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.     

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.     

A note on the fundamental theorem of exact aggregation

If individual i's demands for a commodity are a function of prices, p, income M_i and a vector of attributes A_i, then aggregate demand is

This paper derives the necessary and sufficient conditions of f_i, F and a system of functions g_k(M₁,…,M_N,A₁,…,A_N) symmetric in the M's and A's such that F can be written in the form F(p, g, (M₁,…,M_n,A₁,…,A_N),…, g_n(M₁,…,M_n,A₁,… ,A_n)) for all values of its arguments.     

Analysis of the major drivers of the ecological footprint using the STIRPAT model and the PLS method—A case study in Henan Province, China

Taking Henan Province of China as an example, we computed and analyzed the ecological footprint (EF) in 1983–2006. The results showed that the EF in Henan Province quadrupled in the 23 years, but its ecological carrying capacity (EC) was rather low and was in a state of slow decline, indicating that Henan's ecological deficit (ED) had become a remarkable social problem. Therefore, the major drivers of the EF's change were analyzed. According to the simulations with STIRPAT model, the major drivers of Henan's EF were human population (P), GDP per capita (A₁), quadratic term of GDP per capita (A₂), percent of economy excluded in the service sector (Ta₁) and percent of urban population (Tb₁). However, these drivers themselves had strong collinearity, which might produce some uncertain impact to the final results. In order to avoid the impact of collinearity, the method of partial least squares (PLS) was used. The results showed that the major drivers of EF were P, A₁, A₂ and Tb₁. Ta₁ was excluded. Compared with the results by the STIRPAT model, which showed that P is the most dominant driver and the effect of the other drivers could almost be ignored, the results by PLS method were considered as more reasonable and acceptable because the impacts of the A (Affluence) and T (Technology) conditions to the regional EF were still too important to be ignored. In addition, the results acquired by both methods showed that the curvilinear relationship between economic development and ecological impact (EF) or the classical EKC hypothesis didn't exist in Henan Province.     

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.     

Majority committees

Suppose an m-member committee is to be selected by a set of voters from a set X of M > m nominees. If A is an m-member committee, and if as many voters prefer A to B as prefer B to A for every other committee B of m nominees, then A is a majority committee of size m. Although the existence of majority nominees (m = 1) has been extensively analyzed, little attention has been given to conditions that imply the existence of majority committees of size m ? 2. Known restrictions on voters' preferences on X that guarntee the existence of a majority nominee could be applied directly to voters' preferences on m-member committees. However, this definitional exercise lacks intuitive appeal, and a different approach is taken in this paper. The paper presumes that profiles of voters' preferences on X are either dichotomous or single peaked. Both cases ensure the existence of a majority nominee. Independence-monotonicity assumptions are then used to connect voters' preferences on X to their preferences on committees of equal size. Although these assumptions guarantee the existence of majority committees when m = 1 and when m = M ? 1, they do not generally do so when 1 < m < M ? 1. The latter observation motivates additional restrictions on profiles. In the dichotomous case, we consider profiles in which all voters have the same number k of nominees in their preferred subsets, and show that this restriction guarantees the existence of a majority committee of size m for 1 < m < M ? 1 only when k = 1 or k = M ? 1. In the single-peaked case, we consider profiles in which all voters have the same most-preferred (peak) nominee, and prove that this guarantees the existence of a majority committee of size m for every m between 1 and M ? 1.     

How to gamble against all odds

We compare the power of betting strategies (aka martingales) whose wagers take values in different sets of reals. A martingale whose wagers take values in a set A is called an A-martingale. A set of reals B anticipates a set A, if for every A-martingale there is a countable set of B-martingales, such that on every binary sequence on which the A-martingale gains an infinite amount at least one of the B-martingales gains an infinite amount, too.We show that for two important classes of pairs of sets A and B, B anticipates A if and only if the closure of B contains rA, for some positive r. One class is when A is bounded and B is bounded away from zero; the other class is when B is well ordered. Our results generalize several recent results in algorithmic randomness and answer a question posed by Chalcraft et al. (2012).     

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.     

Is the optimum quantity of money compatible with the unique price level under laissez-faire?

The purpose of this paper is to set forth a general equilibrium model to demonstrate that even if the real social costs of producing money are positive, the optimum quantity of money is incompatible with the unique price level under laissez-faire if zero-degree homogeneity of the production-maintenance cost function in M and P is assumed.     

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.     

Computation of search duration probabilities and the integral of the normal distribution function

The constraction of likelihood functions for data on individuals assumed to be sampling from a price distribution and operating a reservation price policy involves calculation of the probability that their duration of search exceeds, say, t periods, P( T > t). In this note we show how this calculation can be simply done by (a) working in continuous time, and (b) using a result on the integral of the Normal distribution function. We then use the result to study some properties of the model.     

Designer path independent choice functions

Summary. This paper provides an algorithm for the construction of all PICFs on a finite set of alternatives, V, designed by an a priori given set I of initial choices as well as the determination of whether the initial set I is consistent with path independence. The algorithm is based on a new characterization result for path independent choice functions (PICF) on finite domains and uses that characterization as the basis of the algorithm. The characterization result identifies two properties of a partition of the Boolean algebra as necessary and sufficient for a choice function C to be a PICF: (i): For every subset A of V the set is an interval in the Boolean algebra 2 ^V . (ii): If A/B is an interval in the Boolean algebra such that C(A) = C(B) and if M/N is an upper transpose of A/B then C(M) = C(N). The algorithm proceeds by expanding on the implications of these two properties.Received: 5 November 2003, Revised: 20 July 2004, JEL Classification Numbers: D00, D70.     

