An I(2) analysis of Australian inflation and the markup is undertaken within an imperfect competition model. It is found that the levels of prices and costs are best characterized as integrated of order 2 and that a linear combination of the levels (which may be defined as the markup) cointegrates with price inflation. From the empirical analysis we obtain a long-run relationship where higher inflation is associated with a lower markup and vice versa. The impact in the long run of inflation on the markup is interpreted as the cost to firms of overcoming missing information when adjusting prices in an inflationary environment.