Q-Theory and Real Business Cycle Analytics

A mathematical and graphical treatment of the Q-theory extension of the Basic Real Business Cycle model of Prescott indicates that several key results are robust to both investment adjustment costs and to variation in the shape of the utility function and the production function while other customary results are fragile. It also demonstrates some of the richness of general equilibrium analysis. One key result relevant to recent debates about the empirical effects 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 increase in government purchases financed by an increase in lump-sum taxes is also shown to unambiguously raise output, investment and the real interest rate.