Justice,  Taxation  and  Desert   –  Is  desert-­‐adjusted  taxation  feasible?  

Term Paper: Integrative Seminar Professors Braham and Egger

Tobias Grohmann

MA Philosophy & Economics

February, 28 2014

Introduction  

In the recent behavioral economics literature there has been an increased interest in the question whether the perceived fairness of tax schedules matters for taxpayers’ behavioral response to taxes. For example, Corneließen et. al. (2012) show that the extent to which people deem their tax burden to be fair in comparison to others matters for their labor supply decision. They find that “employees who harbor the perception that managers pay too little in taxes accrue 20 percent more sick days” (Corneließen et. al. 2012, 3).

In addition to this and related findings, researchers from other fields have been theorizing about the relation between perceived tax fairness and tax regimes as well. For instance, Sheffrin (2013) develops a theory of fair taxation based on a folk notion of justice. Moreover, many economists inquire into the relation between tax regimes and how lay people perceive these regimes as well (see for example Mankiw 2010). A substantial portion of these accounts suggest that what matters (at least partly) for fairness evaluations of distributive practices, i.e. tax regimes, is whether or not people are considered to deserve the comparative benefits they receive from these practices (e.g. Miller 1999; Schmidtz 2006). Similarly, Corneließen et al.’s results can be interpreted such that employees perceive tax burden as unfair or unjust when they believe that either they deserve, comparatively, higher after-tax income themselves or that their managers deserve lower tax-income.

Given that tax fairness matters for people’s economic decisions, e.g. labor supply decision, and given the intuition that fairness is a matter of desert, it calls for considering what I call the project of desert-adjusted taxation or desert-adjusted welfare distribution. Desert-adjusted taxation means that the individual tax burden is distributed – at least partly – according to individually deserved tax incidence.1 Or conversely, that individual tax burden is distributed such that agents receive the after-tax income that they deserve. In this paper I will inquire into whether desert-adjusted distribution of after-tax income is feasible. To this purpose, I will conceptualize and formalize the notion of desert as I 1I say that the tax burden should be distributed at least partly according to individual desert, because I want to leave open the possibility that other distributional considerations besides desert may play a role in designing tax schedules.

think is required for the project of desert-adjusted distribution. I shall demonstrate that a conceptual formalization of desert is possible. However, the application of this formalized framework to actual welfare economic policies requires reliable information about agents’ beliefs about desert levels in their population. I shall argue that this information is to a great extent inaccessible and that therefore a formal conceptualization of desert-adjusted distribution of after-tax income appears infeasible. I shall reach my conclusion in two steps: first I shall argue that if deserved income is a matter of the contribution of agents to economic welfare, there exists a way to acquire reliable information about desert levels in a population. The idea is that agents deserve the income that they generate in competitive markets by providing marketable services. Call this the market value theory. Surely, income as information about desert levels is in general accessible. Second, with this result in mind I will then show how the project of desert-adjusted taxation can be conceptualized. However, I will argue that, typically, the overall welfare of a population is not equal to its economic welfare and that not all services provided by agents are marketable. Hence, market value theory is not applicable to all contributions to overall welfare. Therefore, I conclude, that information about agents’ desert is to a great extent inaccessible. Note that, for the sake of argument, I will simply assume that it is desirable for the social planner to use a desert-based account for just taxation. That is, I will not attempt a normative justification of desert-adjusted taxation. Rather I will consider desert-adjusted taxation from a positive perspective. Hence, I reject views on desert-adjusted taxation that make normative or prescriptive assumptions. The only normative claim to which I commit is that we should maximize overall utility. In the following it will be clear that, on a desert-based view, overall utility is cashed out in desert-adjusted welfare, that is to say that utility does not only depend on respective welfare levels but also on agents desert levels.

