A new test for D-stability

A sufficient condition for D-stability of an n × n matrix A is the existence of a positive diagonal matrix P such that PA + A′P is negative definite. The search for P is replaced by solving a convex minimization problem.     

Mixed Equilibrium in a Downsian Model with a Favored Candidate

This paper examines competition in the standard one-dimensional Downsian model of two-candidate elections, but where one candidate (A) enjoys an advantage over the other candidate (D). Voters' preferences are Euclidean, but any voter will vote for candidate A over candidate D unless D is closer to her ideal point by some fixed distance δ. The location of the median voter's ideal point is uncertain, and its distribution is commonly known by both candidates. The candidates simultaneously choose locations to maximize the probability of victory. Pure strategy equilibria often fail to exist in this model, except under special conditions about δ and the distribution of the median ideal point. We solve for the essentially unique symmetric mixed equilibrium with no-gaps, show that candidate A adopts more moderate policies than candidate D, and obtain some comparative statics results about the probability of victory and the expected distance between the two candidates' policies. We find that both players' equilibrium strategies converge to the expected median voter as A's advantage shrinks to 0. Journal of Economic Literature Classification Numbers: C72, D72.     

On incentive structures of a socialist economy

This paper considers an incentive structure B_T as an alternative to the incentive structure B_D recently suggested by Domar. Both of these incentive structures induce managers in a planned economy to provide the socially desirable output level while allowing them to set prices. In two aspects B_T is better than B_D. First, B_D works only if demand is elastic at the optimal output level while B_T works whether demand is elastic or inelastic at that level. Second, even when demand is elastic at the optimal level, there are circumstances for which output converges to the optimal level faster under B_T than under B_D.     

Diversification of interdependent prospects

This paper extends the stochastic dominance approach to the problem of diversification of interdependent prospects. One basic result is that a risk averter should always mix any two identically distributed prospects, regardless of the nature of the interdependence between them. A similar result holds for the case of n prospects, provided all the joint distribution functions of dimension n ? 1 are identical. When the n-dimensional joint distribution function is symmetric, then the optimal strategy is to put an equal amount into each prospect. The paper also provides conditions which make diversification optimal in the absence of identical marginal distributions.     

The stability of the cournot oligopoly model: A reassessment

The stability properties of the Cournot oligopoly model are examined for the continuous adjustment process. Sufficient conditions for instability are established which are shown to be of significance when the number of firms, n, is small. Local and global stability are shown under appropriate conditions which for global stability include the restriction n ? 5. The proof of global stability corrects a well-known proof by F. Hahn (Rev. Econ. Stud.29 (1962), 329–331). Results for the discrete time adjustment process are reported and the restrictiveness of the model's assumptions are discussed.     

Cyclic sets in multidimensional voting models

Simple majority rule usually does not yield an unambiguous consistent outcome. Assuming a characterization of the set of potential outcomes as Rⁿ and an odd number of voters with quasiconcave preferences, a unique, nonempty set of majority rule cycles exists. Sufficient conditions are established for the top cycle set to encompass the entire policy space. Generalized quadratic utility functions satisfy these conditions.     

Saddle points of Hamiltonian systems in convex Lagrange problems having a nonzero discount rate

Problems are studied in which an integral of the form ∫₀^+∞L(k(t),k(t))e^?ptdt is minimized over a class of arcs k: [0, +∞) → Rⁿ. It is assumed that L is a convex function on Rⁿ × Rⁿ and that the discount rate ? is positive. Optimality conditions are expressed in terms of a perturbed Hamiltonian differential system involving a Hamiltonian function H(k, q) which is concave in k and convex in q, but not necessarily differentiable. Conditions are given ensuring that, for ? sufficiently small, the system has a stationary point, in a neighborhood of which one has classical “saddle point” behavior. The optimal arcs of interest then correspond to the solutions of the system which tend to the stationary point as t → +∞. These results are motivated by questions in theoretical economics and extend previous work of the author for the case ? = 0. The case ? < 0 is also covered in part.     

