A value function arising in the economics of information

Abstract

The value function for a problem in the economics of the optimal accumulation of information is calculated as a fixed point of a contraction mapping by direct numerical iteration. The optimal policy function is obtained as is the function defined as the sum of current expected reward and the discounted expected value of following the optimal policy in the future. The optimal policy function is shown to be sensitive to the discount factor; indeed for large values of the discount factor (weighting the future heavily) the policy function has a break and the value function is apparently not differentiable.