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We develop a Keynesian cross analysis with a dynamic optimization setting that explains long-run stagnation caused by aggregate demand deficiency. We show that an increase in government purchases boosts GDP through a multiplier process, but the implication is quite different from the conventional Keynesian one. It works not through an increase in disposable income but through moderation of deflation. Thus, countries that have lapsed into long-run stagnation should expand government spending that directly creates employment in order to reduce the deflationary gap.