The contents of this paper are structured as follows. In section 1 I will briefly introduce standard optimal tax theory. More specifically, I will expand on the optimization problem that the social planner faces when it comes to determining the optimal taxation. I shall specifically emphasize the distributive aims of optimal tax policy design. In section 2 I will follow up on the concept of desert. More specifically, I will discuss various interpretations of the appropriate desert basis. I will argue that market value theory is a promising candidate to serve as desert basis. In section 3 I will present Gregory Mankiw’s Just Deserts Theory and show that agents’ deserved income can be determined by the market value theory in competitive markets. In section 4 I will then introduce Gustaf Arrhenius’ formal conceptualization of desert and summarize the basic tenets of his account. I section 5 I will refine his model to accommodate the idea that what matters for desert-adjusted welfare are the agents’ beliefs regarding desert levels in their population. However, I shall also discuss objections to this account. Section 6 finally concludes the discussion.

1  Optimal  Tax  Theory  

In this section I will briefly introduce optimal tax theory as an extension of neoclassical welfare economics. In standard-economic optimal tax theory, optimal taxation is obtained by maximizing an assumed social welfare function such that (1) welfare is

maximized, (2) the cost of taxation/redistribution doesn’t exceed its benefits (efficiency), (3) the government’s budget constraint is satisfied and (4) the government’s redistributive aims are met.

Given these constraints, determining the optimal tax is a rather complicated optimization problem. Let me briefly latch upon some of these difficulties. It is obvious for non-lump-sum taxes that imposing taxes on consumption goods or income will distort relative prices and thus change incentives for consumers and suppliers. For example, if goods are taxed differentially because the government wants to accumulate more revenue from the consumption of some goods for distributional purposes, e.g. cigarettes or luxury goods, budget constraints and budget shares of consumers will be affected. It follows, since income and substitution effects apply, that consumers shift their demand away from highly taxed goods to goods on with lower tax incidence. However, depending on the size of the income and substitution effects, this might imply that the total tax incidence shrinks and the new differential tax doesn’t maximize welfare at all. In total this might lead to a loss in economic efficiency of the tax, since the cost of taxation (welfare loss) exceeds the benefits. Similar optimization problems arise for income taxes as well. For instance, if income taxes rise for a certain income bracket, individuals at the lower end of this bracket will decide to supply less labor in terms of work hours, because their willingness to pay for an additional unit of leisure is higher than the additional after-tax income they acquire for another hour worked. Thus, increasing tax burden for some agents leads to a loss in economic productivity. Yet another example concerns the decision of paying taxes or evading them. Here, the decision to evade taxes on the neoclassical account is modeled as a decision as to whether the expected utility of evading is higher than the expected utility of complying.

Having discussed some of the problems that arise for the social planner when optimizing the welfare function such that welfare is maximized, taxation is efficient, the governments budget constraint and distributional aims are fulfilled, let me briefly introduce the core ingredient of the optimization problem: the social welfare function 𝑊. Typically, the government’s redistributive aims typically determine how welfare is distributed and, thus, determine the specific form of W. For example consider a utilitarian social welfare function. In this case, maximizing overall welfare means maximizing the sum of all individual utility functions in the population. Hence the optimization problem,

max𝑊 = 𝑈!

!

!!!

.

Where the individual utility function 𝑈! is a function with many possible arguments depending on the specific account of what according to the social planner generates utility to the welfare subjects in the population. For instance, the Benthamite utility function is dependent on income per capita only, 𝑈! = 𝑌!. However, there are various other specifications of 𝑈! . For example, exponential utility functions of the form 𝑈! = 1− 𝑒!!!!!, represent maximizing welfare as maximizing expected utility, where 𝑎! is a measure for risk aversion of the individual and 𝑐! itself is a function of the individual’s choices and other exogenous variables.

Yet other accounts do not define distribution of 𝑊 as a maximization of 𝑈!!!!! . For

instance, following Rawls the distributive aims involve maximizing the welfare of the least advantaged (maximin principle), where the optimization problem is,

