Equilibrium selection under changes in endowments: A geometric approach
提出一种几何方法选择均衡价格,通过投影到均衡流形的线性化与指数映射的组合,并证明零曲率与均衡唯一性在任意商品数和两个消费者情况下的等价性。
In this paper we propose a geometric approach to the selection of the equilibrium price. After a perturbation of the parameters, the new price is selected thorough the composition of two maps: the projection on the linearization of the equilibrium manifold, a method that underlies econometric modeling, and the exponential map, that associates a tangent vector with a geodesic on the manifold. As a corollary of our main result, we prove the equivalence between zero curvature and uniqueness of equilibrium in the case of an arbitrary number of goods and two consumers, thus extending the previous result by Loi and Matta (2018).