By Jens Leth Hougaard
This publication makes a speciality of reading fee and surplus sharing difficulties in a scientific type. It bargains an in-depth research of assorted varieties of principles for allocating a typical financial price (cost) among individuals of a bunch or community – e.g. members, companies or items. the consequences may help readers review the professionals and cons of some of the equipment thinking about phrases of assorted elements akin to equity, consistency, balance, monotonicity and manipulability. As such, the publication represents an updated survey of expense and surplus sharing tools for researchers, scholars and practitioners alike. The textual content is followed by means of useful instances and diverse examples to make the theoretical effects simply accessible.
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Additional resources for An Introduction to Allocation Rules
For a given cost sharing problem (q, C) ∈ D, a cost sharing rule φ speciﬁes a unique vector of cost shares x = (x1 , . . , xn ) = φ(q, C) where the cost shares xi add up to the total costs C(Q) or C(Q). In practice, the cost function may be construed either as the costs of production or as a pricing scheme faced by the agents. In the latter case this pricing scheme can be used directly. In the former case, the cost function can be estimated using registered cost data. 4. Although we shall use the framework of cost sharing it can be noted that in terms of sharing some worth (surplus sharing) the model may be given the following equivalent interpretation: suppose that agents N = 1, .
N , q1 qn q1 qn ˆ Thus, under concave cost functions (increasing returns for problems in D. in production) agents with modest demands are penalized whereas under convex cost functions (decreasing returns in production) agents with modest demands are favored by both rules. 5. Assume that agents can choose their demand strategically and let costs be shared using Increasing Serial Cost Sharing φIS . For instance, assume that two departments demand some service in quantity qi delivered at quadratic costs C(q1 + q2 ) = (q1 + q2 )2 .
In terms of the taxation model this result reads: Proportional taxation – called a ﬂat tax – is the only taxation rule that preserves equality in the sense that if pre-tax incomes become more equally distributed then both taxes and post-tax incomes become more equally distributed. Note that in case of taxation it could naturally be argued that the post-tax income of the agent i should be independent of the other agents pretax incomes q−i . The distributional aspects of taxation rules with respect to such a taxation model is, for example, examined in Moyes (1989, 1994).