Bubble Necessity Theorem
证明在长期经济增长快于股息增长且自给自足利率低于股息增长的经济中，所有均衡都必然包含不可忽略的资产泡沫，为泡沫的存在提供了理论必要性。
Asset price bubbles are situations where asset prices exceed the fundamental values defined by the present value of dividends. This paper presents a conceptually new perspective: the necessity of bubbles. We establish the bubble necessity theorem in a plausible general class of economic models: with faster long-run economic growth (G) than dividend growth (Gd) and counterfactual long-run autarky interest rate (R) below dividend growth, all equilibria are bubbly with nonnegligible bubble sizes relative to the economy. This bubble necessity condition naturally arises in economies with sufficiently strong savings motives and multiple factors or sectors with uneven productivity growth.