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Baron (2001) - Theories of Strategic Nonmarket Participation (view source)
Revision as of 04:24, 31 October 2009
, 04:24, 31 October 2009→Joint Surplus Maximization
The principal's utility maximization and conditions (a) and (b) imply:
:<math>U_e(x^*) \ge U_e(x) \; quad \forall x \in \mathbb{R}</math>:<math>u_e(x^*) + c_g^*(x^*) + c_h^*(x^*) \ge u_e(x) + c_g^*(x) + c_h^*(x) \; quad\forall x \in \mathbb{R}</math>
When both agents contribute we can substitute in the linear contribution schedules to get:
:<math>u_e(x^*) + u_g^*(x^*) + \tau_g + u_h^*(x^*) + \tau_h \ge u_e(x) + u_g^*(x) + \tau_g + u_h^*(x) + \tau_h \; quad \forall x \in \mathbb{R}</math>:<math>\therefore u_e(x^*) + u_g^*(x^*) + u_h^*(x^*) \ge u_e(x) + u_g^*(x) + u_h^*(x) \; quad \forall x \in \mathbb{R}</math>
And so the we have both that (as <math>U_e^\hat(x) = u_e(x) + u_g(x) + u_h(x) \quad</math>) the principal's problem is to maximize the joint surplus and that the contribution schedules are truthful.
