The standard Walrasian equilibrium theory requires that the marginal value product of production factor such as labor is equal across firms and industries. However, productivity dispersion is widely observed in the real economy. Search theory allegedly fills this gap by encompassing apparent disequilibrium phenomena in the neoclassical equilibrium framework. Taking up Lucas and Prescott (1974) as a primary example, we show that the neoclassical search theory cannot explain the observed pattern of productivity dispersion. Non-self-averaging, a concept little known to economists, plays the major role. Empirical observation suggests strongly the presence of disturbing forces which dominate equilibrating forces due to optimizing behavior of economic agents. We must seek a new concept of equilibrium different from the standard Walrasian equilibrium in macroeconomics.