Question

1. Jon, Sara, Rohit, and Maria currently earn $100k, $120k, $40, and $20. Assume utility function is U(y)=(y)^(0.5).   Consider a utilitarian social planner deciding on whether to enact the following policy: tax 10% for all earnings above $50k, and transfer it as a lump sum to all earning below $50. Assume further that 30% of the potential revenue based on current earnings is “lost” (leaky bucket) due to reduced work incentives.

Answer 1

Let's calculate the current total of utility derived by the four individuals.

	Income	Utility = Income^(0.5)
John	100000	316.23
Sara	120000	346.41
Rohit	40000	200.00
Maria	20000	141.42
Total	280000	1,004.06

Now let's do income redistribution, deduct the loss of tax revenue due to leaky budget and recalculate the utility. There is an improvement despite loss of 6600 due to leaky bucket

	Income	Tax @10%	Redistribution	Income post redistribution	Utility = Income post redistribution^(0.5)	Leaky bucket @30%
John	100000	-10000		90000	300.00	3000
Sara	120000	-12000		108000	328.63	3600
Rohit	40000		7700	47700	218.40
Maria	20000		7700	27700	166.43
Total	280000	-22000	15400	273400	1,013.47	6600