The dynamics of risk-sensitive allocations

This paper describes Pareto optimal allocations when agents have risk-sensitive preferences as formulated by Hansen and Sargent (IEEE Trans. Automat. Control 40(5) (1995) 968-971). Necessary and sufficient conditions are given for the existence and stability of steady states at which Pareto weights are time-invariant. When all agents are risk-sensitive with the same power reward function there is a unique interior steady state which is stable when the power is positive and unstable when the power is negative. When there is at least one agent with time-additive preferences eventually all risk-sensitive agents have zero Pareto weights.     

OPTIMAL TRANSITION DYNAMICS IN THE LEONTIEF TWO‐SECTOR GROWTH MODEL WITH DURABLE CAPITAL: THE CASE OF CAPITAL INTENSIVE CONSUMPTION GOODS*

We present results on undiscounted optimal policies in the Leontief two‐sector growth model with durable capital. Unlike the results with a labour intensive consumption goods sector, we show that a monotonic optimal programme is only one special case out of many richer possibilities of transition dynamics. Depending on the initial capital stock, and a key parameter ζ that could be interpreted as a marginal rate of transformation of capital between today and tomorrow, an optimal programme may converge to a period‐two cycle; and even when it converges to the golden rule stock, it can do so (damped) cyclically or with a “jump”.     

Sealed bid auctions with uncertainty averse bidders

Summary. Traditional analysis of auctions assumes that each bidder's beliefs about opponents' valuations are represented by a probability measure. Motivated by experimental findings such as the Ellsberg Paradox, this paper examines the consequences of relaxing this assumption in the first and second price sealed bid auctions with independent private values. The multiple priors model of Gilboa and Schmeidler [Journal of Mathematical Economics, 18 (1989), 141–153] is adopted specifically to represent the bidders' (and the auctioneer's) preferences. The unique equilibrium bidding strategy in the first price auction is derived. Moreover, under an interesting parametric specialization of the model, it is shown that the first price auction Pareto dominates the second price auction. Received: December 15, 1995; revised version: February 19, 1997     

Correcting for the Missing Rich: An Application to Wealth Survey Data

It is a well‐known criticism that if the distribution of wealth is highly concentrated, survey data are hardly reliable when it comes to analyzing the richest parts of society. This paper addresses this criticism by providing a general rationale of the underlying methodological problem as well as by proposing a specific methodological approach tailored to correcting the arising bias. We illustrate the latter approach by using Austrian data from the Household Finance and Consumption Survey. Specifically, we identify suitable parameter combinations by using a series of maximum‐likelihood estimates and appropriate goodness‐of‐fit tests to avoid arbitrariness with respect to the fitting of the Pareto distribution. Our results suggest that the alleged non‐observation bias is considerable, accounting for about one quarter of total net wealth in the case of Austria. The method developed in this paper can easily be applied to other countries where survey data on wealth are available.     

The Pareto-Scorza Polemic on Collective Economic Welfare

This paper reviews the 1902–03 polemic between Vilfredo Pareto and Gaetano Scorza, an Italian mathematician, on the validity of what is now referred to as the first law of welfare economics – i.e. the proposition that a point of equilibrium determined under conditions of free competition is Pareto optimal. It establishes that, contrary to the received view, Pareto did not write at cross-purposes to Scorza and his work published after the polemic does not suggest that Pareto eventually sided with Scorza on the issue of collective economic welfare.     

FARSIGHTED COALITIONAL STABILITY OF A PRICE LEADERSHIP CARTEL

This paper analyzes the farsighted behaviour of firms that form a dominant price leadership cartel. We consider stability concepts such as the farsighted core, the farsighted stable sets, and the largest consistent set. We show that: (i) the farsighted core is either an empty set or a singleton set of the grand cartel; (ii) any Pareto efficient cartel is itself a farsighted stable set; and (iii) the set of cartels in which fringe firms enjoy higher profits than the firms in the minimal Pareto efficient cartel is the largest consistent set.     

Implementation of college admission rules

Summary We consider both Nash and strong Nash implementation of various matching rules for college admissions problems. We show that all such rules are supersolutions of the stable rule. Among these rules the lower bound stable rule is implementable in both senses. The upper bound Pareto and individually rational rule is strong Nash implementable yet it is not Nash implementable. Two corollaries of interest are the stable rule is the minimal (Nash or strong Nash) implementable solution that is Pareto optimal and individually rational, and the stable rule is the minimal (Nash or strong Nash) implementable extension of any of its subsolutions.We wish to thank Professor William Thomson for his efforts in supervision as well as his useful suggestions. We are grateful to the participants in his reading class, workshops at Bilkent University, University of Rochester, and in particular Jeffrey Banks, Stephen Ching, Bhaskar Dutta, Rangarajan Sundaram and an anonymous referee for their helpful comments.     

The taxation of trades in assets

When the asset market is incomplete, there typically exist taxes on trades in assets that are Pareto improving. This fiscal policy is anonymous, it is fully and correctly anticipated by traders, and it results in ex post Pareto optimal allocations; as such, it improves over previously proposed constrained interventions.     

Does hidden information make trade liberalization more fragile?

Abstract This paper focuses on the impact of hidden information on strategic interaction in the context of trade agreements. In the presence of informational asymmetry it is possible that a tradeoff between liberalization and sustainability of cooperation emerges. It is shown that it may be optimal to agree on a degree of liberalization associated with a strictly positive ex ante probability of deviation occurring. In that case, cooperation will break down in finite time, and the optimal degree of liberalization cannot be applied indefinitely.     

