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Unformatted text preview: ECO 475 PS2 Solution Yu LIU November 6, 2010 1 Ricardian Equivalence (a) Approach 1: Government levies a one time lumpsum tax τ = G at time T . Consumer's Problem (SME): Given r , max { c t ,b t +1 } ∞ X t =0 β t u ( c t ) subject to c t + b t +1 = y t + (1 + r ) b t , ∀ t 6 = T c t + b t +1 = y t + (1 + r ) b t τ, t = T b = 0 Rewrite the budget constraint into a lifetime one: ∞ X t =0 c t (1 + r ) t = ∞ X t =0 y t (1 + r ) t G (1 + r ) T Approach 2: (Borrow from outside) Government borrows B = G at time T and then levies a lumpsum tax τ = rG each period after T . Consumer's Problem (SME): Given r , max { c t ,b t +1 } ∞ X t =0 β t u ( c t ) subject to c t + b t +1 = y t + (1 + r ) b t , ∀ t ≤ T c t + b t +1 = y t + (1 + r ) b t τ, ∀ t ≥ T + 1 b = 0 Rewrite the budget constraint into a lifetime one: ∞ X t =0 c t (1 + r ) t = ∞ X t =0 y t (1 + r ) t ∞ X t = T +1 τ (1 + r ) t = ∞ X t =0 y t (1 + r ) t G (1 + r ) T 1 Since both the objective functions and the constraints are same for the two approaches, the allocations should be the same. So the consumers are indi erent between the two approaches. As long as the government and the consumers (with in nite lifetime) can borrow and lend at the same rate, it does not matter whether a government nances its expenditure with debt or a tax increase Ricardian equivalence. [(Borrow from the consumers) Consumer's Problem (SME): Given r , max { c t ,b t +1 } ∞ X t =0 β t u ( c t ) subject to c t + b t +1 = y t + (1 + r ) b t , ∀ t ≤ T 1 c t + b t +1 = y t...
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This note was uploaded on 09/06/2011 for the course ECO 475 taught by Professor Hong during the Fall '07 term at Rochester.
 Fall '07
 Hong

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