Econ 450 Winter 2015 HW 4 Solutions - Econ 450 Winter 2015 HW 4 1 Suppose that in a country with a generous unemployment insurance system we see longer

# Econ 450 Winter 2015 HW 4 Solutions - Econ 450 Winter 2015...

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Econ 450 Winter 2015 HW 4 1. Suppose that in a country with a generous unemployment insurancesystem, we see longer unemployment spells than in another that isless generous. Does this clearly indicate the program istoogenerous,and should be reduce? Explain why or why not.If these longer employment spells are not leading to better job matches,then all the program is doing is subsidizing unproductive leisure, andare therefore too generous. If they are leading to better matches how-ever, then long spells are not evidence the programs are too generous. 2. Explain a dollar-for-dollar phase out of a cash transfer as earned in- come rises has a negative effect of labor supply relative to a 33 cent per dollar phase out, as was implemented in the 1996 welfare reform. This requires an illustration of the AFDC vs. TANF budget contraints, to show that for many utility function, a consumer who would choose to exit the labor market under AFDC will not do so under TANF. See Attached. 3. Suppose Dennis has utility function over consumption U D = 50 c D , While Emily has utility U E = 50 c E + . 2 U D That is, Emily derives utility from her own consumption, as well as from Dennis’s consumption. Society has income of 200 to divide be- tween Dennis and Emily; currently, Dennis has income 100 and Emily has income 100. (a) Are any pareto-improving redistribution possible here? From this distribution of income, no. Any income removed from Emily and given to Dennis will not increase Emily’s utility enough to compensate her for the lost income. If Dennis had less income, so that his marginal utility of income was high enough, then re- distribution might be possible, since Emily will gain utility from Dennis’s rise in utility (she is altruistic). 1

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(b) Find the income distribution that would maximize a simply util- itarian social welfare function. You can do this by setting up the lagrangian: L = 50 c D + 50 c E + . 2(50 c D ) - λ ( c E + c D - 200) and solving:

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