University, College, Department or Program Pays
This entails an annual contract based on a projected volume of grading, but billing would be on actuals.  Alternatively, the service can be set up as a subscription, if the institution requires faculty to internally "request" a grader.

Instructor-Generated, Institution-Pays Model
In core courses, doubling of class-size directly results in halving the number of sections offered. Where that's infeasible or in the case of electives, faculty could teach either a larger section, increasing productivity as follows: 

     Faculty Course-Load of 2+2
        - 1 extra section per semester yields a 50% rise
        - 1 extra section per year results in a   25% rise

     Faculty Course-Load of 3+3
        - 1 extra section per semester yields a 33% ris
        - 1 extra section per year yields a 17% rise

Given pay differentials between faculty and graders, the extra section more than offsets the cost of hiring a grader. 

Organizations Sponsoring Research or Expert Testimony

Faculty are sometimes called upon to provide expert testimony, carry out externally-funded research, or lend their expertise in other ways. So that such activities don't compromise grading, especially feedback to students, faculty would ask the sponsor to pay for a grader, as happens in grant applications. 

Alumni Sponsorship

Where funding cuts result in larger classes or higher teaching loads, alumni funding a grader, with a focus on rich feedback, is a fulfilling way for alumni to contribute to student learning.

Academic, Co-/Extra-Curricular, Recreational Activity Fees
Institutions routinely charge fees for a host of academic, co-curricular, extra-curricular and recreational activities. A 2017 survey by US News & World Report identified ten different types of fees charged by universities. Given the centrality of feedback to student learning, a feedback fee would pay for graders. .

Instructor-Mandated Course Requirements
Textbooks, coursepacks, online homework-cartridges, self-paced learning modules, homework-problem sites, online video catalogues and other e-learning resources are now part of the learning-materials landscape. These resources are paid for separately by students as part of their course requirements. Feedback should be no different, and constitutes an essential component of student engagement and learning through high-impact teaching practices.

Life happens! There are times when faculty run into exigencies due to personal circumstances or professional duties. Ready access to a pre-qualified grader can help an instructor get through a stressful period, without sacrificing timely feedback and student learning.