# Insecure property rights to land

Now consider what may occur if private property rights over land are insecure. Suppose that there are overlapping claims to *T*, and both individuals devote resources to clarify and enforce their claims over it. Let the resources devoted to clarifying property rights be G_{1} and *G _{2}. *Individuals engage in costly conflict over land. There is a probability

*p*that individual 1 will, as a result of this conflict, ultimately gain the right to the land, where:

Here *w* (where 0 < *q> <* 1) is a measure of the relative security of individual 1's right to the land. If *w =* 0, for example, then individual 1 has perfectly secure property rights to the land. If *w =* 0, then individual 2 has perfectly secure property rights to the land. Any value of *w* in between these two values represents a situation with insecure property rights.

Note that holding the choice of G by individual 2 fixed, a higher G for individual 1 increases the probability that they will prevail in the conflict. However, this comes at a cost, because individual 1 will then have less labour available for production should he win the conflict over land.

If 1 loses the conflict and 2 wins, then 1 has no land and can only produce with the labour that he has left over. Therefore, individual 1's expected benefits are:

and for individual 2 we have:

and where the constraint on labour for each party is:

The first-order conditions are:

For individual 1, and

The first term in each of these equations is the marginal benefit of an additional unit of G, given the choice of the other individual. The second term (-1) is the opportunity cost of a unit of G. Individuals simply take the level of G of the other party as given and choose G up to the point where expected marginal benefit equals marginal cost. There is a unique symmetric Nash equilibrium in which each party chooses the same amount of G. That is, in equilibrium, G* = G* = G*. Plugging this in to equation (7.5) yields:

*T **a*

so that *Ц **= **R*_{i} - *G** = *R** _{{} -* ф(1

*-*

*ф*—. The equilibrium expected benefits here are:

and:

Thus, *ex ante**,* the aggregate production possibilities frontier when there are insecure property rights satisfies:

*7.4.1.2.1 The costs of insecure property rights.* We can now examine the welfare losses from insecure property rights. The first cost is the *ex ante* loss in welfare which comes about because the Edgeworth Box has shrunk as a result of resources being devoted to distribution rather than production. This welfare loss here is equal to the sum of the *G*_{1}^{*} and

_{T}*a*

G*, which is 2G* = 2ф(1 *-**ф**)* . These are the *rent-seeking costs* due to

*a*

insecure property rights, and they are illustrated in Figure 7.4.2, where the dashed box is the old Edgeworth Box, and the solid box is the new Edgeworth Box. Investing in G shrinks the box horizontally, reducing the 'size of the pie'.

The second class of costs comes about because after conflict occurs only one of the parties will end up with the land, whereas efficiency dictates that the land be shared equally between the parties. To isolate this cost, suppose that after the parties chose their G's, they agreed to split the land according to their equilibrium win probabilities, which are *w* and 1 - w. Then aggregate production would be equal to:

*Figure 7.4.2* Rent-seeking costs shrink the Edgeworth Box

*Figure 7.4.3* The cost of "winner takes all" conflict

To compare this with the *ex ante* benefits if such a split did not occur, *(фТ* )^{a} *T ^{a}*

we need to show that *>ф* , or that: *ф ^{а} >ф.* But this is always

*a a*

true if 0 < *ф <* 1 and 0 < a < 1. These costs are illustrated in Figure 7.4.3, where the expected benefits in the absence of the split are *B _{1}* and

*B*whereas after the split they are

_{2 }*B'*and

_{1}*B'*Notice that

_{2}.*B{*and

*B'*need not be on the contract curve.

_{2}The final class of costs come about because even if the parties split land according to their win probabilities *p* and 1 - *(p,* this is not generally Pareto optimal. Efficiency here requires the split to be equal, whereas *p* and 1 - *p* will not, in general, be equal to one half. These are the costs of not being able to exchange land and labour when property rights over the former are insecure.