PPOL 507 Professor Thomas DeLeire Problem Set 3 Due April 10 Problem 1: Inequality

Instructions Download the excel spreadsheet PS3.xls from the class website on blackboard. You will use the data in this spreadsheet to answer Problems 1 and 3.

(a) Using the 2011 U.S. pre-­‐tax income distribution in columns A, B, and C of the spreadsheet, please calculate the gini coefficient.

What does this coefficient tell us about the degree of inequality in pre-­‐tax pre-­‐ transfer income in the U.S.?

(b) Suppose the government were to impose a 20% flat tax on all individuals. Thus the income tax each person pays is simply 20% of their income.

Please calculate the after-­‐tax gini coefficient if this tax rate were applied to the 2011 distribution of income. (You may assume that the revenue raised is distributed equally among all citizens on something like national defense. Thus, there is no need at this stage to how the money is spent this into your calculation.)

(c) Now instead suppose that the revenue raised by the tax system is distributed equally as (a non-­‐taxed) cash transfer to all citizens with incomes less than $100,000.

Please calculate the after-­‐tax after-­‐transfer gini coefficient.

Problem 2: Medicare

One feature of Medicare is that Hospital Insurance (Part A) has a deductible but no co-­‐insurance (for hospital stays lasting less than 60 days), while Physician Insurance (Part B) has both a deductible and 20% co-­‐insurance for most services.

Using what you have learned about moral hazard and optimal insurance design, please provide an explanation for why Medicare might have designed Parts A and B differently (in terms of co-­‐insurance).

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Problem 3: Budget Constraints under a Welfare Program

Julia is a single mother with two kids. If she applies for welfare and does not work at all, she receives cash benefits of $5,000 a year and health insurance for her family through Medicaid that she values at $2,000 a year. If she works, she earns $10 per hour and can work up to 2000 hours per year. She loses $1 in welfare benefits for every $2 she earns. She loses her Medicaid coverage if she earns enough so that she is no longer eligible for welfare benefits (i.e. she loses Medicaid when welfare = $0). Her job does not provide health insurance.

Julia’s income is low enough that she does not pay income taxes (also assume that she does not pay Social Security taxes).

(a) Graph Julia’s budget constraint with leisure (hours not worked) on the x-­‐axis and consumption on the y-­‐axis. Be sure to label the slope of