Essays on Trade and Imperfectly Competitive Markets

This dissertation is a collection of three essays on markets with imperfect competition, with implications for international economics. The first essay presents an analytic solution framework applicable to a wide variety of general equilibrium international trade models, including those of Krugman (1980), Eaton and Kortum (2002), Anderson and van Wincoop (2003), and Melitz (2003), in multi-location cases. For asymptotically power-law trade costs and in the large-space limit, it is shown that there are parameter thresholds where the qualitative behavior of the model economy changes. In the case of the Krugman (1980) model, the relevant parameter is closely related to the elasticity of substitution between different varieties of goods. The geographic reach of economic shocks changes fundamentally when the elasticity crosses a critical threshold: below this point shocks are felt even at long distances, while above it they remain local. The value of the threshold depends on the approximate dimensionality of the spatial configuration. This work bridges the gap between empirical work on international and intranational trade, which frequently uses data sets involving large numbers of locations, and the theoretical literature, which has analytically examined solutions to the relevant models with realistic trade costs only for the case of very few locations. The second essay, coauthored with Glen Weyl, extends the incidence-based framework for the analysis of perfectly competitive markets to imperfect competition. We show how, just as under perfect competition, a wide range of comparative statics and policy analyses turn on simple properties of incidence, particularly the rate at which unit taxes are passed through to consumer prices. We derive local and global incidence properties, the division of surplus among deadweight loss, consumer surplus and profits and show how these are linked to one another under a range of imperfectly competitive environments. We then show how incidence functions as a simplifying analytic and pedagogic device, an empirical sufficient statistic and a key structural parameter in both classic and recently popular topics in industrial economics including platforms, concession auctions, mergers, entry, price discrimination, product design, supply chains and advertising. The third essay, coauthored with Gita Gopinath and Oleg Itskhoki, studies pricing of durable goods by producers with market power. The durable nature of these products makes their pricing differ from that of nondurables, since consumer demand depends not only on prices today but also on their expectation of future prices. When firms cannot commit to future prices, pass-through of cost shocks into prices is incomplete and the adjustment is gradual. This is the case even when prices are fully flexible and in environments where non-durable pricing would generate complete pass-through. Prices are also sensitive to demand shocks and mark-ups are pro-cyclical, in contrast to the case of cost shocks when mark-ups are countercyclical. We present these results for the case of a monopolist, for oligopolistic competition and for monopolistic competition.Economic

Prospecting a Possible Quadratic Wormhole Between Quantum Mechanics and Plurality

We illustrate some formal symmetries between Quadratic Funding (Buterin et al., 2019), a mechanism for the (approximately optimal) determination of public good funding levels, and the Born (1926) rule in Quantum Mechanics, which converts the wave representation into a probability distribution, through a bridging formulation we call "Quantum Quartic Finance". We suggest further directions for investigating the practical utility of these symmetries. We discuss potential interpretations in greater depth in a companion blog post

Casimir Effect Between World-Branes in Heterotic M-Theory

We study a non-supersymmetric $E_8\times\bar E_8$ compactification of M-theory on $S^1/Z_2$, related to the supersymmetric $E_8\times E_8$ theory by a chirality flip at one of the boundaries. This system represents an M-theory analog of the D-brane anti-D-brane systems of string theory. Alternatively, this compactification can be viewed as a model of supersymmetry breaking in the ``brane-world'' approach to phenomenology. We calculate the Casimir energy of the system at large separations, and show that there is an attractive Casimir force between the $E_8$ and $\bar E_8$ boundary. We predict that a tachyonic instability develops at separations of order the Planck scale, and discuss the possibility that the M-theory fivebrane might appear as a topological defect supported by the $E_8\times\bar E_8$ system. Finally, we analyze the eventual fate of the configuration, in the semiclassical approximation at large separations: the two ends of the world annihilate by nucleating wormholes between the two boundaries.Comment: 26 pp, 3 figures, harvmac (b); v2: typos correcte

