Working Papers

We propose a new solution to the two-player bargaining problem of Nash (1950). The new solution is the same as the Nash solution when the Nash solution makes sense and different from the Nash solution when the Nash solution clashes with our common sense.

In this paper, we consider a broad class of network models where a large number of heterogeneous agents simultaneously interact in many ways. We provide an iterative algorithm for calculating an equilibrium and offer sufficient and “globally necessary” conditions under which the equilibrium is unique. The results arise from a multi-dimensional extension of the contraction mapping theorem which allows for the separate treatment of the different types of interactions. We illustrate that a wide variety of heterogeneous agent economies – characterized by spatial, production, or social networks – yield equilibrium representations amenable to our theorem's characterization.

In this paper, we develop a quantitative general equilibrium model of a city that incorporates the many economic interactions that occur over the space of the city, including commuting, trade, and personal interactions. We show that, despite the many spatial linkages, in the absence of externalities the competitive equilibrium is efficient; conversely, in the presence of spillovers, there exists opportunities for a city planner to increase the welfare of the city inhabitants by restricting the use of land (“zoning”). We provide sufficient conditions for the optimal zoning policy that depend solely on observables and several key model parameters. Finally, we illustrate the flexibility of the model by applying it to study the observed zoning policy of the city of Chicago. Preliminary results suggest that the welfare if residents of Chicago would increase if more area in the central business was allocated to residents district and more area in the outlying neighborhoods was allocated to businesses.

Work In Progress

The Bargaining Problem (without threat)

We consider the Nash (1950) bargaining problem but remove the threat. Within the simplest bargaining problem, we investigate the essence of bargaining by comparing two solutions: one is the Consensus solution, which is introduced in our companion work; the other solution is new, which features compromise.

Toward a Complete Understanding of Optimal Income Tax

We consider the classic optimal income tax model of Mirrless (1972). With two more (mild) conditions, we establish the duality, existence, uniqueness, and visual characterization of the optimal income tax. Additionally, we propose a way to identify the social welfare function used in the model.