More nonconcavities in information processing functions

The productivity of (human) information processing as an economic activity is a question that is raising some interest. Using Marschak's evaluation framework, Radner and Stiglitz have shown that, under certain conditions, the production function of this activity has increasing marginal returns in its initial stage. This paper shows that, under slightly different conditions, this information processing function has repeated convexities with ongoing processing activity. Even for smooth changes in the signals' likelihoods, the function is only piecewise smooth with non-differentiable convexities at points of conditional changes of action. For linear likelihood functions the processing value proves to be piecewise linear with convexities at these levels. This revised version was published online in June 2006 with corrections to the Cover Date.