\$title Parts Supply Problem w/ Inefficient Type w/o Asymmetric Information (PS2_F_inf,SEQ=361) \$onText Hideo Hashimoto, Kojun Hamada, and Nobuhiro Hosoe, "A Numerical Approach to the Contract Theory: the Case of Adverse Selection", GRIPS Discussion Paper 11-27, National Graduate Institute for Policy Studies, Tokyo, Japan, March 2012. http://www.grips.ac.jp/r-center/en/discussion_papers/11-27/ Keywords: nonlinear programming, contract theory, principal-agent problem, adverse selection, parts supply problem \$offText option limCol = 0, limRow = 0; Set i 'type of supplier' / inf /; Parameter theta(i) 'efficiency' / inf 0.3 /; Positive Variable x(i) "quality" b(i) "maker's revenue" c(i) "cost"; Variable Util "maker's utility"; Equation obj "maker's utility function" rev(i) "maker's revenue function" pc(i) "participation constraint"; obj.. Util =e= sum(i, (b(i) - c(i))); rev(i).. b(i) =e= x(i)**(0.5); pc(i).. c(i) - theta(i)*x(i) =e= 0; * Setting Lower Bounds on Variables to Avoid Division by Zero x.lo(i) = 0.0001; Model FB1 / all /; solve FB1 maximizing Util using nlp; Parameter db(i) 'derivative of b' w(i) 'price'; db(i) = 0.5*x.l(i)**(-0.5); w(i) = c.l(i); display x.l, b.l, c.l, util.l, db, w;