All that wealth will trickle down from the rich people.
Their reply would simply be, "No, it won't."
No it won't isn't a good defense in debating. At the very least they'll have to provide some reasoning as to why it does not happen, or they'll look blunt.
Anyway, When debating, it's often best to identify a problem and work from that problem to show your solution is optimal. The problem at hand that would be most beneficial to your position is that the west is falling behind. You can then take this several directions.
-You can claim that government involvement in many businesses is creating skewed relations and preventing alternative methods from becoming mainstream (good example: Swimming pools still use chlorine as a cleaning agent while ozone or UV based cleaning would be better. Nobody is working on alternative cleaning agents though, because chlorine is mandatory).
-Tangential to that would be the claim that the current system, in which minimal pay is ensured and people have a state-sponsored backup plan does not promote a fighter mentality and is making the west sleepy. There is no longer any drive to rise up from newspaper delivery boy to chef of the newspaper because the government is keeping people down trough meaningless rules and oppressive economic policy. Lifting these restrictions would make it significantly easier for people to once again pursue the American dream, which is exactly what is needed to compete with the east.
-On a completely different note, you could claim that a night-watch state puts power into the hands of the people. Instead of pinning them to one system of social services and drowning out all other systems, people would become engaged again, setting up their own systems to help each other. A very early example can be seen in Egypt, where people organize themselves in absence of state support to ensure security and provide basic services like food and blankets to the protesters. Bottom-up systems like these would be significantly more efficient and friendlier to those that have to rely on it then monolithic nation-wide systems.