max𝑊 = min  (𝑈!,… ,𝑈!) Given this brief treatment of optimal tax theory and the involved optimization of the social welfare function, let me finally return to the project of desert-adjusted taxation. To capture the idea of desert-adjusted taxation, I will develop and scrutinize what may be called a desert-adjusted utilitarian social welfare function. Hence, optimizing this welfare function in order to obtain the distributional aims requires maximizing total utility. However, departing from the accounts I have introduced earlier, every individual utility function 𝑈! that goes into W is a function of the agent’s desert. For sake of simplicity assume that utility is measured in deserved after-tax income. The idea behind adjusting income by desert is that the utility of income for a person is increased or decreased depending upon whether it is justly or unjustly enjoyed. (cf. Feldman 1995, p.573) Thus, a conceptualization of desert-based accumulation of tax revenue requires to, first, justify that redistribution should follow people’s desert and, second, to find an appropriate measure and formalization of what people deserve in order to provide a desert-sensitive optimization of the social welfare function. As anticipated, I will not engage in discussions about the justification of desert-based accounts. For this paper I shall simply assume that some government were to have desert-sensitive distributive aims. Given this presumption, I shall set out to explore, the possibility of how desert can be conceptualized in order to formalize desert-sensitivity into an optimization of the social welfare function. Let me begin this project by inquiring in greater detail into the concept of desert.

2  Desert  and  its  proper  basis  

In this section I will briefly sketch the conceptual setting of the folk notion desert. To begin, in the recent philosophical literature authors have argued that desert is in some sense a basic concept, i.e. it is not further reducible to other concepts. By claiming so, philosophers emancipated themselves from Rawls’ Theory of Justice in which there is no place for pre-institutional desert. According to Rawls individuals deserve only because they are entitled to something according to the institutional rules that emerge as a result of the social contract. However many argue that either desert solely constitutes social justice (McLeod 1996) or that desert is one of the constituents of social justice (Miller 1999; Schmidtz 2006). For the purpose of this paper it suffices to say that desert matters for social justice. I will only inquire into that part of social justice and the redistributive implications that hinge on desert and I shall bracket out other considerations pertaining to other concepts such as need. Desert is a three-place relation, between the deserving subject S, the deserved object O that S receives, and the desert basis B on grounds of which S deserves B. Hence,

S deserves O on grounds of B.

For the purpose of this paper it suffices to define S as economic agents and O as after-tax income. It seems more difficult to pin down the appropriate desert basis on grounds of which economic agents deserve their after-tax income. On most accounts that are

interesting for an economic treatment of desert bases, what agents deserve is linked to their performance. For the purpose of this discussion assume that performance is the act of providing contributions to society’s welfare.

Pertaining to the question which desert base is appropriate McLeod (1996) discusses several interpretations of the appropriate desert basis for wages. His analysis is interesting for the present discussion since what applies to wages, intuitively also applies to after-tax income. For example consider effort theory:

ET “Worker A deserves a higher wage than worker B iff A exerts more effort than B; A and B deserve the same wage iff A exerts the same amount of effort as B.” (McLeod 1996, p.207)

Although intuitive and commonly used, this definition of the desert basis as the amount of effort exerted isn’t appealing on further inspection. As McLeod notes, this is because it is not necessarily the case that a higher amount of effort corresponds to a higher quality of the workers performance. So if worker A exerts a lot of effort and delivers a performance that is of lower quality than worker B’s performance who doesn’t exert an equally high amount of effort, then surely it seems implausible to claim that worker A deserves a higher wage than worker B.

Another example is compensation theory: CT “S deserves wage W for doing job J iff (i) S does J; and (ii) W

is adequate compensation for the training, responsibility, and working conditions that J involves for S.” (ibid., p.213)

However, also desert as compensation for performances, given the level of training, responsibility and working conditions doesn’t seem to catch a proper definition of the desert basis of wages. This is so because of the simple fact that workers deserve wages, even if there is nothing they should be compensated for in their jobs. It seems possible to imagine a job that doesn’t require training, that doesn’t involve responsibility and where the working conditions are such that workers have no reason to complain.

Finally consider the third interpretation of the appropriate desert basis in McLeod’s paper, the market value theory:

MVT “S deserves a wage W at t for providing some service R in market M at t iff (i) provides R in M at t; and (ii) if M were free at t, then W would be the market price for R at t.” (ibid., 211)

