In a market capitalist system, capital and land are private property. Enterprises may be formed by individuals who can get access to land and equipment, either because they own it or can rent or borrow to get it, and who can hire labor or employ themselves. Enterprises organize and direct production, and they are operated for the private benefit of the person who organizes the enterprise. Private benefit is interpreted as profit, so we say that the enterprises maximize profits.
In a capitalist economy or in any economy, production is limited by existing resources and technology. We can express this limit with a concept from neoclassical economics: The production possibility frontier. Once again, we will use the simplified production possibility frontier for Economia, which produces only machinery and food. Here it is, to help jog your memory. The idea is that economia can produce any combination of food and machinery on or below the curve.

Figure 1
The economy can produce only combinations on or below the curve. But what combination of goods will be produced? Of course, that will be determined by and equilibrium of supply and demand, but we can skip over a many of the details from chapters 3-14 above. In an ideal market, production at market equilibrium will give the highest possible market value.

Figure 2
But combination * is not just the greatest market value. In the ideal market capitalist system, the prices reflect consumers' "marginal benefits," and that means that the combination of outputs at * is efficient.
Of course, there may be other things about capitalism that are more important than this. Some economists would argue that it is the creative act of forming enterprises and discovering new technologies that is most important, especially in the long run, and that even a capitalism that departs quite far from this ideal could still have great advantages. But this discussion summarizes the argument for market economies in neoclassical economics, and thus it summarizes the neoclassical ideal conception of capitalism.