Exam 2 Solution

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.

Question 1

(a) Extra L revenue = $200k; `WTA_H` = $300; new `Q_L` = 9000; new `Q_H` = 1900; new L revenue = $360k; new H subsidy = $342k; overall surplus of $18k, solves the deficit; `\Delta CS_L` = -$190k; `\Delta CS _H` = -$39k.

Question 2

(a) New `Q` = 32M; `\Delta CS` = -$168M; `\Delta PS` = + 72M; DWL = $96M; consumers who keep buying lose $96M, consumers who stop buying lose $72M, and the firm gains the $96M from consumers less $24M in PS on foregone sales for $72M net. Extra credit: the equivalent tax would be $4.

Question 3

Step 1: insert the demand equations into the utility function:

`U=( (0.5M+50P_y)/P_x)^0.5 (-50+(0.5M)/P_y + 100 )^0.5`

Simplifying:

`U=( (0.5M+50P_y)/P_x)^0.5 ((0.5M)/P_y + (50P_y)/P_y )^0.5`

`U=( (0.5M+50P_y)/P_x)^0.5 ((0.5M+50P_y)/P_y )^0.5`

`U=(0.5M+50P_y)/(P_x^0.5 P_y^0.5 )`

Step 2: solve for M:

`P_x^0.5 P_y^0.5U=0.5M+50P_y`

`P_x^0.5 P_y^0.5U-50P_y=0.5M`

`M=2P_x^0.5 P_y^0.5U-100P_y`

Question 4

(a) Household B is Cobb-Douglas with `b` = 0.4. Diagram omitted but should include the BC, the equilibrium with X and Y labeled, and at least one IC.

(b) `X_2` = 100; `Y_2` = 150; overall revenue = $0 and the policy breaks even; `CV` = $24 and the household is worse off; `\Delta SS` = -$24.

Question 5

(a) `X_1` = 820; `Y_1` = 780; `X_2` = 685; `CV` = 3918 and the household is worse off; substitution effect = -70; income effect = -65.

Question 6

(a) PVIs: BAU = $160k, A = $184k, B= $192k, so B is best; `C_0` = 72; `C_1` = 144; borrows $30k;  diagram omitted but should show BC for option B, the consumption bundle, net incomes `I_0^N` and `I_1^N`, and at least one perfect complements IC.