Cost Functions and Utility-Based Market Makers We wish to find the cost function that matches a given utility function. Actually what we are trying to solve is: For example, for the logarithmic utility function with b>0: ,the cost function for two outcome event is: Verify it for homework – just show that substituting the derivatives of (**) and (***) into (*) gives a correct equality. This topic is addressed in part 5.2 of the paper (A Utility Framework for Bounded-Loss Market Makers)