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.
(a) Derivation omitted; result is X = M/(Px + b*Py) and Y = (b*M)/(Px + b*Py).
(b) Household A has perfect complements preferences and b = 2.5.
(a) New consumption: X=90, Y=225. Diagram omitted.
(b) CV = $900; household is worse off.
(c) Tax revenue = $900; subsidy value = $225; net cost to household = $900 - $225 = $675; share of income = $675/$2700 = 0.25 or 25%.
(a) Household C has Cobb Douglas preferences; a = 0.5.
(b) Derivation omitted; result is M = U * (Px/a)^a * (Py/(1-a))^(1-a).
(a) New consumption: X=30, Y=150; diagram omitted.
(b) CV = $317; household is worse off.
(c) Tax revenue = $300; subsidy value = $150; net cost = $300 - $150 = $150; share of income = $150/$1200 = 0.125 or 12.5%.
(d) The policy is progressive. The higher-income household in part 1 pays a larger net share of its income (25%) than the lower-income household in part 2 (12.5%).
(a) Initial equilibrium: X=75, Y=125; new equilibrium: X=25, Y=150.
(b) CV = $536; household is worse off.
(c) Diagram omitted; value of X if the household were compensated: X3=38.4. Thus, the income effect = -13.4 and the substitution effect = -36.6.
(d) Revenue raised = $250.
(a) New equilibrium: X=51.9, Y=120.4.
(b) CV = $339.6.
(c) Revenue = $276 ($156 on X and $120 on Y).
(d) The second policy is clearly better: it raises more revenue and has a lower CV. This is true in general: broad taxes on many goods with low rates are better than taxes that fall on few goods but have high rates.