Although McLeod seeks to refute also this definition of desert as the market value, I think his arguments are not entirely convincing and do not get to the core of MVT of desert. In my view, what is at stake in MVT is that the basis of desert is the action of providing services, that is an agent’s performance. In other words, an agent deserves a certain wage determined by the market price according to his contribution to the provision of marketable services. Therefore, an agent deserves a certain wage for his contribution to overall economic welfare generated in the market. I use “welfare generated in the market” in this context to discriminate from welfare after redistribution. However, note an interesting implication of MVT, which shows that not only mere performance matters for desert. To see this, consider the following. If an agent deserves a certain wage according to the provision of services on the market, then what makes him deserving his wage is not only that he performs, viz. provides services, but also that

others demand his services. More specifically, whether the agent deserves anything at all according to MVT depends on whether others demand his services. And, how much he deserves depends on other agent’s willingness to pay for his services. Thus, an agent’s desert hinges on what other agents think he deserves. To conclude this section, the previous treatment of the different bases of desert shows that for the purpose of determining the deserved wage MVT appears to be a promising candidate. There seem to be two conditions under which an agent deserves his wage. First, that he performs economically, in the sense that he provides marketable services in the market and thus contributes to overall economic welfare in the market. Second, what equally seems to matter is that others appreciate his contribution, i.e. his services, by demanding these services at a certain price. In this sense, the income of an agent seems to be a rich measure as it carries information about an agent’s desert.

3  Market  value  as  the  proper  basis  of  desert?  

To refine the idea that MVT is a promising candidate to determine an agent’s deserved income, let me introduce in an argument by Gregory Mankiw, who spells out the MVT interpretation of the proper desert basis in greater detail.

In his 2010 paper Mankiw argues for what he calls a Just Deserts Theory. According to this theory agents should get what they deserve and that a “person who contributes more to society deserves a higher income that reflects those greater contributions.” (Mankiw 2010, p.295). Clearly, these claims indicate that Mankiw proposes a version of MVT that I introduced in the previous section. Furthermore, Mankiw poses an argument that invites the conclusion that a competitive equilibrium yields a desert-adjusted distribution of income. His argument (ibid.) can be phrased as follows:

(P1) In a competitive equilibrium, the factors of production (i.e.

economic agents) are paid the value of their marginal product. (P2) Each agent’s income reflects the value of what he contributed to

societies production of goods and services. (P3) Economic agents deserve to receive the value of their marginal

product. (MVT) (C) In a competitive equilibrium each agent receives what he

deserves. This argument, I think, is persuasive. It shows that a competitive equilibrium is a rich concept for welfare economics. A competitive equilibrium not only satisfies the standard economic welfare theorems (see for example Mas-Colell et al. 1995, p.311 ff.), but they also seem to provide the basis for desert evaluations on the basis of MVT. That is, given that a competitive equilibrium exists and given MVT is plausible, then agents receive their deserved income.

Of course whether or not agents’ deserts can be determined in competitive markets crucially depends on whether or not the conditions for a competitive equilibrium are satisfied. These conditions typically are, for example, that agents (consumers and producers) are price takers, i.e. market prices are unaffected by the agents actions, that markets clear, i.e. that demand equals supply, that agents have full information about

prices, that all relevant goods are traded on the market, and so forth. Only if these conditions are fulfilled, the income that agents generate in the market reflects their desert according to their performance and the valuation of their performance by others.

The obvious question concerning this argument for the project of desert-adjusted after-tax income distribution is whether or not MVT under the conditions of competitive equilibrium theory can be applied to taxation. For the sake of argument, however, let me for now assume that desert-adjusted after-tax income can be determined in a competitive equilibrium by MVT. To work towards a formalization of desert-adjusted after-tax income distribution, viz. a desert-adjusted social welfare function, let me briefly recapitulate the important prerequisites that should go into such formalization. Against the background of the discussion, desert is a three-place relation between the deserving subject, the deserved object and the desert basis. The deserving subjects are welfare subjects in a given population and the deserved object is desert-adjusted after-tax income. As the discussion so far indicates, the desert basis for income is an agent’s economic performance on a market, measured by how other agents valuate this performance in terms of their demand and the price they are willing to pay for this performance. This captures the general idea that agents evaluate the desert situation in their population themselves and that the social planner designs redistributive policies according to these evaluations.

To conclude this section, if welfare economics and taxation is about achieving redistributive aims, which are cashed out in terms of desert, then what matters is what people think about who deserves what. Hence, what is necessary is that we come to grips with what people think about desert. In a market environment the beliefs about desert of others seem to be sufficiently captured by the income they generate by providing services. However, it may be asked whether MVT can capture the desert of agents in a society, where desert relevant contributions are not merely their provisions of marketable goods, but rather their contribution to society as a whole. Before I come to consider this particular issue in section 5, let me outline a formal framework by which it might be possible to properly specify social welfare functions according to which desert-adjusted welfare distribution is possible.

