Complete Comparative Static Differential Equations*

Equations having form (1) arise as first-order conditions in microeconomic constrained optimization models, as defining characterizations for general equilibrium and macroeconomic models, and as steady-state solution characterizations for descriptive and optimal growth models. (See Silberberg [12], Hansen [7], Cass and Shell [3], and Brock [l].) If Y :R"' -+ R" is continuously differentiable over a neighborhood of a point (x0, a”) in R n+l for which Y(xO, LX’) = 0 and IY,( x0, or’)] # 0, then the implicit function theorem guarantees the existence of a continuously differentiable function x: N(cr’) + R" over some open neighborhood N(crO) of CX’ in R such that dx z (ix) = YX(X(X), a)-lYJx(a), X), G! E N(cP). (2)