Alpha Geek
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The country of Adventureland’s two citizens, Bill and Ted, both earn $1,000 per week working the same job at the same company. Bill and Ted each face some risk of being laid off due to bad market conditions next year, in which case they will have an income of only $250 from an alternative parttime job that they would fall back on. There is a 10% probability that Bill we be laid off, and a 30% probability that Ted will be laid off. Bill and Ted have the same utility function U = ln(C).
The government is considering providing some social unemployment insurance. In particular, they are considering two plans: The first would pay any worker who loses his job $100, and the second would pay any worker who loses his job $600. Both would be financed by collecting a tax from any worker who keeps his job.
a. Under each plan, how high would the government have to set the tax so that it would not expect to lose money on the plan?
b. Assuming it sets the tax rate you found in part a, compute the well-being of Bill and Ted under each of the plans. How do Bill and Ted rank the three possibilities (the two policies and the status quo)? Explain the pattern that you see in terms of redistribution and risk aversion.
c. Which plan is best if the society has a utilitarian social welfare function? A Rawlsian social welfare function? (See Chapter 3 if you need a reminder about social welfare functions!)