Question

2. Suppose there is only one consumption good, while there are two individuals. Agent 1 has utility function u1-9q1, while agent 2 has utility function u2 can choose any non-negative values of q1 and q2 such that: q2. The policymaker 1 q2 10 (a) What choice of values of q1 and q2 maximize a utilitarian social welfare function (SWF), subject to the above constraint? (b) What choice of values of q1 and q2 maximizes the Rawlsian SWF?

Answer 1

u_1 = 9q_1, u_2 = q_2, q_1 + q_2 = 10 a) utilitarian swf = u_1 + u_2 u = 9q_1 + q_2 rightarrow of perfect substitute type now max u st q_1 + q_2 = 10 if q_1 = 10, then u = 90 q_2 = 10, u = 10 thus u is max q_1 = 10, & q_2 = 0 b) Now for raisin swf u_1 = min {u_1, u_2}, maximize the welfare of the worst off individual qq_1 = q_2 & q_1 + q_2 = 10 so put q_2 = 10 - q_1, then 9q_1 = 10 - q_1 so 10q_1 = 10 thus q_1 = 1, & q_2 = 9