Most grant solicitations require that an applicant demonstrate that they have “maximized the cost effectiveness of award expenditures” in the budget narrative. What level of detail is needed to maximize my scoring in this section?

The degree of detail needed will vary depending on the nature of the project.  However, it is essential that every expenditure be explained thoroughly.  A sample budget narrative can be found at the following link: https://www.ojp.gov/funding/grants101/sample-materials.