March 23, 2016
Intermediate Macroeconomics
Homework 3
Professor: Edouard Schaal
TA: Gilberto Noronha
Part A: ABC Exercise

1. Chapter 3. Analytical problem 7 a) Sally earns $150,000 per year, which means she earns far above the cap. Therefore, the Social Security tax doesn’t affect her after-tax wage, which means there is no substitution effect. The higher tax only affects her income and due to this there is only an income effect. Since both proposals reduce Sally’s income by the same amount, she’ll increase her labor supply by the same amount under both proposals. b) Fred, however, is below the cap. Therefore, under proposal A, Fred’s labor supply doesn’t change because his tax rate stays the same and he remains below the cap. So there’s neither an income effect nor a substitution effect. Under proposal B, the Social Security tax rate Fred faces would rise to 13% from 10.4%, so Fred’s after-tax wage rate declines and there’s both an income effect and a substitution effect. The income effect leads Fred to work more, since the higher tax leads to a reduction in Fred’s income. The substitution effect leads Fred to reduce his supply of labor, since the after-tax wage is lower, so there’s less reward to working. Whether Fred will supply more labor or less labor under proposal B will depend on whether the substitution effect is stronger or weaker than the income effect.

Part B: Unemployment Insurance

1. State the maximization problem of the household with the new budget constraint. Do not solve yet, but show that it is the same problem as the original one, with simply a different wage w1 and a different level of wealth or non-labor income a1, which you will both give (no derivations). [Hint: you just need to rearrange terms in the budget constraint and identify the constant term and the term that depends on N.]
MaxC,N U(C) + V(Ñ – N) subject to