Fall 2018 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

New Q=950,000; `\Delta PS`=-$97.5M; `\Delta CS`=$93.75M; `\Delta SS`=-$3.75M; DWL=$3.75M. The transfer ($95M) is much larger than the DWL ($3.75M) because the supply curve is so inelastic: even though the price change is large, there's very little change in Q, so most of the change in PS ends up as a transfer to buyers.

Question 2

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

`U=( ((P_y M)/(P_x (P_x + P_y)))^0.5 + ((P_x M)/(P_y (P_x + P_y)))^0.5 )^2`

Step 2: factor out M:

`U=( (P_y/(P_x (P_x + P_y)))^0.5 * M^0.5 + (P_x/(P_y (P_x + P_y)))^0.5  * M^0.5)^2`

`U=( (P_y/(P_x (P_x + P_y)))^0.5  + (P_x/(P_y (P_x + P_y)))^0.5 )^2 * (M^0.5)^2`

`U=( (P_y/(P_x (P_x + P_y)))^0.5  + (P_x/(P_y (P_x + P_y)))^0.5 )^2 * M`

Step 3: solve for M to obtain the expenditure function:

`M=U/( (P_y/(P_x (P_x + P_y)))^0.5  + (P_x/(P_y (P_x + P_y)))^0.5 )^2`

Evaluating the function when U=400, `P_x`=$10 and `P_y`=$15 gives $2400.

The following isn't necessary, but with a little algebra the function can be simplified considerably. The denominator can be rewritten as follows:

`( (P_y/(P_x (P_x + P_y)))^0.5  + (P_x/(P_y (P_x + P_y)))^0.5 )^2 = ( P_y/(P_x P_y (P_x + P_y))^0.5  + P_x/(P_x P_y (P_x + P_y))^0.5 )^2 = ((P_x + P_y)/(P_x P_y))`

Using that, the expenditure function can be simplified to:

`M=U(P_x P_y)/(P_x + P_y )`

Question 3

(a) Household D is CD; b = 0.75; graph omitted.

(b) `X_2` = 135; `Y_2` = 37.5; `\Delta` Rev = $5; slightly better than neutral; CV = $26; household is worse off; `\Delta` SS = -$21.

Question 4

(a) Derivation omitted; result is:

`Y = M/(h P_x + P_y)`

`X = (hM)/(h P_x + P_y)`

Household B is PC; h = 3.

(b) `X_2` = 147; `Y_2` = 49; `\Delta` Rev = 46; slight surplus, not as close to neutral as the previous question; CV = $42, household is worse off; diagram omitted.

Question 5

`X_1` = 780; `Y_1` = 360; `X_2` = 560; `\Delta` Rev = $8960; CV = $11,460, household is worse off; `X_3` = 662; substitution effect = -118; income effect = -102.

Question 6

PVI without training = $120k; PVI with training = $130k; she should take the training. `C_0` = 65k; `C_1` = 78k; borrows $35k; diagram omitted.