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) `Rev_O = $7M`; `WTP_P = $0.56`; `Q_O=120M`; `Q_P=14M`; `\Delta CS_O=+$7.7M`; `\Delta CS_P=-$7.14M`; `\Delta Rev=+$1.4M`; `\Delta SS=+$1.96M`
(a) `Q=800k`; `\Delta PS=-$3.6M`; `\Delta CS=+$2.4M`; `\Delta SS=-$1.2M` or `DWL=$1.2M`. Buyers who can still get gas win; buyers who can't get gas lose; sellers lose.
Step 1: insert the demand equations into the utility function to give:
`U=(10+(0.5M-5P_x+5P_y)/P_x -10)^0.5 (-10+(0.5M-5P_x+5P_y)/P_y +10)^0.5`
Solving for M:
`U P_x^0.5 P_y^0.5 =0.5M-5P_x+5P_y`
`U P_x^0.5 P_y^0.5 +5P_x- 5P_y=0.5M`
`M=2U P_x^0.5 P_y^0.5 +10P_x-10P_y`
(a) Household B is PC and with `b=0.5`. Derivation omitted; result is:
`X = M/(P_x + bP_y)`
`Y = (bM)/(P_x + bP_y)`
Diagram omitted but should include the BC, the equilibrium with X and Y labeled, and at least one IC.
(b) `X_2=184`; `Y_2=92`; `\Delta Rev=96`; `CV=108` (household is worse off); `\Delta SS=-12`.
(a) `X_1=1000`; `Y_1=1000`; `X_2=1800`; `CV=-$12k` (household is better off); `\Delta X_S=+440`; `\Delta X_I=+360`.
(a) `PVI_BAU=$168k`; `PVI_A=$184k`; `PVI_B=$174k`; A is best; `C_0=92k`; `C_1=115k`; saves $4k; diagram omitted but should show BC, `I_0^N`, `I_1^N`, `C_0`, `C_1` and at least one IC.