Multiple choice Questions

Question

1. Consider an hypothetical society with two types of agents only. Their welfare is measured in utils. Assume that only the following allocations are feasible (the first number is the utility of type-1 agents, while the second is the utility of type-2 agents):

• X:{11,22}• Y:{22,22}• W:{22,11}• Z:{245,11}

(a) The set of Pareto-Optimal allocations

(A) is empty

(B) consists of allocations Y and Z

(C) consists of allocation Z alone

(D) consists of allocation {267, 22}

(b) A benevolent dictator equipped with a Rawlsian welfare function would se- lect

(A) either X, W, or Z

(B) X

(C) X and W

(D) Y

(c) An utilitarian dictator would select

(A) either Y or Z

(B) Z

(C) X and Y

(D) none of them

Answer 1

What an interesting question!!

The main issue is to look at the welfare values of the possible allocations. The key allocations are Y with equal allocation to both agents, and Z which has massively more total utility than any other choice.

The three questions choose an allocation based on different methods of assessing welfare.

(a)

A Pareto Optimal allocation is when no agent can be better off, without making at least one other agent worse off. With Y and Z together (answer B) the total allocation is {267, 33}. Changing from this allocation to any other option will make either type-1 or type-2 agents (or both) worse off.

(b)

A Rawlsian Welfare Function measures the society welfare by the worst-off member. It requires maximization of the worst case.

X, W, Z all have agents with only 11 utils. Hence Y is better as no agent has less than 22 utils. However, X and W together (answer C) would give a minimum welfare of 33 utils per agent!

(c)

A utilitarian measure society welfare based on the total welfare (regardless of inequality). Z (answer B) has a total of 256 utils, far more than the other options.