Deconstructing Noncommutativity with a Giant Fuzzy Moose

We argue that the worldvolume theories of D-branes probing orbifolds with discrete torsion develop, in the large quiver limit, new non-commutative directions. This provides an explicit `deconstruction' of a wide class of noncommutative theories. This also provides insight into the physical meaning of discrete torsion and its relation to the T-dual B field. We demonstrate that the strict large quiver limit reproduces the matrix theory construction of higher-dimensional D-branes, and argue that finite `fuzzy moose' theories provide novel regularizations of non-commutative theories and explicit string theory realizations of gauge theories on fuzzy tori. We also comment briefly on the relation to NCOS, (2,0) and little string theories.Comment: 22 pages, 3 figures, typos caught and refs added; expanded interpretation of discrete torsio

D-Sitter Space: Causal Structure, Thermodynamics, and Entropy

We study the entropy of concrete de Sitter flux compactifications and deformations of them containing D-brane domain walls. We determine the relevant causal and thermodynamic properties of these "D-Sitter" deformations of de Sitter spacetimes. We find a string scale correspondence point at which the entropy localized on the D-branes (and measured by probes sent from an observer in the middle of the bubble) scales the same with large flux quantum numbers as the entropy of the original de Sitter space, and at which Bousso's bound is saturated by the D-brane degrees of freedom (up to order one coefficients) for an infinite range of times. From the geometry of a static patch of D-Sitter space and from basic relations in flux compactifications, we find support for the possibility of a low energy open string description of the static patch of de Sitter space.Comment: 46 pages, harvmac big; 14 figure

Clean Time-Dependent String Backgrounds from Bubble Baths

We consider the set of controlled time-dependent backgrounds of general relativity and string theory describing ``bubbles of nothing'', obtained via double analytic continuation of black hole solutions. We analyze their quantum stability, uncover some novel features of their dynamics, identify their causal structure and observables, and compute their particle production spectrum. We present a general relation between squeezed states, such as those arising in cosmological particle creation, and nonlocal theories on the string worldsheet. The bubble backgrounds have various aspects in common with de Sitter space, Rindler space, and moving mirror systems, but constitute controlled solutions of general relativity and string theory with no external forces. They provide a useful theoretical laboratory for studying issues of observables in systems with cosmological horizons, particle creation, and time-dependent string perturbation theory.Comment: 38 pages, harvmac big, 6 figure

On Smooth Time-Dependent Orbifolds and Null Singularities

We study string theory on a non-singular time-dependent orbifold of flat space, known as the `null-brane'. The orbifold group, which involves only space-like identifications, is obtained by a combined action of a null Lorentz transformation and a constant shift in an extra direction. In the limit where the shift goes to zero, the geometry of this orbifold reproduces an orbifold with a light-like singularity, which was recently studied by Liu, Moore and Seiberg (hep-th/0204168). We find that the backreaction on the geometry due to a test particle can be made arbitrarily small, and that there are scattering processes which can be studied in the approximation of a constant background. We quantize strings on this orbifold and calculate the torus partition function. We construct a basis of states on the smooth orbifold whose tree level string interactions are nonsingular. We discuss the existence of physical modes in the singular orbifold which resolve the singularity. We also describe another way of making the singular orbifold smooth which involves a sandwich pp-wave.Comment: 24 pages, one figur

Pass-Through, Welfare, and Incidence under Imperfect Competition

政策の費用対効果を考えるための新たな枠組みの提案 --生産、消費、労働など多分野への応用に期待--. 京都大学プレスリリース. 2022-07-27.To tax or not to tax, is that even a question?: Resolving issues related to tax efficiency assessments. 京都大学プレスリリース. 2022-07-28.This paper provides a comprehensive framework to study welfare effects of multiple policy interventions and other external changes under imperfect competition with emphasis on specific and ad valorem taxation as a leading case. Specifically, in relation to tax pass-through, we provide “sufficient statistics” formulas for two welfare measures under a fairly general class of demand, production cost, and market competition. The measures are (i) marginal value of public funds (i.e., the marginal change in consumer and producer surplus relative to an increase in the net cost to the government), and (ii) incidence (i.e., the ratio of a marginal change in consumer surplus to a marginal change in producer surplus). We begin with the case of symmetric firms facing both unit and ad valorem taxes to derive a simple and empirically relevant set of formulas. Then, we provide a substantial generalization of these results to encompass firm heterogeneity by using the idea of tax revenue that is specified as a general function parameterized by a vector of policy instruments including government and non-government interventions and costs other than taxation