Here are the final numerical results for each section of the exam. You can use them to check your work if you do the exam for practice. If you have trouble with the problems, or don't get the answers shown here, stop by during office hours or make and appointment and we can go over them.
(1a) Household B, a=0.4;
(1b) X = 40, Y = 100;
(2a) result of derivation: M = U*((Px/a)^a)*((Py/(1-a))^(1-a)) ;
(2b) Initial utility = 69.314; CV = $93;
(2c) new X = 32; tax revenue = $80.
(3a) result of derivation: X = a*M/(a*Px+Py), Y = M/(a*Px+Py);
(3b) Household C, a = 2.
(4a) X = 100, Y = 50;
(4c) CV = -$200;
(4d) Household is better off: would have to take income away to shift them to their old utility.
(5a) X = 55, Y = 100;
(5b) Initial utility = 70.711, CV = -$141.
(6a) CD Pd = $2, PC Pd = $6;
(6b) CD CV = $148, PC CV = $1,000;
(6c) Net gain under CD: $300 - $148 = $152; Under PC = $300 - $1,000 = -$700. If CD, policy is a net gain and is Pareto efficient but under PC, it's a significant net loss and is inefficient.