Property Rights and the Incentive to Work

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This is an example to answer the question do we need Property Law? There are 2 kinds of examples, both are numerical.

Example 1

The first example is that assume there is a farmer, he can produce $2\sqrt{x}$ units of good by exerting $x$ units of effort.

This means that the cost would be $x$ also, and the profit would be $2\sqrt{x}-x$, after a simple calculation, his choice of the production would be $x=1$.

However, if he lost some of the production due to the stealing from others, for example, say $\alpha$ , now his production is $2\sqrt{\alpha x}$

So the society would lose $1-\alpha$ units, it could be more if the products are used in fighting (for the goods).

And this would decrease the incentive to work, since the farmer is not rewarded according to the marginal productivity.

Example 2

The example 2 is more like a question in Game Theory.

Consider there are 2 farmers in the economy society. And,

• Cost of farm is 5
• Revenue is 15
• Cost of stealing is 3

After a simple calculations, the Nash Equilibrium would be (Steal, Steal).

The social optimum would be $(10,10)$ , while the Nash Equilibrium would be $(0,0)$

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That means the protection of propery rights are really important. But How Should Property Rights Be Assigned?