Optimal control problems from second-order difference equations

We examine solutions x?l_∞(Rⁿ) of the equations $\text{F}{}_{\mathrm{t}}\text{(}\text{x}{}_{\mathrm{t?1}}\text{,}\text{x}{}_{\mathrm{t}}\text{,}\text{x}{}_{\mathrm{t+1}}\text{) = 0}$ and derive conditions for the existence of objective functions G_t so that $\text{x}$ solves max_x?l∞ΣG_t(x_t, x_t+1). We specialize the conditions to time autonomous equations and apply them to a competitive industry in temporary equilibrium. The objective function in the example is of the cost-benefit form: consumer surplus minus opportunity cost of labor minus industry-wide cost of investment.     

Recursive preferences and balanced growth

We study a class of utility functions that are defined recursively by an aggregator W(x,y) where u_t=W(c_t,u_t+1). In single-agent economies it is known that a sufficient condition for the existence of a balanced growth path is that utility should be homogenous of degree γ. In the context of a multi-agent economy we show that this restriction implies that either a balanced growth equilibrium fails to exist or all agents have the same constant discount factor. We suggest a generalization of recursive preferences wherein the intertemporal utility function is time dependent. Within this class we establish that there may exist a balanced growth equilibrium even if agents are different.     

Tiebout equilibria in local public good economies with spillovers

This paper analyzes the effects of spillovers on the equilibrium population distribution across jurisdictions in a local public good economy with free mobility. Spillovers are parametrized by a matrix [α_ij] where α_ij ∈ [0, 1]. When spillovers are symmetric and close to 0 or 1 (pure local public goods and pure public goods), all equilibrium jurisdiction structures are symmetric. However, any population distribution can be sustained in equilibrium for some value of the spillover parameter α. In the class of utility functions with additive externalities, we identify the unique family of utility functions for which equilibria are symmetric except for an isolated value of α. This is a class of utility functions which are linear in the public good and a power function of the private good, u(c, γ) = − A(1 − c)^β + γ. With this specification of utility, we show that an increase in α results in a more fragmented equilibrium population distribution, and that when spillovers are asymmetric and large, a jurisdiction which is more centrally located (i.e. benefits more from the public goods provided in other jurisdictions) has a larger population in equilibrium.     

On the existence of equilibria in economies with infinitely many commodities and without ordered preferences

The present paper deals with the existence of equilibria in economies whose commodity space is L_∞(M, M, μ) and where the agents' preferences need not be complete or transitive. Applying a fixed point theorem of Browder, an equilibrium existence theorem for abstract economies (generalized qualitative games) is proven where each agent's choice set is contained in an arbitrary topological vector space. With the help of this theorem the existence of Walrasian general equilibrium for a suitably specified economic model is obtained. The final result is a generalization of T. F. Bewley's (J. Econ. Theory4 (1972), 514–540) equilibrium existence theorem to the case of non-ordered preferences.     

An admissible set occurring in various bargaining situations

Given a set of alternatives S and a binary relation M on S the admissible set of the pair (S, M) is defined to be the set of maximal elements with respect to the transitive closure of M. It is shown that existing solutions in game theory and mathematical economics are special cases of this concept (they are admissible sets of a natural S and M). These include the core of an n-person cooperative game, Nash equilibria of a noncooperative game, and the max-min solution of a two-person zero sum game. The competitive equilibrium prices of a finite exchange economy are always contained in its admissible set. Special general properties of the admissible set are discussed. These include existence, stability, and a stochastic dynamic process which leads to outcomes in the admissible set with high probability.     

Selden's model of inflation: A reexamination

Selden has presented a model which appears to offer strong support for a monetary explanation of inflation. Using bivariate regression to relate percentage changes in quarterly prices to percentage changes in M1 in previous quarters, he finds values of R² from 0.70 to 0.88 and t-statistics of 12 or more when using data for the U.S., Canada, Belgium, and the Netherlands. Unfortunately, the unreported DW statistics for the regressions range from 0.30 to 0.46. Reestimated with a correction for autocorrelation, the t-statistics collapse, values of rho are almost unity, and there is little evidence to support a monetary explanation of inflation.     

A New Matrix Theorem: Interpretation in Terms of Internal Trade Structure and Implications for Dynamic Systems

Economic systems often are described in matrix form as x = Mx. We present a new theorem for systems of this type where M is square, nonnegative and indecomposable. The theorem discloses the existence of additional economic relations that have not been discussed in the literature up to now, and gives further insight in the economic processes described by these systems. As examples of the relevance of the theorem we focus on static and dynamic closed Input-Output (I-O) models. We show that the theorem is directly relevant for I-O models formulated in terms of difference or differential equations. In the special case of the dynamic Leontief model the systems behavior is shown to depend on the properties of matrix M = A + C where A and C are the matrices of intermediate and capital coefficients, respectively. In this case, C is small relative to A and a perturbation result can be employed which leads directly to a statement on the systems eigenvalues. This immediately suggests a solution to the well-known problem of the instability of the dynamic Leontief model.     

Cheap talk in games with incomplete information

The paper studies Bayesian games which are extended by adding pre-play communication. Let Γ be a Bayesian game with full support and with three or more players. The main result is that if players can send private messages to each other and make public announcements then every communication equilibrium outcome, q, that is rational (i.e., involves probabilities that are rational numbers) can be implemented in a sequential equilibrium of a cheap talk extension of Γ, provided that the following condition is satisfied: There exists a Bayesian Nash equilibrium s in Γ such that for each type t_i of each player i the expected payoff of t_i in q is larger than the expected payoff of t_i in s.