Extension of Oi's price instability theorem

Oi's theorem that product price variability raises the average profit of a single-product perfectly competitive firm is generalized in this paper to cover the case of an n-commodity firm. Under similar conditions to those mentioned by Oi for the single-product case, commodity (factor or product) price instability raises the average profit of an n-commodity perfectly competitive firm.     

A Solomonic solution to the problem of assigning a private indivisible good

A benevolent Planner wishes to assign an indivisible private good to n claimants, each valuing the object differently. Individuals have quasi-linear preferences. Therefore, the possibility of transfers is allowed. A second-best efficient mechanism is a strategy-proof and anonymous mechanism that is not Pareto dominated by another strategy-proof and anonymous mechanism. In this context, we identify three conditions that are necessary and, together with Voluntary Participation, sufficient for a mechanism to be second-best efficient. This set includes mechanisms that destroy the good at certain profiles. For domains comprising two individuals we provide an explicit characterization of the family of second-best efficient mechanisms.     

Stimulating different types of eco-innovation in the UK: Government policies and firm motivations

In this paper, we adopt a recent OECD framework and examine the role of external policy tools and internal firm specific factors for stimulating three different types of eco-innovations that range on a spectrum of lower to higher technological and environmental impacts: End-of-Pipeline Pollution Control Technologies, Integrated Cleaner Production Technologies and Environmental R&D. Using a novel firm-level dataset from a DEFRA survey, we estimate a Tobit model, which provides empirical evidence showing that these eco-innovations are motivated by different external policy tools and internal firm specific factors. Our findings indicate that End of Pipeline Technologies and Integrated Cleaner Production Technologies are mainly driven by equipment upgrade motives with a view of improving efficiency while environmental regulations are effective in stimulating the End-of-Pipeline technologies and Environmental R&D. Interestingly, alongside government induced regulations, we find that market factors, mainly motivated by cost savings, are effective in driving Environmental R&D. Finally, ISO14001 certification is effective in strengthening the positive impact of environmental management systems on both End-of-Pipeline technologies and Environmental R&D while CSR policies have no significant impact on motivating any of the eco-innovations.     

Substituting one risk increase for another: A method for measuring risk aversion

This paper defines the rate of substitution of one stochastic change to a random variable for another. It then focuses on the case where one of these changes is an nth degree risk increase, and the other is an m  th degree risk increase, where n>m?1$n>m?1$. The paper shows that the rate of substitution for these two risk increases can be used to provide a broader definition and two additional characterizations of the nth degree Ross more risk averse partial order. The implications for local intensity measures of nth degree risk aversion are also examined. The analysis organizes the existing results as well as generates new ones.     

People,skills, and resources: an interaction model for world population growth

A model is set up that yields the equation followed by world population (P), past and present: P = A/(D - t)^M, where t is time and A, D, and M are constants. Cumulated historical population estimates confirm this hyperbolical pattern first noticed by Cailleux, Meyer, and Foerster. Technological indices should grow according to the same pattern; partial confirmation of this part of the model is presented. The growth acceleration crisis that we are now facing may have had a counterpart around 4500 B.C., during the neolithic agricultural revolution. World-population projections up to 2000 A.D. are discussed in the light of the interaction model, with and without resource limitations.     

Tops-only domains

In this paper we consider the standard voting model with a finite set of alternatives A and n voters and address the following question: what are the characteristics of domains \({\mathcal D}\) that induce the property that every strategy-proof social choice function \({f: {\mathcal D}^n \rightarrow A}\) satisfying unanimity, has the tops-only property? We first impose a minimal richness condition which ensures that for every alternative a, there exists an admissible ordering where a is maximal. We identify conditions on \({\mathcal D}\) that are sufficient for strategy-proofness and unanimity to imply tops onlyness in the general case of n voters and in the special case, n = 2. We provide an algorithm for constructing tops-only domains from connected graphs with elements of A as nodes. We provide several applications of our results. Finally, we relax the minimal richness assumption and partially extend our results.     

