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Using a two-period version of the model, this appendix shows that Pigou cycles are not possible when the Hosios condition holds, that is, when the surplus is divided such that the competitive equilibrium corresponds to the social planners' solution. The matching friction used in this paper is similar to a quadratic adjustment cost; both imply that an increase in employment is too costly to implement within one period, but should be spread out over several periods. It is, thus, not surprising that investment in new projects increases in advance of the anticipated increase in productivity.
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