Convince everyone that we have arrived in a period of abundance and maybe corruption will subside.
Well, we are already convinced, to a great extent - and, in realty, our corruption is very limited, comparing to what's going on in Russia, India, Brazil, or Mexico (to name a few countries of comparable size and social complexity).
But I suspect that the instinct you are talking about, while quite real, plays a secondary role. Most of corruption stems from the structural flaws that can be fixed by limiting the scope and role of government. It should be a cop and a guard, not a business partner or distributor of goodies.
All such rosters should be taken with a grain of salt, but if we look, for example, at the dozen of "least corrupt" and the dozen of "most corrupt" polities of the world in the Corruption Perception Index of the Transparency International, you see strong negative correlation between liberalism (in the European sense - "libertarianism") and corruption. The free-market havens of New Zealand, Switzerland, Canada, Australia, Singapore, Denmark, etc are viewed as the least corrupt (Chile being the least corrupt in Latin America and the developing world at large), while authoritarian socialists are bunched up at the bottom: North Korea, Uzbekistan, Turkmenistan, Venezuela, Zimbabwe, Ukraine...). (
2012 Corruption Perceptions Index -- Results)
Of course, it may be just that liberalism works in places that are culturally resistant to corruption, and fails elsewhere, but it is hard to believe that Chile (#20) and Ecuador (#118) or Argentina (#102) are THAT different culturally. Or that Taiwan, Hong Kong and Singapore (## 37, 14, 5) are populated by some different kinds of Chinese (China: #80)