Question

General Equilibrium — End of Chapter Problem Dante and Naia get utility from having money. Dante’s utility function is ??=10?13 ; Naia’s utility function is ??=10?12 . Dante currently has $1,000; Naia has $400.

a. The Rawlsian social welfare function values egalitarianism. Compute the value of the Rawlsian social welfare function for Dante and Naia.
A. 100 B. 200
C. 300 D. 400

b. A transfer program will take $100 from Dante and transfer it to Naia. Such a transfer program (decreases increases does not affect welfare) under a Rawlsian social welfare function.

c. Suppose, instead, that the program described in part b will take $100 from Naia and transfer it to Dante. Such a transfer program (decreases increases does not affect welfare) welfare under a Rawlsian social welfare function.

d. Consider the following social welfare function, which places some value on egalitarianism: ?=??+??−0.3(|??−??|) Under this social welfare function, Dante’s and Naia’s utilities are added together, but as the difference between their utilities increases, social welfare declines. Given Dante's and Naia's initial wealth levels, the value of this social welfare function is
a. 290 b. 225
c. 254 d. 270

e. Suppose again, as in part b, that a transfer program takes $100 from Dante and transfers it to Naia. As a result of this transfer, welfare under this social welfare function (decreases increases does not affect welfare)

Answer 1

a) Answer ) 100

U_D = 10M^(1/3) = 10(1000)^1/3 = 10 x 10 = 100

U_N = 10M^(1/2) = 10(400)^1/2 = 10 x 20  = 200

Rawlasian welfare function = min { U_D , U_N } = 100

b) Answer) Will DECREASE welfare

U_D = 10M^(1/3) = 10(900)^1/3 = 10 x 9.65 = 96.5

U_N = 10M^(1/2) = 10(500)^1/2 = 10 x 20  = 223.6

c) Answer) INCREASE

U_D = 10M^(1/3) = 10(1100)^1/3 = 10 x 10.29 = 102.9

U_N = 10M^(1/2) = 10(300)^1/2 = 10 x 17.3 = 173

d) Answer ) 270

W = U_D + U_N - 0.3| U_D - U_N | = 100 + 200 - 0.3 (100) = 300 - 30 = 270

e) Answer) INCREASES

W = U_D + U_N - 0.3| U_D - U_N | = 96.5 + 223.6 - 0.3 (100) = 320.1 - 38.1 = 282