In the context of matrix displacement decomposition, Bozzo and Di Fiore introduced the so-called $\tau_{\epsilon,\phi}$ algebra, a generalization of the more known $\tau$ algebra originally proposed by Bini and Capovani. We study the properties of eigenvalues and eigenvectors of the generator $T_{n,\epsilon,\phi}$ of the $\tau_{\epsilon,\phi}$ algebra. In particular, we derive the asymptotics for the outliers of $T_{n,\epsilon,\phi}$ and the associated eigenvectors; we obtain equations for the eigenvalues of $T_{n,\epsilon,\phi}$, which provide also the eigenvectors of $T_{n,\epsilon,\phi}$; and we compute the full eigendecomposition of $T_{n,\epsilon,\phi}$ in the specific case $\epsilon\phi=1$. We also present applications of our results in the context of queuing models, random walks, and diffusion processes, with a special attention to their implications in the study of wealth/income inequality and portfolio dynamics.

This paper proposes a model where consumption bundle heterogeneity is derived from a network of connections between consumers and firms. In it, consumers slowly become ‘aware’ of differentiated products, adding connections and expanding their choice sets.

Common wisdom in financial markets is that there is temporary arbitrage, or at least a skewed split of surplus, that can be exploited by agents using private information. This is reflected in the enormous investment in market data and trading technologies in the financial services sector. However, Milgrom and Stokey (1982) and Grossman and Stiglitz (1980) show that asymmetric information alone cannot be exploited by an agent in a Walrasian equilibrium, and that this prevents private gains to investment in information precision - which, in turn, can make markets informationally inefficient. This research attempts to resolve this paradox by introducing a model with asymmetric information and precision, but where the micro-structure of market clearing introduces private returns to investment in signal precision, and frictions in the speed of information diffusion are reflected in the aggregate price distribution.

Walrasian market clearing requires solving a large-scale optimization (or, potentially, fixed-point) problem. Algorithms for the auctioneer to solve these problems may be bounded by the curse-of-dimensionality - known in computer science as *infeasibility* - or, with some luck and structure, polynomial algorithms in number of agents and/or the number of signals. Moreover, high information content of idiosyncratic states could exhaust the limited (information-theoretic) bandwidth or computational resources of the auctioneer. The core questions in applying computational bounds to equilibrium are: (1) if there are a huge number of agents, do limitations on the computability and/or bandwidth in calculating the equilibrium lead to misallocation?; and (2) do these constraints change the optimal market structure?.

The least productive agents in an economy can be vital in generating growth by spurring technology diffusion. We develop an analytically tractable model in which growth is created as a positive externality from risk taking by firms at the bottom of the productivity distribution imitating more productive firms. Heterogeneous firms choose to produce or pay a cost and search within the economy to upgrade their technology. Sustained growth comes from the feedback between the endogenously determined distribution of productivity, as evolved from past search decisions, and an optimal, forward-looking search policy. The growth rate depends on characteristics of the productivity distribution, with a thicker-tailed distribution leading to more growth.

Will fast growing emerging economies sustain rapid growth rates until they “catch-up” to the technology frontier? Are there incentives for some developed countries to free-ride off of innovators and optimally “fall-back” relative to the frontier? This paper models agents growing as a result of investments in innovation and imitation. Imitation facilitates technology diffusion, with the productivity of imitation modeled by a catch-up function that increases with distance to the frontier. The resulting equilibrium is an endogenous segmentation between innovators and imitators, where imitating agents optimally choose to “catch-up” or “fall-back” to a productivity ratio below the frontier.