How are capitalism and private property related?
Private property rights are central to a capitalist economy, its execution and its legal defenses. Capitalism is built on the free exchange of goods and services between different parties, and nobody can rightfully trade property they do not own. Conversely, property rights provide a legal framework for prosecuting aggression against nonvoluntary means of acquiring resources; there is no need for capitalist trade in a society where people could simply take from others what they want by force or the threat of force.
Private Property, Ownership and Homesteading
Contemporary notions of private property stem from John Locke's theory of homesteading. In this theory, human beings gain ownership of a natural resource through an act of original cultivation or appropriation; Locke used the expression "mixing of labor." For example, if a man discovered an unknown island and began to clear the land and build a shelter, he is considered the rightful owner of that land. Since most resources have already been claimed at some point in history, the modern acquisition of property takes place through voluntary trade, inheritance, gifts or as collateral on a loan or a gambling wager.
Private Property Promotes Economic Efficiency
Most political theorists and nearly all economists argue that capitalism is the most efficient and productive system of exchange. Private property promotes efficiency by giving the owner of resources an incentive to maximize its value. The more valuable a resource, the more trading power it provides the owner of the resource. This is because, in a capitalist system, someone who owns property is entitled to any value associated with the property.
When property is not privately owned, but rather shared by the public, a market failure emerges known as the Tragedy of the Commons. The fruit of any labor performed with a public asset does not belong to the laborer but is diffused among many people. There is a disconnect between labor and value, creating a disincentive to increase value or production. People are incentivized to wait for someone else to do the hard work and then swoop in to reap the benefits without much personal expense.
The owners of private property have the right to transfer ownership as they see fit. This naturally cultivates trade between those with different resources and different wants. Since most people want to maximize the value of their trade, competitive bids are accepted to receive the highest exchange value. Owners of a similar kind of resource compete with each other for exchange value. This system of competition creates supply and demand.
Consider this simplistic example: someone owns a goat and would rather have chickens. He decides to sell his goat to purchase chickens. All of the sellers of chickens compete for his money, which drives prices lower. He must similarly compete with all other goat sellers when trading his goat.
Private Property and Law
The reason humans are willing to compete with each other in voluntary trade is precisely because there are laws that protect private property. For a person to receive property he believes is valuable, he must provide a service that someone else believes is valuable. Everyone gains in the ex-ante sense.