The General Theory of Second Best Is More General Than You Think

Lipsey and Lancaster's "general theory of second best" is widely thought to have significant implications for applied theorizing about the institutions and policies that most effectively implement abstract normative principles. It is also widely thought to have little significance for theorizing about which abstract normative principles we ought to implement. Contrary to this conventional wisdom, I show how the second-best theorem can be extended to myriad domains beyond applied normative theorizing, and in particular to more abstract theorizing about the normative principles we should aim to implement. I start by separating the mathematical model used to prove the second-best theorem from its familiar economic interpretation. I then develop an alternative normative-theoretic interpretation of the model, which yields a novel second best theorem for idealistic normative theory. My method for developing this interpretation provides a template for developing additional interpretations that can extend the reach of the second-best theorem beyond normative theoretical domains. I also show how, within any domain, the implications of the second-best theorem are more specific than is typically thought. I conclude with some brief remarks on the value of mathematical models for conceptual exploration

City Size and the Henry George Theorem under Monopolistic Competition

We analyze the equilibrium and the optimal resource allocations in a monocentric city under monopolistic competition. Unlike the constant elasticity of substitution (CES) case, where the equilibrium markups are independent of city size, we present a variable elasticity of substitution (VES) case where the equilibrium markups fall with city size. We then show that, due to excess entry triggered by such pro-competitive effects, the "golden rule" of local public finance, i.e., the Henry George Theorem (HGT), does not hold at the second best. We finally prove, within a more general framework, that the HGT holds at the second best under monopolistic competition if and only if the second-best allocation is first-best efficient, which reduces to the CES case.City size, Henry George Theorem, monopolistic competition, first-best and second-best allocations, variable elasticity

The Henry George Theorem in a second-best world

経済学 / EconomicsThe Henry George Theorem (HGT) states that, in first-best economies, the fiscal surplus of a city government that finances the Pigouvian subsidies for agglomeration externalities and the costs of local public goods by a 100% tax on land is zero at optimal city sizes. We extend the HGT to distorted economies where product differentiation and increasing returns are the sources of agglomeration economies and city governments levy property taxes. Without relying on specific functional forms, we derive a second-best HGT that relates the fiscal surplus to the excess burden expressed as an extended Harberger formula.JEL Classification Codes: D43, R12, R13http://www.grips.ac.jp/list/jp/facultyinfo/kanemoto_yoshitsugu

City size and the Henry George theorem under monopolistic competition

We analyze the equilibrium and the optimal resource allocations in a monocentric city under monopolistic competition. Unlike the constant elasticity of substitution (CES) case, where the equilibrium markups are independent of the city size, we present a variable elasticity of substitution (VES) case where the equilibrium markups fall with the city size. We then show that,due to excess entry triggered by such pro-competitive effects, the 'golden rule' of local public finance, i.e., the Henry George theorem (HGT), does not hold in the second best. We finally prove, within our framework, that the HGT holds in the second best if and only if: (i) the second-best allocation is first-best efficient, which turns out to be equivalent to the CES case;or (ii) a marginal change in the city size has no impact on equilibrium product diversity at the second best.city size, Henry George theorem, monopolistic competition, first-best and second-best allocations, variable elasticity

On the convergence of monotone schemes for path-dependent PDE

We propose a reformulation of the convergence theorem of monotone numerical schemes introduced by Zhang and Zhuo for viscosity solutions of path-dependent PDEs, which extends the seminal work of Barles and Souganidis on the viscosity solution of PDE. We prove the convergence theorem under conditions similar to those of the classical theorem in the work of Barles and Souganidis. These conditions are satisfied, to the best of our knowledge, by all classical monotone numerical schemes in the context of stochastic control theory. In particular, the paper provides a unified approach to prove the convergence of numerical schemes for non-Markovian stochastic control problems, second order BSDEs, stochastic differential games etc.Comment: 28 page

Optimal Taxation of Education with an Initial Endowment of Human Capital

Bovenberg and Jacobs (2005) and Richter (2009) derive the education efficiency theorem: In a second-best optimum, the education decision is undistorted if the function expressing the stock of human capital features a constant elasticity with respect to education. I drop this assumption. The household inherits an initial stock of human capital, implying that the aforementioned elasticity is increasing. In a two-period Ramsey model of optimal taxation, I show that the education efficiency theorem does not hold. In a second-best optimum, the discounted marginal social return to education is smaller than the marginal social cost. The household overinvests in human capital relative to the first best. The government effectively subsidizes the return to education.Optimal taxation, human capital

The Coordinate-Wise Core for Multiple-Type Housing Markets is Second-Best Incentive Compatible

We consider the generalization of Shapley and Scarf''s (1974) model of trading indivisible objects (houses) to so-called multiple-type housing markets. We show (Theorem 1) that the prominent solution for these markets, the coordinate-wise core rule, is second-best incentive compatible. In other words, there exists no other strategy-proof trading rule that Pareto dominates the coordinate-wise core rule. Given that for multiple-type housing markets Pareto efficiency, strategy-proofness, and individual rationality are not compatible, by Theorem 1 we show that applying the coordinate-wise core rule is a minimal concession with respect to Pareto efficiency while preserving strategy-proofness and individual rationality.microeconomics ;