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

`Rev_L` = $7 M; `WTA_H` = $8,000; `Q_L` = 14,560; `Q_H` = 1,120; `\Delta CS_L` = $7.14 M; `\Delta CS_H` = -$8.58 M; `\Delta Rev_L` = -$7 M; `\Delta Rev_H` = $11 M; `\Delta SS` = $2.56 M.

Question 2

New `Q` = 950,000; lowest price = $400; `\Delta CS` = $93.75 M; `\Delta PS` = -$97.5 M; `\Delta SS` = -3.75 M; government gains $95 M from lower prescription costs; 50,000 unserved patients lose $1.25 M; producers lose $97.5 M.

Question 3

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

`U = M/P_y - (100^2 P_x P_y)/( P_x + P_y )^2 - (100-(100 P_y)/(P_x+P_y))^2`

Step 2: solve for M, which is especially simple for these preferences since `M` only appears in one place:

`U + (100^2 P_x P_y)/( P_x + P_y )^2 + (100-(100 P_y)/(P_x+P_y))^2 = M/P_y `

`M = P_y U + P_y (100^2 P_x P_y)/( P_x + P_y )^2 + P_y (100-(100 P_y)/(P_x+P_y))^2`

It was not required but with a few extra steps the expenditure function can be simplified a lot:

`M = P_y U + P_y (100^2 P_x P_y)/( P_x + P_y )^2 + P_y ((100(P_x+P_y)-100 P_y)/(P_x+P_y))^2`

`M = P_y U + P_y (100^2 P_x P_y)/( P_x + P_y )^2 + P_y( (100 P_x)/(P_x+P_y))^2`

`M = P_y U + P_y (100^2 P_x P_y)/( P_x + P_y )^2 + P_x (100^2 P_x P_y)/(P_x+P_y)^2`

`M = P_y U + (100^2 P_x P_y)/( P_x + P_y )`

Question 4

(a) Household C has PC preferences with `b` = 1.5. The derivation is omitted here but the results are:

`Y = M/(bP_x +P_y)`

`X = (bM)/(bP_x +P_y)`

The diagram is also omitted but should include the BC, the equilibrium with X and Y labeled, and at least one IC which should have a corner.

(b) `X` = 360; `Y` = 240; `\Delta Rev` = $270; CV = $310, worse off; `\Delta SS` = -$40.

Question 5

`X_1` = 980; `Y_1` = 500; `X_2` = 600; `U_1` = 2880, `M_3` = $50,400 so the CV = 8400, worse off; `X_3` = 720 so `\Delta X_S` = -260, `\Delta X_I` = -120.

Question 6

`PVI_(BAU)` = $150k, `PVI_A` = $175k, `PVI_B` = $168k, so A is best; `C_0` = $105k; `C_1` = $84k; borrows $30k.

The diagram is omitted but should include the BC with `I_0^(Net)`, `I_1^(Net)` and the PVI shown, the equilibrium with `C_0` and `C_1` labeled, and at least one IC, which should not have a corner.