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Recent turmoil in financial and commodities markets has renewed questions regarding how well markets discover equilibrium prices, particularly when those markets are highly complex. A relatively new critique questions whether markets can realistically find equilibrium prices if computers cannot. For instance, in a simple exchange economy with Leontief preferences, the time required to compute equilibrium prices using the fastest known techniques is an exponential function of the number of goods. Furthermore, no efficient technique for this problem exists if a famous mathematical conjecture is correct. The conjecture states loosely that there are some problems for which finding an answer (i.e., an equilibrium price vector) is hard even though it is easy to check an answer (i.e., that a given price vector is an equilibrium). This paper provides a brief overview of computational complexity accessible to economists, and points out that the existence of computational problems with no best solution algorithm is relevant to this conjecture.

Mathematics --- Physical Sciences & Mathematics --- Algebra --- Computational complexity. --- Electronic data processing. --- ADP (Data processing) --- Automatic data processing --- Data processing --- EDP (Data processing) --- IDP (Data processing) --- Integrated data processing --- Complexity, Computational --- Computers --- Office practice --- Electronic data processing --- Machine theory --- Automation --- Macroeconomics --- Noncooperative Games --- Microeconomic Behavior: Underlying Principles --- Price Level --- Inflation --- Deflation --- Asset prices --- Prices

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This paper describes how behavioral elements are relevant to financial supervision, regulation, and central banking. It focuses on (1) behavioral effects of norms (social, legal, and market); (2) behavior of others (internalization, identification, and compliance); and (3) psychological biases. It stresses that financial supervisors, regulators, and central banks have not yet realized the full potential that these behavioral elements hold. To do so, they need to devise a behavioral approach that includes aspects relating to individual and group behavior. The paper provides case examples of experiments with such an approach, including behavioral supervision. Finally, it highlights areas for further research.

Financial services industry --- Banks and banking, Central. --- Services, Financial --- Service industries --- Banker's banks --- Banks, Central --- Central banking --- Central banks --- Banks and banking --- State supervision. --- Risk management. --- Banks and Banking --- Public Finance --- Industries: Financial Services --- Business and Financial --- Microeconomic Behavior: Underlying Principles --- Intertemporal Consumer Choice --- Life Cycle Models and Saving --- Central Banks and Their Policies --- Financial Institutions and Services: General --- Corporate Finance and Governance: Government Policy and Regulation --- Law and Economics: General (including Data Sources and Description) --- Illegal Behavior and the Enforcement of Law --- Corporate Culture --- Diversity --- Social Responsibility --- Marketing and Advertising: Government Policy and Regulation --- Personnel Economics: Compensation and Compensation Methods and Their Effects --- Cultural Economics --- Economic Sociology --- Economic Anthropology: General --- Cultural Economics: Religion --- Banks --- Depository Institutions --- Micro Finance Institutions --- Mortgages --- Taxation, Subsidies, and Revenue: General --- General Financial Markets: Government Policy and Regulation --- Debt --- Debt Management --- Sovereign Debt --- Banking --- Public finance & taxation --- Financial services law & regulation --- Legal support in revenue administration --- Financial regulation and supervision --- Financial sector --- Government debt management --- Revenue --- Law and legislation --- Debts, Public --- United States