Q-Theory and Real Business Cycle Analytics

I would like to thank Philippe Weil, Matthew Shapiro and Kenneth West for
their encouragement in writing this paper and many cohorts of students who gave
reactions to the initial, rough versions of this material.

Abstract

A mathematical and graphical treatment of the Q-theory extension of the
Basic Real Business Cycle model of Prescott indicates that several key re-
sults are robust to both investment adjustment costs and to variation in the
shape of the utility function and the production function while other custom-
ary results are fragile. It also demonstrates some of the richness of general
equilibrium analysis. One key result relevant to recent debates about the em-
pirical e®ects of technology is that an immediate, permanent improvement
in technology unavoidably raises output, investment and the real interest
rate, given uncontroversial assumptions such as normality of consumption
and leisure and constant returns to scale in production. A permanent in-
crease in government purchases ¯nanced by an increase in lump-sum taxes is
also shown to unambiguously raise output, investment and the real interest
rate.