Economic activity involves countless consumers, firms, and governments interacting at once. Hicks and Arrow provided mathematical conditions under which demand and supply balance in every market simultaneously—this is general equilibrium. They also organized how that equilibrium influences people’s welfare and suggested criteria for judging whether taxes or subsidies can raise overall satisfaction. Today’s public-policy and environmental cost-benefit analyses rely heavily on this framework.

Hicks reconstructed welfare economics under the assumption of Pareto efficiency, introducing compensating variation and the Hicks–Allen substitution effect, which enabled rigorous comparative statics. Arrow, together with Debreu, proved the existence of competitive equilibrium by applying fixed-point theorems to continuous excess-demand functions and examined its stability under homogenous-of-degree-one price systems. He generalized the welfare theorems, showing that competitive equilibrium is Pareto efficient, while his impossibility theorem in social choice uncovered institutional limits when aggregating individual preferences. These achievements form the theoretical bedrock for modern fields such as financial engineering, environmental economics, and public economics.

Hicks extended the Slutsky decomposition, established duality via indirect utility and expenditure functions, and, through the IS–LM construct, paved a path toward dynamic general equilibrium. Arrow–Debreu (1954) formulated the Walrasian competitive economy as a fixed-point problem on a manifold and proved existence via Kakutani’s theorem, deriving the Arrow-Hahn stability conditions. Arrow’s measures of risk aversion (Arrow–Pratt) and his analysis of incomplete markets with state-contingent Arrow securities laid foundations for asset-pricing theory and incentive theory. These contributions remain indispensable for DSGE consistency tests and for discussions of efficiency and implementability in mechanism design.