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.     

The multi-country transfer problem

A general formula is derived for the welfare effects of a set of transfers among several countries in a two-good model with production and substitution, and compatible with Walrasian stability. The relation to recent work on transfer paradoxes is sketched.     

The problem of the uninsured

The problem of the uninsured cannot be fully understood without considering the role of non-market alternatives to ‘market insurance’ called ‘self-insurance’ and ‘self-protection’ (SISP), including the public ‘health care safety-net’ system. We tackle the problem by formulating a ‘full-insurance’ paradigm that accounts for all four interacting insurance measures. We apply two versions of the full-insurance model to estimate, via calibrated simulations, the impacts of SISP on the fraction of uninsured, health spending, and health levels, and to assess how the mandated Affordable Care Act might affect these outcomes in comparison with the CBO projections in 2010. The results indicate that policy analyses which overlook the role of the real price of market insurance relative to the shadow prices of SISP in determining the decision to insure can grossly distort the capacity of mandated reforms like the ACA to insure the uninsured, contain overall health care costs, and improve health and welfare outcomes.     

The fundamental problem of accounting

The fundamental problem of economic accounting is to determine a forward‐looking schedule of rentals, user costs or quasi‐rents to provide for the recovery of irreversible investments. The method derived herein relaxes some restrictive assumptions that are common in capital theory. There can be multiple forms of comprehensive capital. Accounting for all forms of capital, including tangible and intangible capital, is symmetrical. The analytical focus becomes one of fixities and frictions and not optimality. Rentals obey inequalities as opposed to marginal conditions. If discounted profit is positive, rentals, depreciation, and capital value are not unique.     

The college admissions problem is not equivalent to the marriage problem

Two-sided matching markets of the kind known as the “college admissions problem” have been widely thought to be virtually equivalent to the simpler “marriage problem” for which some striking results concerning agents' preferences and incentives have been recently obtained. It is shown here that some of these results do not generalize to the college admissions problem, contrary to a number of assertions in the recent literature. No stable matching procedure exists that makes it a dominant strategy for colleges to reveal their true preferences, and some outcomes may be preferred by all colleges to the college-optimal stable outcome.     

The complexity of the consumer problem

A literal interpretation of neo-classical consumer theory suggests that the consumer solves a very complex problem. In the presence of indivisible goods, the consumer problem is NP-Hard, and it appears unlikely that it can be optimally solved by a human. Two implications of this observation are that (i) households may imitate each other’s choices; (ii) households may adopt heuristics that give rise to the phenomenon of mental accounting.     

The best choice problem under ambiguity

We model and solve best choice problems in the multiple prior framework: An ambiguity averse decision maker aims to choose the best among a fixed number of applicants that appear sequentially in a random order. The agent faces ambiguity about the probability that a candidate—a relatively top applicant—is actually best among all applicants. We show that our model covers the classical secretary problem, but also other interesting classes of problems. We provide a closed form solution of the problem for time-consistent priors using backward induction. As in the classical case, the derived stopping strategy is simple. Ambiguity can lead to substantial differences to the classical threshold rule.     

The big problem of forecasting small change

The United States Mint recently reviewed approaches to forecasting the demand for new coin. This paper reports on methods used to determine fundamental attributes of the data, and uses these to help better determine appropriate model specification in order to better plan coin production. In particular, the debate regarding trend versus difference stationarity in macroeconomic trending data is considered. The interest in the present paper is limited to applying a well known unit root test procedure to an untested macrodata set – changes in US Coin demand – to see whether the test is useful in guiding the specification to improved forecast performance. It is found that the forecast results are somewhat sensitive to the way in which the data are seasonally adjusted, and lessons learned from this ‘case study’ indicate that unit root tests are useful in guiding model specification.     

The problem of political calculation in autocracies

Autocrats depend on their followers to remain in power. They compensate the followers in exchange for their support. Yet, they have few tools to guide them in determining the compensation commensurate with the value of each follower’s support. The failure of political calculation can easily lead to the autocrat’s demise. In semi-authoritarian and democratic regimes, elections provide a solution to the problem of political calculation. In elections, citizens cast votes in exchange for public or private goods. Thus, the number of votes received by candidates and parties can be used as a proxy for the value of their support.     

The principal-agent problem with a satisficing agent

The principal-agent problem is formulated with an expected utility maximizing principal and a satisficing agent. If the outcome set is finite and if there is only one aspiration level, then there are always optimal incentive schemes which can be represented by vectors having only the unique aspiration level and zero as coordinate values. The relation between the monotone likelihood ratio property and the monotonicity of optimal incentive schemes is investigated. This is done not only in the above model, but also in a continuous model with outcomes in an interval, which is much more interesting.     

The energy problem in a small open economy

The paper deals with the economic consequences of an oil price shock in a small open economy. The analysis along neoclassical lines is based upon a three-factor nested CES production function. The model takes account of capital accumulation. Analytical solutions for the short- and long-run are presented for a linearized version of the original model, which makes existing results more tractable.     

辽宁休闲观光农业发展问题分析

在对辽宁休闲观光农业发展现状研究基础上,从供求角度分析辽宁观光农业存在的三大问题,并提出针对性的对策建议。     

Stability under learning: The endogenous growth problem

A local dynamic analysis, in the neighborhood of the steady state, is developed for one and two-sector endogenous growth models. The problem differs from the conventionally assumed growth setups because one considers that expectations concerning the next period value of the control variable (consumption) are formed through adaptive learning. In such scenario, the found stability conditions reveal that convergence to the unique steady state point is feasible if a minimum requirement regarding the quality of learning in the long run equilibrium is fulfilled. Therefore, stability of growth under learning is dependent on the efficiency with which expectations are generated.