How does lowering a corporate tax rate benefit a nation? When governments talk about about lowering corporate tax rates they claim there is benefit in one form or another. The problem is the mechanism of how the benefit can work is never explained. 

The closest I've seen is that it will result in more investment but often the corporate tax is only after an organisation has made a profit. 

Some sort of worked example of how this may affect decision processes or some analysis of changes that have occurred when companies have lowered corporate tax rates will also be nice.
I. The case for government revenue

The rationale behind this argument is that it it possible to increase the tax revenue by lowering the tax rate. A. Laffer draw a curve which represent this:



The idea is that if your tax rate is above $t^*$, then taxpayers try to evade taxes, develop the shadow economy, avoid taxes, or simply reduce the amount of work that they do because their is a lesser incentive to do more when the state takes a bigger share of the reward.

So the debate is therefore to know whether we are already beyond this optimal tax rate $t^*$ or below. Emmanuel Saez and Thomas Piketty argue that this optimal tax rate is about 70%. Others, such as Arthur Laffer, believe that it is much lower, and that the government revenue would actually increase if the tax rates were lower.

II. The case for growth

Lower tax rates can also be adopted in order to increase the attractiveness of the country to foreign investors, and hopefully develop the economic activity. Many countries have been known recently to struck tax deals in order to attract business: The UK with Google, Ireland with everybody, Luxembourg with Amazon and others, etc. 

Similarly, developing countries tend to create special economic zones where foreign firms can develop their activities and build factories in return for lower taxation.