible nominal prices with a fixed or shrinking money supply is seriously considered by the Austrian school of economics. The main idea is that total macroeconomic output and real wages can increase even while nominal prices decrease providing the government does not institute policies that impair downward flexible market prices.
Economist Hyman Minsky, by contrast, argues that the private credit sector provides long term financing for long lived real assets and that the future nominal cash payment obligations associated these long term finance contracts must be repaid from future sources of income, or from the ability to refinance debt, or from the sale of real assets. If the money supply is fixed and nominal prices are falling it is almost certain to disrupt the ability to make nominal long term debt repayment.
There are two theories about the problems of systemic debt default. One is that the markets would recover rapidly without interference from the government. The other is that the markets will not recover rapidly if the government does nothing.
Roughly speaking nominal wages should remain fixed but things would still get invented and production would become ever more efficient. So real wages would increase as deflation boosted the purchasing power of your wages.
However, it may not be such a good idea to have a completely fixed money supply and deflation - it may become unstable if people noticed that storing money under your mattress was a perfectly effective way to save. If many savers started doing this then it could induce cycles of bubbles and crashes in the value of money. It would probably be better to deliberately increase the money supply by a few percent each year - just enough so that people were not inclined to save simply by storing money.