4 10.D The Fundamental Welfare Theorems in a Partial Equilibrium Context

• 一般均衡と同じように、部分均衡においても厚生経済学の第一定理、第二定理が成立する。
• ただし、効用が準線形であることが必要。

4.1 The First Fundamental Theorem of Welfare Economics

Proposition 10.D.1 (The First Fundamental Theorem of Welfare Economics)

If the price \(p^{*}\) and allocation \((x^{*}_{1}, ... x^{*}_{I}, q^{*}_{1}, ..., q^{*}_{J})\) constitute a competitive equilibrium, then this allocation is Pareto optimal.

• When consumer preferences are quasilinear, the boundary of the economy’s utility possibility set is linear and all points in this boundary are associated with consumption allocations that differ only in distribution of the numerarire among consumers.

4.2 The Second Fundamental Theorem of Welfare Economics

Proposition 10.D.2 (The Second Fundamental Theorem of Welfare Economics)

For any Pareto optimal levels of utility \((u^{*}_{1}, ..., u^{*}_{I})\), there are transfers of the numeraire commodity \((T_{1}, ..., T_{I})\) satisfying \(\sum_{i}T_{i} = 0\), such that a competitive equilibrium reached from the endowments \((\omega_{m1} + T_{1}, ..., \omega_{mI} + T_{I})\) yields precisely the utilities \(u^{*}_{1}, ..., u^{*}_{I}\).