On the Shape of Information Processing Functions

The productivity of (human) information processing as an economicactivity is a question raising some interest. Using Marschak’s evaluationframework, Radner and Stiglitz have shown that under certainconditions the production function of this activity has increasing marginalreturns in the beginning. This paper shows that under slightlydifferent conditions this information processing function has repeatedconvexities with ongoing processing activity. Even for smooth changesin the signals’ likelihoods, the function is only piecewise smooth withindifferentiable convexities at conditional changes of action. For linearlikelihood functions the processing value shows to be piecewiselinear with convexities at these levels.