DISTRIBUTING THE GAINS FROM TRADE WITH INCOMPLETE INFORMATION*

We argue that the incomplete information which the government has about domestic agents means that tariffs become an optimal instrument to protect them from import competition. Using a model where agents have private information about their endowments, we solve for the optimal government policy subject to the political constraint of ensuring Pareto gains from trade, the incentive compatibility constraint, and the government's budget constraint. We find that the optimal policy takes the form of nonlinear tariffs. These tariffs are never complete, in the sense of bringing prices back to their initial level, but always allow some individuals to be strictly better off than at the initial prices.     

Eliciting information from a committee

The paper addresses the mechanism design problem of eliciting truthful information from a committee of informed experts who collude in their information disclosure strategies. It is shown that under fairly general conditions full information disclosure is possible if and only if the induced outcome is Pareto undominated for the committee members.     

Exchange and optimality

Summary. A feasible social state is irreducible if and only if, for any non-trivial partition of individuals into two groups, there exists another feasible social state at which every individual in the first group is equally well-off and someone strictly better-off. Competitive equilibria decentralize irreducible Pareto optimal social states. Received: September 9, 1996; revised version: February 11, 1998     

Budget Balancedness and Optimal Income Taxation

We make two contributions to the theory of optimal income taxation. First, assuming conditions sufficient for existence of a Pareto optimal income tax and public goods mechanism, we show that if agents' preferences satisfy an extended notion of single crossing called capacity constrained single crossing, then there exists a Pareto optimal income tax and public goods mechanism that is budget balancing. Second, we show that, even without capacity constrained single crossing, existence of a budget balancing Pareto optimal income tax and public goods mechanism is guaranteed if the set of agent types contains no atoms.     

An iterative allocation mechanism in the edgeworth box

This paper considers an iterative allocation mechanism which resolves the problem of multiplicity of allocations given by a mechanism in commodity space. At each stage, the average of the extreme allocations is taken and used as the starting point of the next stage. As long as the mechanism is individually rational and Pareto optimal, this iterative procedure yields a unique final allocation which is also individually rational and Pareto optimal. (JEL C63, C71)This paper was written while both authors were at the State University of New York at Buffalo.     

A comparison of city size distributions for China and India from 1950 to 2010

We examine the distributions of Chinese and Indian city sizes for seven decades (1950s to 2010s) using lognormal, Pareto, and general Pareto distributions. We ascertain which distribution fits the data and how the city size distributions change during these periods. The Chinese city size distribution is represented by lognormal in the early periods (1950–1990) and by Pareto in 2010, but is not characterized by Zipf, which could be attributed to Chinese government’s restrictions of migration from rural to urban areas and the one-child policy. In contrast, the Indian city size distribution transitions from lognormal in the earlier periods to Zipf in the later periods.     

A model of political parties

This paper presents a new model of political parties. I assume that the role of parties is to increase the commitment ability of politicians vis-à-vis the voters. Whereas a politician running alone can only offer his ideal policy, the set of policies that a party can commit to is the Pareto set of its members. I show that the commitment mechanisms provided by the institution of parties has no effect when the policy space is unidimensional; the policies parties can induce in equilibrium arise also when politicians are running independently. However, when the policy space is multidimensional, politicians use the vehicle of parties to offer equilibrium policies that they cannot offer in their absence.     

Social security and risk sharing

In this paper we identify conditions under which the introduction of a pay-as-you-go social security system is ex ante Pareto-improving in a stochastic OLG economy with capital accumulation and land. We argue that these conditions are consistent with realistic specifications of the parameters of the economy. In our model financial markets are complete and competitive equilibria interim Pareto efficient. Therefore, a welfare improvement can only be obtained if agents? welfare is evaluated ex ante, and arises from an improvement in intergenerational risk sharing. We also examine the optimal size of a given social security system as well as its optimal reform.     

REMARKS ON A PROCEDURAL CONDITION FOR THE VOTING PARADOX

Schwartz [A Procedural Condition Necessary and Sufficient for Cyclic Social Preference, J. Econ. Theory 137 (2007), 688–695] provides a generalization of the voting paradox by using the impotence‐partition condition. This paper aims to clarify his result by providing several remarks. We show that a main result of Schwartz can be strengthened by replacing strong Pareto by weak Pareto. We also discuss how the impotence partition is related to the standard concept of decisiveness, which is widely employed in the literature on social choice.     

Age‐related Optimal Income Taxation*

In most countries, average income varies with age. In this paper we investigate if and how it is possible to enhance the redistributive mechanism by relating tax payments to age. Using an OLG model where some individuals are low skilled all their life while others are low skilled when young but high skilled when old, we first show how an age dependent optimal income tax can Pareto improve upon an age independent income tax. We then characterize the optimal age dependent income tax. A tax on interest income is part of the optimal tax structure.     

The roommates problem revisited

One of the oldest matching problems is Gale and Shapley's (1962) [8] “roommates problem”: is there a stable way to assign 2N students into N roommate pairs? Unlike the classic marriage problem or college admissions problem, there need not exist a stable solution to the roommates problem. However, stability ignores the key physical constraint that roommates require a room and is therefore too restrictive. This motivates a new matching problem: matching agents subject to an initial assignment. A particularly important example is kidney exchange where after an assignment has been made, subsequent tests may determine that a patient and donor are incompatible. This paper introduces an efficient algorithm for finding a Pareto improvement starting from any status quo roommates assignment.