# Economics: The Ricardian equivalence

Let r = 0 and β = 1. Households live for two periods and have utility log(c1) + log(c2) and pre-tax income \$3000 each period. The government needs to fiance a project in the first period that costs \$300 each household. Policy 1: tax \$300 in the first period. Policy 2: issue debt in the first period and pay back in the second period. Let T1 and T2 be the lump-sum taxes in period 1 and period 2.

(a) Write down the consolidated life time budget constraint for the households using T1 and T2

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(3 pts)

(b) Write down the household’s maximization problem. (3 pts)

(c) What are T1 and T2 under policy 1? (3 pts)

(d) What are T1 and T2 under policy 2? (3 pts)

(e) What are c ∗ 1 and c ∗ 2 under policy 1? (3 pts) (Hint: c ∗ 1 = I 1+β and c ∗ 2 = β(1+r)I 1+β )

(f) What are c ∗ 1 and c ∗ 2 under policy 2? (3 pts)

(g) Does Richardian Equivalence hold? (3 pts)

(h) What are the savings s under policy 1? (3 pts)

(i) What are the savings s under policy 2? (3 pts)

(j) If the household can not borrow at all, does the solution under policy 1 change? If yes, what are the new c ∗ 1 and c ∗ 2 ? (4 pts) (Hint: Write down the per period budget constraint first.)

(k) If the household can not borrow at all, does the solution under policy 2 change? If yes, what are the new c ∗ 1 and c ∗ 2 ? (3 pts)

(l) If the household can not borrow at all, Does Richardian Equivalence hold? (3 pts)

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