Lenin and Marx may not recognize nor approve of China today. But to not recognize the hand, communist inspired and dedicated, in every aspect of their society, including the economy is myopic. Even my 18 year old came away from a trip to China this summer with the observation that the free small businesses that proliferate are actually just selling products produced by government manufactures, at the largess of the government. Funny he described China almost exactly as A4's did, large grey prison.
I should have made clear from the beginning that when I say China is no longer truly communist, I'm referring specifically to its economy, not its governmental institutions, because I don't disagree with A4s nearly as much as our argument makes it appear I do. The Communist Party's absolute hold on power remains virtually the same as it's been since 1949. And I don't disagree with the statement that China is a big gray prison either. It's big, it's gray, and you can't leave.
I'm interested to know, however, how your son or daughter could tell which products in Chinese shops were made by government manufacturers. I'm sure that in order to set up the factory, the correct local government officials had to be paid off and that those same officials maintain a close and lucrative relationship with the factory (corruption is par for the course in China). But the business itself is mostly free to succeed or fail on its own according to how its goods fare in the market--there's no central planning giving the factory quotas to meet like we'd associate with the Soviet Union or Maoist China. Heck, a rapidly growing number of Chinese now own stocks, and virtually everyone (excluding China's millions of peasants, for whom little has changed) is out to increase their personal wealth. I'm sorry, but that's not what I call communism.
Free market? Well... no, and I probably should never have thrown that term out there, but then again, a true free market is just theoretical anyway. But despite government involvement China's economy is still more market-driven than it is centrally controlled.
Free people? Nooooo, not by a long shot. There is only rule of government in China, not rule of law, and as I've said before, Chinese citizens have no civil rights to speak of. The government may not try to control people's personal lives as much as they used to, but they're still very diligent about silencing dissent, and their punishments are swift and usually severe. Who knows how long they'll be able to keep that up, especially with a growing middle class, but from that perspective, China is as communist now as it ever was.