On VoxEU, Steven Durlauf offers an excellent overview over Kenneth Arrow’s work. Durlauf emphasizes five areas of research:
The impossibility theorem, in the tradition of Condorcet.
General equilibrium theory and the welfare theorems, in the tradition of Walras.
Decision-making under uncertainty, the Arrow-Pratt measures of risk aversion and contingent commodities.
Imperfect information, in the context of medical care and as a source of statistical discrimination.
Economics of knowledge, anticipating the endogenous growth literature.
Like Faust, limitless curiosity and passion for knowledge meant that Arrow strove without relenting; but unlike Faust, Arrow needed no redemption. His intellectual integrity was pristine and unparalleled at every stage of his life. His character was as admirable and admired as his intellect. Arrow’s personal and scholarly example continues to inspire, nurture, and challenge.
On his blog A Fine Theorem, Kevin Bryan discusses the history of economic thought leading from the classical economists and Walras to Arrow and Debreu.
My read of the literature on GE following Arrow is as follows. First, the theory of general equilibrium is an incredible proof that markets can, in theory and in certain cases, work as efficiently as an all-powerful planner. That said, the three other hopes of general equilibrium theory since the days of Walras are, in fact, disproven by the work of Arrow and its followers. Market forces will not necessarily lead us toward these socially optimal equilibrium prices. Walrasian demand does not have empirical content derived from basic ordinal utility maximization. We cannot rigorously perform comparative statics on general equilibrium economic statistics without assumptions that go beyond simple utility maximization. From my read of Walras and the early general equilibrium theorists, all three of those results would be a real shock.
CEPR Discussion Paper 11482, August 2016, with Martin Gonzalez-Eiras. PDF. Also published as CESifo Working Paper 6062, Study Center Gerzensee Working Paper 16-05. PDF, PDF.
We propose a theory of tax centralization and inter governmental grants in politico-economic equilibrium. The cost of taxation differs across levels of government because voters internalize general equilibrium effects at the central but not at the local level. This renders the degree of tax centralization and the tax burden determinate even if none of the traditional, expenditure-related motives for centralization considered in the fiscal federalism literature is present. If central and local spending are complements and the trade-off between the cost of taxation and the benefit of spending is perceived differently across levels of government, inter governmental grants become relevant. Calibrated to U.S. data, our model helps to explain the introduction of federal grants at the time of the New Deal, and their increase up to the turn of the twenty-first century. Grants are predicted to increase to approximately 5.5% of GDP by 2060.