I think we need more work on this.
capitalism
Pronunciation: (kap'i-tl-iz"um), [key]
n.
an economic system in which investment in and ownership of the means of production, distribution, and exchange of wealth is made and maintained chiefly by private individuals or corporations, esp. as contrasted to cooperatively or state-owned means of wealth.
In the future, let's try not to have any more confusion as to who controls the markets and what system has the government controlling prices.
"I think we need more work on this"
I think we need more cowbell.
A market economy is the method by which resources are allocated, by the individual decisions of buyers and sellers.
Capitalism is better as a description of ownership of resources. The definition you quote is good, but can be misleading ( one could confuse resource allocation with resource ownership ).
In other words, one could see a centrally planned capitalist economic model. Unfortunately, examples to date include Japan ( and by extension, Germany and Italy of the 1930's )
Additionally, people tend to mistake the US as a pure market-capitalist system. It is not. The US has a mixed economic system.