(b) Express the incentive compatibility condition that a consumer of type d prefers to select the plan q"(0) at the price *(0) to selecting any plan q*(0') at the price t* ('). (c) Write down the first order condition for surplus maximization of a consumer of type d associated with the incentive compatibility condition expressed in part (b). (d) Use part (c) to establish that to(0) is uniquely determined, up to a constant t* (8). (e) Derive a condition expressing that the expected revenues collected from consumers pur- chasing health care plans weakly exceeds the expected cost of serving them. (HINT: use the expression for t*(0) derived in part (d). (f) Use part (e) to derive a necessary and sufficient condition for the first best to be imple- mentable