This paper argues that in an economy where at least some firms incur price adjustment costs, aggregate output is influenced by perfectly anticipated inflation even if no agent in the economy suffers from money illusion. More interestingly, it demostrates that the magnitude and direction of the output effect may depend critically on the rate of inflation. In particular, under meaningful demand and cost specifications, the relationship between inflation and aggregate output is positive at relatively low rates of inflation, but negative at higher rates. Thus, the Phillips curve is backward-bending and the output-maximizing rate of inflation is positive.
Quarterly Journal of Economics, 101 (May 1986): 407-418.