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.
M = U * (Px/a)^a * (Py/(1-a))^(1-a)
a = Px*X/M
Values of a for household A: 2007 a=10*30/1000 = 0.3, 2008 a=12*30/1200 = 0.3. Since the values match, household A has Cobb-Douglas preferences with a = 0.3. The households do not have Cobb-Douglas preferences: their values of a in 2007 and 2008 do not match.
X = 50, Y = 175.
X = 25, Y = 210, revenue on X = 225, subsidy on Y = 210, net revenue = 15, CV = 125. Household is worse off: would need $125 of compensation to achieve the same utility as 1b. Net gain to the government is 15 so the overall effect is a DWL of 110.
Y = M/(a*Px + Py), X = a*M/(a*Px + Py). Solving for a in the Y equation: a = M/(Y*Px) - Py/Px. Alternatively, a = X/Y. Household B's value of a: 0.25 in 2007 and 0.11 in 2008; not perfect complements. Household C's value of a: 5 in 2007, 5 in 2008; C has perfect complements preferences with a = 5.
X = 155, Y = 31. Expenditure needed to buy 2008 X and Y at 2009 prices: $867. CV = 867 - 1581 = -$714. The negative CV indicates that the household is better off in 2009.
PV of income = 358k. C0 = 159k; C1 =239k; initial borrowing = 9k. The graph should show the intertemporal budget constraint with the endowment at (150k,250k), 358k as the X intercept and 430k as the Y intercept. It should also show the equilibrium at (159k,239k) and at least one indifference curve.