4  Desert-­‐adjusted  welfare  

In this section I will present and discuss a formal framework to conceptualize the notion of desert into social welfare functions. This framework has been proposed by Arrhenius (2006). Arrhenius conceptualizes desert as fit between an agent’s desert level and the received benefit. This idea is expressed also in Kagan (2012) and Feldmann (1995). The latter writes, “[t]he closer the fit between desert and receipt, the more just the outcome.”(Feldman 1995, p.573). Hence, desert as fit says that the higher the degree of fit between desert and receipt the higher the value of welfare. Desert as fit is opposed to desert as merit, which says that the higher the desert-level the higher the value of welfare. To make the case for desert as fit, a population, in which desert levels are satisfied – no matter their magnitude – , is better off than a population, in which desert levels are high but where these high levels are not satisfied. The desert as fit approach to evaluate welfare levels for agents or groups of agents has intuitive appeal. It seems natural to claim that it is more just when agent A deserves 75 units of welfare and receives these 75 units, than when agent B deserves 100 units of

welfare but receives 75 units. Likewise, it is more just when A deserves 75 units of welfare and receives 75 units, than when C deserves 100 and receives 125. However, if A deserves 75 and receives 75 and D deserves 100 and receives 100, then both welfare positions are equally just. Note that welfare here must be defined as desert-adjusted welfare. It cannot be measured on an income scale or in hedonic states like pleasure and pain. Thus the value of agent A’s desert-adjusted welfare is given by the function 𝑊! 𝑟!,𝑑! , where 𝑟! denotes a numerical expression of A’s level of receipt, and 𝑑!  his level of desert. The closer 𝑟! and 𝑑! the higher we have to evaluate A’s welfare. Thus, in the above case, 𝑊! 75,75 ∼𝑊! 100,100  ≻𝑊! 75,100 ∼𝑊! 125,100 .

Further, Arrhenius defines the functions 𝑅𝑉!(𝑟! ,𝑑!)  and 𝐷𝑉!(𝑟! ,𝑑!)  as value functions for receipt and desert respectively that yield the receipt level of an agent and a desert factor from an agent’s welfare position (𝑟! ,𝑑!) . Thus, in the case of taxation 𝑅𝑉!(𝑟! ,𝑑!)  gives the receipt level 𝑟! in after-tax income, and 𝐷𝑉!(𝑟! ,𝑑!) gives a factor, which expresses the fit between the received income and the deserved income.2 It follows that 𝑊! 𝑟! ,𝑑! is a function of 𝑅𝑉! and 𝐷𝑉!, i.e. 𝑊! 𝑅𝑉! ,𝐷𝑉! . Thus, in line with Arrhenius’ account I define the desert-adjusted social welfare function for population Π as the sum of the desert-adjusted welfare levels in Π,

𝑊! = 𝑊!

!

!!!

𝑅𝑉! ,𝐷𝑉! .

Thus the optimization problem for the social planner for optimal taxation is,

𝑚𝑎𝑥  𝑊! = 𝑊!

!

!!!

𝑅𝑉! ,𝐷𝑉! ,

under the typical constraints of optimal tax theory; that tax revenue be maximized, that taxation is efficient, that the government’s budget constraint is satisfied.

With these definitions settled, let me now cash out the most central tenets of Arrhenius desert as fit account. First, he formalizes the idea that the better the fit between receipt and desert, the higher the desert value, with the additional requirement that the value of over- or under-deserved receipt is symmetric (Arrhenius 2006, p.10). In other words, what matters for desert-adjusted welfare evaluations is how big the distance between the desert-level and receipt – it doesn’t matter in which direction receipt differs from desert. So for example, a deviation of 5 units of receipt from desert is worth the same, no matter whether the agent receives 5 units more or 5 units less than he deserves. Formally,

If   𝑟! − d <   𝑟! − d , then  DV 𝑟!, d >  DV 𝑟! , d ;    and  if   𝑟! − d =   𝑟! − d , then  DV 𝑟!, d =  DV 𝑟! , d .

