ABSTRACT
UF ¼ PcðsÞ2 CðsÞ þ bðs2 sÞ: In contrast, if the venture is nonprofit, the entrepreneur is forced, because of the nondistribution constraint, to consume profits as perquisites. We assume that the entrepreneur strictly prefers cash to perquisites; her utility from perquisites is thus modeled as a fraction 0 , d , 1 of the profits, which leads to the following utility function
UN ¼ dðPcðsÞ2 CðsÞÞ þ bðs2 sÞ:
Maximizing utility with respect to s allows us to define the optimal level of community benefits for a for-profit (sF) entrepreneur and for a nonprofit (sN) entrepreneur, respectively, as
P0cðsFÞ2 C0ðsFÞ þ b ¼ 0; d P0cðsNÞ2 C0ðsNÞ � �þ b ¼ 0:
8< :
As d , 1, we have that C0ðsNÞ2P0cðsNÞ ¼ b=d . b ¼ C0ðsFÞ2P0cðsFÞ. Then, a sufficient condition to have sN . sF is that C0ðsÞ2P0cðsÞ increases with s, or that C00ðsÞ . P00cðsÞ. Take, for instance, CðsÞ ¼ ðg=2Þs2; then, the conditionC00ðsÞ . P00cðsÞ is equivalent to g . 2=ð4sþ 1Þ3, which is certainly satisfied if g $ 2.
