2. ( 30 points) There are 3 voters voting over healthcare budget. Let hi[0,) be the healthcare budget for Voter i for i=1,2,3. The utility of Voter 1 is u1= h12h12. The utility of Voter 2 is u2=h24h22 and the utility of Voter 3 is u3= h38h32 a. (10 points) Show that preference of each voter is single-peaked. Find the "peak" of each voter, that is, find the level of hi which maximizes ui for i=1,2,3. b. (20 points) Suppose each voter is reporting their peak level of healthcare to the government. And government is choosing the median peak, that is, the peak which is in the middle among three reported peaks. Find the dominant strategy equilibrium and sophisticated equilibrium. 2. ( 30 points) There are 3 voters voting over healthcare budget. Let hi[0,) be the healthcare budget for Voter i for i=1,2,3. The utility of Voter 1 is u1= h12h12. The utility of Voter 2 is u2=h24h22 and the utility of Voter 3 is u3= h38h32 a. (10 points) Show that preference of each voter is single-peaked. Find the "peak" of each voter, that is, find the level of hi which maximizes ui for i=1,2,3. b. (20 points) Suppose each voter is reporting their peak level of healthcare to the government. And government is choosing the median peak, that is, the peak which is in the middle among three reported peaks. Find the dominant strategy equilibrium and sophisticated equilibrium