Asymmetric English auctions

This paper studies equilibria of the n-bidder single-object English, or open ascending price, auction in a setting with interdependent values and asymmetric bidders. Maskin (in: H. Siebert (Ed.), Privatization, Institut fur Weltwirtschaften der Universität Kiel, Kiel, 1992, pp. 115-136.) showed that if the values satisfy a “single crossing” condition, then the two-bidder English auction has an efficient equilibrium. In this paper, two extensions of the single crossing condition, the “average crossing” condition and the “cyclical crossing” condition, are introduced. The main result is that under either of these conditions the n-bidder English auction has an efficient equilibrium.     

An experimental study of bidding in contests of incomplete information

In many contest situations, such as R&D competition and rent seeking, participants’ costs are private information. We report the results of an experimental study of bidding in contests under different information and symmetry conditions about players’ costs of effort. The theory predicts qualitatively different comparative statics between bids under complete and incomplete information in contests of two and more than two players. We use a 2×3 experimental design, (n=2, n=4)×(symmetric complete information, asymmetric complete information, incomplete information), to test the theoretical predictions. We find the comparative statics of bids across the information and symmetry conditions, and the qualitative differences in comparative statics across group sizes, in partial agreement with the theory.     

R&D,innovation activity,and the use of external numerical flexibility

We address theoretically and empirically the impact of R&D and innovation activity (IA) on the use of external numerical flexibility (ENF). We build a firm-sided model showing that a first-order stochastic dominance shift in the productivity distribution function decreases the probability of hiring workers with temporary contracts, while a second-order shift has ambiguous effects. Next, using a dataset based on a survey of Italian manufacturing firms, we find that R&D and IA increase the extensive and intensive margins of employing workers with temporary contracts. Moreover, we disentangle the impact of different types of R&D and IA, finding that extra muros R&D always has a positive effect, while the effect of intra muros R&D is generally null. Also the effect of IA changes according to the type of activity: positive with product innovation, null with process innovation.     

The expected probability of Condorcet's paradox

Let P(n,p) be the probability that there is a Condorcet winner on three alternatives for n (odd) voters. The vector p defines the probability that a randomly selected voter will have any of the six linear rankings on three alternatives as his or her preference ranking. It is shown that if all p vectors are equally likely, the expected value of P(n,p) is given by 15(n+3)²/[16(n+2)(n+4)].     

Relative prices and real factor rewards: A reinterpretation

Two devices are generally available to increase the reward of a productive factor: (i) a direct subsidy to the factor, and (ii) an alteration in relative commodity prices. The Stolper-Samuelson result, whereby method (ii) suffices to improve the real reward of a productive factor in a 2×2 setting with no joint production is shown to be valid in the n-commodity, n-factor model.     

The duality implications of a concave aggregator function

Suppose a production or utility function F is continuous, increasing and quasiconcave on the non-negative orthant. Let C be the associated cost function, G the associated indirect function, and D the associated distance or deflation function. The implications of the concavity of F on the other three dual representations are exhibited.     

Bargaining one-dimensional social choices

We analyze bargaining over the one-dimension characteristic of a public good among n impatient players when decisions require q favorable votes, q?2. Stationary subgame perfect equilibrium strategies are characterized for all games with deterministic protocol. We provide a monotonicity condition (satisfied by all single-peak, strictly quasi-concave and concave utilities) that assures uniqueness for every q whenever player's utilities are symmetric around the peak. Without symmetry, the monotonicity condition assures uniqueness for qualified majorities, q>n/2, provided that agents are sufficiently patient and utilities satisfy an additional regularity condition. Asymptotic uniqueness is assured for qualified majorities by imposing only the monotonicity condition.