# 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

### 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.

URL: https://wilcoxen.maxwell.insightworks.com/pages/4680.html
Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 12/03/2018