## [answered] Long Question Assume preferences are "time-separable&q

Long Question

Assume preferences are ?time-separable?

U(c, c?) =?u(c) +??u(c?)

where?????(0,?1) and?u?is a concave increasing di?erentiable function.Assume there is a government who uses a sales tax to ?nance?G?and?G?(there is nolump-sum tax).That is, for each unit of?c?the household purchases, they must pay??cto thegovernment and for each?c?must pay???c?.Answer the following:

1.Derive the two-period budget constraint of the household.2.Derive the lifetime budget constraint of the household.3.Derive the two-period budget constraint of the government.4.Derive the lifetime budget constraint of the government.5.Write down the household problem.6.What is the household?s FOC? This is also called the Euler equation.7. If??(1 +?r) = 1 and???=???>?0, what must be the relationship between?c?and?c?? How

does this relationship compare with the zero tax environment,???=???= 0?8.What is credit/bond market clearing here?9.What is the de?nition of competitive equilibrium here?10.Does Ricardian equivalence hold in this environment?That is, suppose???and???change,

G?and?G?remain the same, and the government budget constraint still holds.Is thereany e?ect on?c,?c?,?s, or?r?What is the economic reason for your answer?

HINT: hereMRSc,c?= (1 +?r)

1 +??1 +??

If????, then????.Does this change the household?s consumption decision?

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This question was answered on: Sep 18, 2020

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