2 Note that in this paper I depart from Arrhenius’ notation and interpretation of the respective variables. Where he defines the dependent variable in the model as IV, the intrinsic value of agents’ lives, I am interested in their desert-adjusted welfare levels 𝑊! 𝑟! ,𝑑! . Instead of my variable 𝑟! he uses 𝑝! not to denote the level of receipt in after-tax income, but as receipt in terms of hedonic states, pleasure and pain.

So if two agents are on the same desert level d, then, if the difference between A’s receipt and d is smaller (greater/equal to) than the difference between B’s receipt and d, then A’s desert value is greater (smaller/equal to) than B’s. The implication for desert-adjusted after-tax income distribution is straightforward. Given a certain desert level of, say, 100 units the fully just distribution of after-tax income is when the agents receives exactly 100 units. The second basic tenet in Arrhenius’ account formalizes the idea that “[t]he contributive value of a given increase in fit decreases the closer to the desert level one gets.” (Arrhenius 2006, p.12). That is, the closer the fit between receipt and desert, the less valuable is an increase in receipt. Formally, 𝐼𝑓   𝑒! = 𝑒! , 𝑟! − 𝑑 > 𝑟! + 𝑒! − 𝑑 , 𝑟! − 𝑑 > 𝑟! + 𝑒! − 𝑑 , 𝑎𝑛𝑑   𝑟! − 𝑑 > 𝑟! − 𝑑 ,  𝑡ℎ𝑒𝑛  𝐷𝑉(𝑟! + 𝑒! ,𝑑) − 𝐷𝑉(𝑟! ,𝑑)  <  𝐷𝑉(𝑟! + 𝑒!,𝑑) − 𝐷𝑉(𝑟!,𝑑).  

Hence, the value of welfare is marginally decreasing in an increase in fit between desert and receipt. This accounts for the intuitive idea that if we were to distribute one additional unit of receipt, we would rather give this unit to W(3,10) than to W(8,10). This result is interesting because, although Arrhenius’s account is straightforward utilitarian, it seems to be possible to accommodate the idea that we should first care about the least well-off in terms of desert. Given these two tenets, Arrhenius shows that if two individuals deserve the same, an equal distribution of receipts is always better than an unequal distribution of incomes. The same holds for different populations. 3 If all agents in a population, say, people in sufficiently similar jobs and sufficiently similar circumstances, deserve the same after-tax income, then an equal distribution of income, even if desert levels are not met, is better than any other unequal distribution, where some desert levels are satisfied and others are not.

To conclude, with a desert-adjusted social welfare function it seems possible to integrate many distributional ideas. For example, by maximizing the desert-adjusted welfare function in a purely utilitarian fashion, it is even possible to satisfy the Rawlsian maximin principle. This is due to the decreasing marginal effect of receipt increases in an increase in desert as fit levels. It seems also possible to derive straightforward implications for tax-policy design from this account. For example desert-adjusted taxation implies that if income increases disproportionally with desert, then the income, which exceeds the desert level, should be taxed higher. Redistribution would then claim that individuals who cannot satisfy their desert level with their own payroll income should receive tax benefits in one form or another. Thus, progressive tax systems are, to a certain degree, in line with these considerations. Yet, since the tax basis in progressive tax systems is income, not adjusted to desert, some individuals will receive undeserved benefits, and others will forego deserved benefits.

5  Refinements  and  objections  to  desert-­‐adjusted  welfare  

In this last section I will present some refinements and objections to the proposed desert-based taxation account that I have presented so far. Some of these objections will

3 For formal proofs of these results, see (Arrhenius 2006, pp.13–15).

prove useful to clarify basic misunderstandings; others will turn out to be difficult to counter. Let me start off with a simple example. Imagine agent A whose welfare position is (100, 75), viz. he receives 100 units whereas he only deserves 75 units. A’s welfare position is surely not bad for A. In fact he might gain a lot of utility from his 100 units of receipt. So there is nothing wrong or objectionable with his personal welfare position for him. So why not leave him with his 100 units of welfare?

