90 Appendix 9: Shutdown point Appendices net out the benefits that the college can provide absent state and local government support, represented as Z% of the college’s current CHE production in Figure A9.2. To clarify the argument, it is useful to consider the role of enrollment in the larger benefit-cost model. Let B equal the benefits attributable to state and local government support. The analysis derives all benefits as a function of student enrollment, measured in terms of CHEs produced. For consistency with the graphs in this appendix, B is expressed as a function of the percent of the college’s current CHE production. Equation 1 is thus as follows: 1) B = B (100%) This reflects the total benefits generated by enrollments at their current levels. Consider benefits now with reference to Z. The point at which state and local government support is zero nonetheless provides for Z% (less than 100%) of the current enrollment, and benefits are symbolically indicated by the following equation: 2) B = B (Z%) Inasmuch as the benefits in equation 2 occur with or without state and local government support, the benefits appropriately attributed to state and local government support are given by equation 3 as follows: 3) B = B (100%) − B (Z%) Figure A9.1: Student demand and government funding by tuition and fees Tuition and fees 100% C% 0% 100% D p' CHE production Govt. funding (% of total) Figure A9.2: CHE production and government funding by tuition and fees Tuition and fees D p' p" CHE production Govt. funding (% of total) 100% C% 0% 100% Z%
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