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` = $200k; subsidy to each H rider = $3 so `WTA_H` = $5; `Q_2^L` = 190k; `Q_2^H` = 78k; new revenue in L = $237,500 so `\Delta REV_L` = $37,500; new subsidy in H = $214,500 so subsidy decreases by $25,500 (net gain). New overall budget surplus = $237,500 - $214,500 = $23,000. Yes, it eliminates the deficit.

Question 2

`%\Delta P` = -90%; `%\Delta Q` = -1.8% so `Q_2` = 2.946M; `\Delta PS` = -$802.71M; `WTP` at `Q_2` = $354 so `\Delta CS` = $795.42M - $1.458M = $793.962M; `\Delta SS` = -$8.748M. Policy causes a transfer of $795 M from producers to consumers.

Question 3

Step 1: insert the demand equations into the utility function. It's not required but it's handy to define a symbol, `\Gamma`, to represent the complex part of the demand equations:

`Gamma = M + 20P_x - 60P_y`

Using this, the demand equations can be written:

`X = -20 + (0.4\Gamma)/P_x` and `Y=60+(0.6\Gamma)/P_y`

Inserting them into the utility function:

`U = (-20 + (0.4\Gamma)/P_x +20)^0.4 (60 + (0.6\Gamma)/P_y - 60)^0.6`

`U = ( (0.4\Gamma)/P_x)^0.4 ( (0.6\Gamma)/P_y )^0.6`

Step 2: solve for M:

`U = (0.4/P_x)^0.4 \Gamma^0.4 (0.6/P_y )^0.6 \Gamma^0.6 = (0.4/P_x)^0.4 (0.6/P_y )^0.6 \Gamma`

`U/((0.4/P_x)^0.4 (0.6/P_y )^0.6) = \Gamma`

`U/((0.4/P_x)^0.4 (0.6/P_y )^0.6) = M + 20P_x - 60P_y`

`M = U/((0.4/P_x)^0.4 (0.6/P_y )^0.6) - 20P_x + 60P_y`

An additional step that's not required but makes the function slightly more compact:

`M = U (P_x/0.4)^0.4 (P_y/0.6 )^0.6 - 20P_x + 60P_y`

Question 4

(a) Household B is CD with `b` = 0.8. Diagram omitted but the axes should be labeled (X and Y), the diagram should show the BC, the IC, and the equilibrium, and the coordinates of the equilibrium (X = 320, Y = 120) as well as the intercepts of the BC (X = 400, Y = 600). The IC should not have a corner.

(b) `M_2` = $4200; `X_2` = 336, `Y_2` = 70; `\Delta Rev` = $208; CV = $299, household is worse off; `\Delta SS` = -$91 or, alternatively, DWL = $91.

Question 5

`X_1` = 550, `Y_1` = 450; `X_2` = 500; CV = $5,369; `X_3` = 524 (rounded to the nearest integer) so `\Delta X_S` = -26 and `\Delta X_I` = -24.

Question 6

PVs: BAU = $196 k, A = $224 k, B = $232.4 k. Program B is best. `C_0` = 166 k, `C_1` = 83 k; borrows $76 k. Graph omitted but but axes should be labeled (`C_0` and `C_1`), the diagram should show the BC for program B, the IC, and the equilibrium, and the coordinates of the equilibrium (`C_0` = 166 k, `C_1` = 83 k) as well as the PVI ($232.4 k). The IC should have a corner at the equilibrium.