There are two ways to answer this question. The first says that one must carefully distinguish the notion of desert and other bases of re-distributional policies, e.g. need, or standard utility maximization. From a standard utilitarian point of view, it is always better, viz. it generates more utility, when agents get more than some pre-defined threshold – even if this threshold is defined according to desert. However, defending the desert-based account I respond the following. Surely, it might be better for A if he receives more, but is it better for the welfare of the population? So for example, if there is not enough income to distribute to satisfy deserts, or if there is so much income as to over-satisfy deserts, then it seems plausible to claim that the deviation from desert levels is minimized. This can only be obtained if the deviation from desert levels is equal, no matter what the individual agents’ desert levels. This follows from Arrhenius’ marginal decreasing value of welfare in receipt-desert fit. Some large deviations from deserts reduce the welfare values and thus the value of 𝑊! to a great amount. On the other hand, the weight of equal deviations from desert levels on the value of 𝑊!is in total lower. So, on the desert-based account it maximizes utility if deviations from desert levels are equalized. The second way to answer the question whether or not to leave A with his undeserved 100 units of welfare is the following. To repeat, there is nothing wrong or objectionable with his personal welfare position for him. The point is that there might be something wrong with A’s welfare position for others, in the case they think A doesn’t deserve his receipt (see Persson 1997, p.320 for a similar point). To accommodate other agents’ perception of what a specific agent deserves, recapitulate the discussion of the proper desert basis for income and Mankiw’s Just Deserts Theory. It demonstrated that determining an agent’s deserved income depends on his performance and whether and to which extend other agents valuate his performance. Hence, an addendum to the desert-adjusted welfare account that I have introduced in the previous section specifies that the desert levels 𝑑! are determined by what the agent believes that he deserves and by what other agents believe he deserves. Hence, 𝐷𝑉! is a function of the beliefs of agent i and the beliefs of all other agents concerning i’s desert. Given these considerations, an agent’s individual welfare function is not only dependent on his own desert, but also by other agents’ beliefs about his desert. So, the agent’s perception of his own welfare position with regard to desert is penalized in some sense by how other agents perceive his welfare position with regard to desert. Hence, desert-adjusted welfare evaluations of states of affairs do not only involve a personal viewpoint, but rather they involve more. As anticipated, what is important are the viewpoints of other agents in the population. To formalize this idea, I propose the following function for 𝐷𝑉!,

𝐷𝑉! =!!

𝐵!(𝑟! ,𝑑!)!

!!!

.

This expression of 𝐷𝑉!, says that the desert value of i depends on the averaged sum of what all agents in population believe about the fit between receipt and desert of agent i. Thus, the higher the population as a whole perceives the fit between i’s desert and receipt, the higher the value of the factor 𝐷𝑉! and vice versa.

Hence, the optimization for the social planner yields,

𝑚𝑎𝑥  𝑊! = 𝑊!

!

!!!

𝑅𝑉! ,𝐷𝑉!    

𝑤𝑖𝑡ℎ  𝑅𝑉! = 𝑟!  𝑎𝑛𝑑  𝐷𝑉! =!!

𝐵!(𝑟! ,𝑑!)!

!!!

.

An obvious objection against this formalization of desert-adjusted welfare distribution is that information about agent’s beliefs about their desert value is inaccessible; not to mention beliefs about other agents’ desert values. Yet, in the case where agents’ deserts are determined according to their contributions to economic welfare, MVT is a promising candidate to come to grips with what other agents believe about the desert of others. Recall that the discussion of Mankiw’s Just Deserts Theory demonstrated that given a competitive equilibrium agents’ deserved income was determined by the demand of the services they supply in the market. However, this result obtains only if those services are in fact exchanged on a market, which fulfills the conditions of a competitive equilibrium.

As I have anticipated earlier and dismissed for the moment, it seems questionable whether it is possible to determine agents’ deserts when their contributions to the overall welfare of society is at stake. Surely, if society’s overall welfare is defined only in economic welfare, then MVT does the job. However, typically overall welfare is not a matter of economic welfare alone. Consider for example the case of positive or negative externalities, which are not objects of exchanges in the market but nonetheless determine societies overall welfare. It seems impossible to attribute a market price to them on the basis of which an agent’s contribution to overall welfare can be cashed out.

