If John's preferences are given by U(c,D)=log(c)+D where c is consumption and D is total donations and a wealthy individual sets up a matching fund campaign where John's total donation (D) is given by D=kd where k is the expansion factor and d is John's personal contribution and his budget constraint is c+d=m.

Question

A) Find John's total donation function D* and his consumption demand function c*
B) What are John's private contributions, d*
C) In the absence of a matching funds campaign what is John's private donation, d*? How much Does John devote to consumption c*? What is the donation D*?