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=(b*M)/(b*Px+Py) and Y=M/(b*Px+Py).
(b) Household C has perfect complements preferences and b = 3.
(a) X=231, Y=77. Diagram should include the BC, at least one IC, and the equilibrium.
(b) CV = $108; household is worse off.
(c) Taxes paid on X=$231; subsidy received on Y=$77.
(d) DWL = CV - net tax revenue. Net tax revenue is $231 less the $77 subsidy and the $52 transfer, or $102. DWL = $108 - $102 = $6.
(a) Household B has Cobb-Douglas preferences and a = 0.25.
(b) Derivation omitted; result is M = U*(Px/a)^a * (Py/(1-a))^(1-a).
(a) Tax rate is $2 and the new equilibrium is X=40, Y=120. Diagram should include the BC, at least one IC, and the equilibrium.
(b) CV = $92.
(c) Revenue = $80. DWL = CV - Revenue = $12.
(d) Ratio = 0.15 or 15%.
(a) Initial equilibrium: X = 86, Y = 86. New equilibrium: X = 45, Y = 125.
(b) CV = $135; household is worse off.
(c) Income effect = -3.4; substitution effect = -37.6.