If people lower the incentive to save, does the money supply goes up?

Are you asking about reality or an over-simplified classical theoretical model?

In reality, personal savings rates in the developed countries have essentially no effect on investment:

1. Most of the saving is done by corporations, not by private individuals.
http://www.economist.com/node/4154491
http://seekingalpha.com/article/259371-it-s-not-structural-unemployment-it-s-the-corporate-savings-glut

2. There is a surplus of savings just sitting in U.S. banks right now, waiting to be invested
http://research.stlouisfed.org/fred2/series/EXCRESNS

3. Then there is the global savings glut - international capital looking for a place to invest:
http://en.wikipedia.org/wiki/Global_saving_glut
http://www.economist.com/blogs/freeexchange/2010/10/global_imbalances
http://krugman.blogs.nytimes.com/2010/03/16/capital-export-elasticity-pessimism-and-the-renminbi-wonkish/

Even in China, where individuals save much of their income, most of the savings that go into investment are from the government and corporations, not individuals.
http://seekingalpha.com/article/629661-new-chinese-government-spending-binge-creates-investment-opportunities
http://blogs.wsj.com/chinarealtime/2011/02/15/chinese-savings-binge-to-end/

So then the question becomes, if personal saving doesn't affect investment, what happens to the money supply when people spend more.

And that clearly depends on the state of the economy. When the economy is depressed, as it is in the U.S. at present, people spending more does increase the money supply - because it encourages producers to borrow in order to invest to provide additional goods.