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.
Q = 500 million kg; change in CS = -$1.5 billion; change in PS = -$750 million; DWL = $2.25 billion; black market price = $3.20/kg (16 times the official price of $0.20/kg).
B is CD and g = 0.4. Derivation and diagram omitted.
Qx = 55; Qy = 165; change in revenue = -$470; government runs a deficit and the policy does not break even; CV = -$264 (household is better off). Not required: total change in SS = $264 - $470 = -$206.
(a) Derivations omitted; C is PC and d = 2.
(b) Qx = 63; Qy = 126; CV = -$144 (household is better off); net effect on revenue = -$168; policy does not break even and causes a deficit; change in SS = $144 - $168 = -$24; diagram omitted.
Qx1 = 150; Qy1 = 50; Qx2 = 130; net revenue = $130-$10 = $120; CV = $135 (household is worse off); Qx3 = 141; substitution effect = -9; income effect = -11.
Qx1 = 200; Qy1 = 100; Qx2 = 170; net revenue = $170+$10 = $180; effective tax rate on L = $120/$1000 = 0.12; effective tax rate on H = $180/$1500 = 0.12; yes, the adjustment has kept the policy from being regressive (in fact the burden is proportional).
Extra credit: using the initial Qx and M values for the L and H households allows the income elasticity to be computed (i.e., looking at how Qx changes when M changes). It's 0.67 so X is a necessity and consumption doesn't rise in proportion to income. Without the means-tested lump-sum adjustment the tax would be regressive.