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.
Extra revenue in G = $2M; `WTA_B` = $400; new `Q_G` = 24k; new `Q_B` = 6k; new overall surplus = $0 (breaks even).
Normal equilibrium: P = $20, Q = 1000; peak period with surge pricing: P = $40, Q = 2000; quantity with price control = 1000; `\Delta PS`= -$30k; `\Delta CS` = -$20k; 1000 riders who get rides gain $20k; 1000 riders who can no longer get rides lose $40k; drivers lose $30k. Not explicitly requested but computed as part of the CS calculation: `WTP` during peak periods at Q=1000: $120.
Step 1: insert the demand equations into the utility function to give:
The 100's cancel out:
`U=(0.5M+50P_y)^0.5/P_x^0.5 \cdot (0.5M+50P_y)^0.5/P_y^0.5`
Solving for M:
`M=2 U P_x^0.5 P_y^0.5 -100P_y`
M at the indicated U and prices: $4160.
(a) Household C has CD preferences with `b=0.6`. Diagram omitted but it should contain the budget constraint, the equilibrium, and at least one indifference curve.
(b) `M_2` = $3620; `X_2` = 543; `Y_2` = 362; the policy has a strong impact: it raises X by 36% and lowers Y by 55%; `\Delta Rev` = $18 and the policy succeeds in roughly breaking even; CV = 518 and the household is worse off; `\Delta SS` = -500.
`X_1` = 252, `Y_1` = 112; `X_2` = 140; `\Delta Rev` = 560; CV = 840, worse off; substitution effect = -77, income effect = -35.
PVIs: BAU = 120k, A = 125k, B = 123k; program A is best; `C_0` = 80,357; `C_1` = 53,571; borrows 40,357; diagram omitted but it should show the BC with training program A, the consumption bundle, and at least one IC.