Question

I consider an economy with two individuals (1 and 2). A, B, and C are three points that belong to the utility possibility frontier of the economy. The individual utilities (Ul. U2) at the three points are as follows: Pointsul U2 A 4 21 B 8 17 C 14 6 Now consider point D. Pointul U2 D 9 15 a. Does point D lie on the utility possibility frontier? How does the answer change if you know the utility possibility frontier is concave? b. Are there any points on the utility possibility frontier that are Pareto preferred to C? Justify your answer. c. Which of the points A, B, C, or D lies on the highest indifference curve of a utilitarian social welfare function? d. Which point is on the highest indifference curve of a Rawlsian social welfare function? Explain the answer using the solution to part a.

Answer 1

Utility possibility frontier (9,15) 4 5 6 7 8 9 10 114 11 12 13 14

A) yes point D= ( 9,15), lies on UPF.

If UPF is Concave (& it is often Concave only )

Then D will lie inside the UPF

.

B) no point is pareto preferred to C,

Bcoz all combination lie on UPF, moving from one point to another one , will lead in making one agent better off & making other person worse off

So they are pareto- non comparable

.

C) Utilitarian SWF = sum of individual utility

So max sum of individual utility levels

At A, U = U1+U2 = 25

At B, U = 25

At C, U = 20

At D, U = 24

So A & B lies on highest IC

.

D) Rawlsian SWF = Min { U1, U2 }

At A, U = Min( 4,21) = 4

At B , U = 8

At C, U = 6

At D, U = 9, Maximum

so D lies on highest IC