Monochromatic and Zero-Sum Sets of Nondecreasing Modified Diameter

Let m be a positive integer whose smallest prime divisor is denoted by p, and let Zm denote the cyclic group of residues modulo m. For a set B = {x1, x2, ..., xm} of m integers satisfying x1 {0, 1} (every coloring Delta : {1, ..., N} -> Zm), there exist two m-sets [see Abstract in the PDF]

Semi-algebraic Ramsey numbers

Given a finite point set $P \subset \mathbb{R}^d$, a $k$-ary semi-algebraic relation $E$ on $P$ is the set of $k$-tuples of points in $P$, which is determined by a finite number of polynomial equations and inequalities in $kd$ real variables. The description complexity of such a relation is at most $t$ if the number of polynomials and their degrees are all bounded by $t$. The Ramsey number $R^{d,t}_k(s,n)$ is the minimum $N$ such that any $N$-element point set $P$ in $\mathbb{R}^d$ equipped with a $k$-ary semi-algebraic relation $E$, such that $E$ has complexity at most $t$, contains $s$ members such that every $k$-tuple induced by them is in $E$, or $n$ members such that every $k$-tuple induced by them is not in $E$. We give a new upper bound for $R^{d,t}_k(s,n)$ for $k\geq 3$ and $s$ fixed. In particular, we show that for fixed integers $d,t,s$, $R^{d,t}_3(s,n) \leq 2^{n^{o(1)}},$ establishing a subexponential upper bound on $R^{d,t}_3(s,n)$. This improves the previous bound of $2^{n^C}$ due to Conlon, Fox, Pach, Sudakov, and Suk, where $C$ is a very large constant depending on $d,t,$ and $s$. As an application, we give new estimates for a recently studied Ramsey-type problem on hyperplane arrangements in $\mathbb{R}^d$. We also study multi-color Ramsey numbers for triangles in our semi-algebraic setting, achieving some partial results

Commodity Taxation and Social Welfare: The Generalised Ramsey Rule

Commodity taxes have three distinct roles: (1) revenue collection, (2) interpersonal redistribution, and (3) resource allocation. The paper presents an integrated treatment of these three concerns in a second-best general equilibrium framework, which leads to the 'generalised Ramsey rule' for optimum taxation. We show how many standard results on optimum taxation and tax reform have a straightforward counterpart in this general framework. Using this framework, we also try to clarify the notion of 'deadweight loss' as well as the relation between alternative distributional assumptions and the structure of optimum taxes.Commodity taxation, efficiency, redistribution, shadow prices

Computation of Equilibria in OLGModels with Many Heterogeneous Households

This paper develops a decomposition algorithm by which a market economy with many households may be solved through the computation of equilibria for a sequence of representative agent economies. The paper examines local and global convergence properties of the sequential recalibration (SR) algorithm. SR is then demonstrated to efficiently solve Auerbach- Kotlikoff OLG models with a large number of heterogeneous households. We approximate equilibria in OLG models by solving a sequence of related Ramsey optimal growth problems. This approach can provide improvements in both efficiency and robustness as compared with simultaneous solution methods.Computable general equilibrium, Overlapping generations, Microsimulation, Sequential recalibration

Taxing capital income: a bad idea

Under a narrow set of assumptions, Chamley (1986) established that the optimal tax rate on capital income is eventually zero. This study examines and extends that result by relaxing Chamley’s assumptions, one by one, to see if the result still holds. It does. This study unifies the work of other researchers, who have confirmed the result independently using different types of models and approaches. This study uses just one type of model (discrete time) and just one approach (primal). Chamley’s result holds when agents are heterogeneous rather than identical, the economy’s growth rate is endogenous rather than exogenous, the economy is open rather than closed, and agents live in overlapping generations rather than forever. (With this last assumption, the result holds under stricter conditions than with the others.)Taxation

Commodity Taxation and Social Welfare: The Generalised Ramsey Rule

Commodity taxes have three distinct roles: (1) revenue collection, (2) interpersonal redistribution, and (3) resource allocation. The paper presents an integrated treatment of these three concerns in a second-best general equilibrium framework, which leads to the "generalised Ramsey rule for optimum taxation. We show how many standard results on optimum taxation and tax reform have straightforward counterpart in this general framework. Using this framework, we also try to clarify the notion of "deadweight loss", as well as the relation between alternative distributional assumptions and the structure of optimum taxes.