Mankiw makes a similar point when he discusses the desert of the likes of Steve Jobs or J.K. Rowling. “The public perceives them (correctly or incorrectly) as getting more than they contributed to society.” (Mankiw 2010, p.295) Note that Mankiw doesn’t distinguish between economic welfare and overall welfare. Thus, “contributing to society” must be understood as contributing to economic welfare. However, Steve Job’s or J.K. Rowling’s contributions to overall welfare to society cannot simply be understood on the ground of the economic welfare generated by their contributions – although this contribution is definitely considerable.

In fact, their contributions to overall welfare are positive externalities without explicit market value. It doesn’t seem possible to price the value of Steve Job’s contribution in terms of his inspiration to other entrepreneurs in Silicon Valley or the pleasure that children experience when they re-play scenes from Harry Potter books. Intuitively though, it is plausible to claim that, although some portion of their contributions to

society is not marketable, they deserve to be rewarded also exactly for this portion of their contributions. However, MVT cannot account for this intuition. This is because MVT cannot determine deserts other than on a basis of contributions to economic welfare. Other desert bases such as pleasure, which don’t result necessarily in any economic activity, do not seem to fall under the scope of MVT.

To conclude this section, although it seems possible to defend desert-adjusted welfare distribution against some worries and to present some refinements, there seems to be a insurmountable limitation to it. This limitation concerns the scope of MVT, which does not go beyond marketable goods. Hence, as I see it, there is no possible way to gain reliable information concerning the beliefs of agents about desert levels when it comes to contributions to society as a whole.

Conclusion  

In this paper I set out to inquire whether the project of desert-adjusted welfare distribution is feasible. I have argued that, although there is a comprehensive formal framework to conceptualize the notion of desert for welfare economics, this framework cannot deliver in practice what it promises in theory. This spurning conclusion is due to the seeming impossibility of gaining all the relevant information about what agents believe about their own desert and the desert of others.

To reach this conclusion I have developed a formal framework of desert-adjusted welfare distribution in two steps. First, I have inquired into the question regarding the appropriate desert basis according to which after-tax income levels should be determined. I have showed on the basis of Mankiw’s Just Deserts Theory that the Market Value Theory about the proper basis of desert can provide reliable information about agents’ deserts. This information is contained in the income that agents generate in competitive markets. According to Market Value Theory agents deserve their income because they provide contributions to economic welfare. The agents’ desert, then, is determined on the grounds that other agents demand their services at a certain price. In a second step I have explored a formal framework of desert-adjusted welfare distribution by Arrhenius. His account provides a consistent procedure to derive a desert-adjusted social welfare function. I have shown that it is possible, at least formally, to include agents’ evaluations of what they believe about their own desert as well of what they believe about other agents’ desert in this framework. Yet, although the resulting account and welfare function seems to conceptually capture all desired considerations, it seems impossible to apply this framework to actual agents and their considerations about desert levels in their population. This is simply because not all contributions to a population’s welfare are strictly economic contributions. Hence, the project of desert-adjusted taxation or welfare distribution appears infeasible.

References  

Arrhenius, G., 2006. Desert as Fit  : An Axiomatic Analysis. In R. Feldman et al., eds. The Good, The Right, Life and Death. Burlington VT: Ashgate Publishing Company, pp. 3–18.

Corneließen, T., Himmler, O. & Koenig, T., 2012. Fairness Spillovers – The Case of Taxation. Preprints of the Max Planck Institute for Research on Collective Goods Bonn, 17.

Feldman, F., 1995. Adjusting Utility for Justice: A Consequentialist Reply to the Objection from Justice. Philosophy and Phenomenological Research, LV(3), pp.567–585.

Kagan, S., 2012. The Geometry of Desert, Oxford: Oxford University Press.

Mankiw, N.G., 2010. Spreading the Wealth Around: Reflections Inspired by Joe the Plumber. Eastern Economic Journal, 36(3), pp.285–298.

Mas-Colell, A., Whinston, M.D. & Green, J.R., 1995. Microeconomic Theory, New York: Oxford University Press.

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Miller, D., 1999. Principles of Social Justice, Harvard University Press.

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Schmidtz, D., 2006. Elements of Justice, Cambridge University Press.