Property Rights as a Means of Economic Organization
The quality map of a property right
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- 5.1 A measure of the quality of property rights: The Q -measure
The quality map of a property right
Figure 5 illustrates the characteristic footprint of some actual property right within the characteristic footprint of a perfect property right. The difference between the two areas enclosed by the two maps provides a an idea of the relative quality of the actual property right. 5.1 A measure of the quality of property rights: The Q-measure Given the multi-dimensional nature of property rights, it may be useful to construct an aggregate numerical measure of the quality of a property right. Such a measure can serve in at least two ways. First, it can be used to compare the quality of a given property right with some other property rights of interest. Thus, for instance, it may facilitate the comparison of the property rights content of individual quotas across fisheries and nations. Second, an aggregate measure of the quality of property rights may help social managers to judge the economic efficiency of the institutional framework of the activity in question. Let us for convenience refer to measure of the quality of property rights as the Q-measure. What properties should the Q-measure satisfy? First, is should clearly be increasing in all property rights characteristics. The higher their numerical value (on a scale from 0 to 1) the more perfect the property right. Second, it is convenient to restrict its value to the same numerical range as the characteristics, namely the closed interval [0,1], which "0" indicating zero quality property rights and "1" perfect property rights. Third, since it appears that a positive level of some property rights characteristics, e.g. security and permanence, is necessary for the property right as a whole to be worth anything, a zero value of any of these characteristics should imply a Q-measure of zero as well. We refer to these particular property rights characteristics as essential. Fourth, the Q-measure should be flexible with respect to the individual weights of the various property rights characteristics. The following Q-measure seems to satisfy all these requirements: (1) Q 
This Q-measure comprises M characteristics. The first N, xi, i = 1,2…,N, are essential property rights characteristics, i.e. those that render the property right worthless if they are zero. The remaining M-N property rights characteristics, i.e. xj, j = N+1,N+2,…,M, are non-essential. The exponents, aI, i = 1,2…,M are all positive. So are the weights, w1 and w2,j, which moreover sum to unity. It is easy to check that this Q-measure satisfies all four of the requirements stated above.6 It is, moreover, flexible in the sense that it can account for any number of essential and nonessential characteristics. In our special case of four property rights characteristics, the Q-measure corresponding to (1) is: (2) Q SEP(w1+ w2T), , , , , w1, w2>0 and w1 + w2 =1 where S denotes security, E exclusivity, P permanence and T transferability. The first three characteristics are considered essential. Note that the Q-measure is homogenous with respect to these characteristics. , and represent the elasticity of the Q-measure with respect to the these characteristics, respectively. A fairly natural assumption is that of unitary homogeneity, i.e. “constant returns to scale” where the sum, ++=1. w1 and w2 are weights. w1 is actually the maximum value of Q given that there is no transferability. Due to the non-homogeneous entry of transferability, T, in the Q-measure, the elasticity of Q with respect to transferability is somewhat complicated. More precisely, this is given by the expression E(Q,T)=T/(w1+w2T). Example: The Q-measure, even for our simple case of four property rights characteristics, is far too complicated to be illustrated graphically in a useful manner. However a couple of numerical examples may throw some light on how it works. Let's first of all assume that the exponents , and are all equal and exhibit constant returns to scale, i.e. ++=1. Second let , equal unity. Finally, let w1= 0.6 and w2 =0.4. Table 1 provides an example of the value of the four property rights characteristics for two imaginary property rights. The first is strong in all four characteristics. The other is also strong in security and exclusivity but weak in duration and transferability. For concreteness, we may think of the former as ownership of an apartment and the latter as a rental contract for the same apartment. The numerical details and the corresponding Q- values are given in Table 1.
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