[Ricardian Equivalence] Consider a three-period model instead of a two-period mo

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[Ricardian Equivalence] Consider a three-period model instead of a two-period model as shown in class. The environment of the model is the same as the two-period model expect the time horizon. As in the two-period model, all private agents are identical, we can model this as a representative agent model. There is a government in the economy, who can levy lump-sum taxes and issue government bonds to finance its expenditure (g0), g1, g2) at t = 0, 1, 2, respectively. Notice that the government can issue both one-period bonds and two-period bonds in the first period at t = 0. Consider the following policy changes. The government cuts the tax in period 0 by Delta . To finance the cut, the government increases one-period bonds by delta 1 and delta 2 in period 0 and period 1 respectively, raise taxes by Delta 1 and Delta 2 in period 1 and period 2, respectively, and issues A units of additional two-period bonds in period 0. (all these changes can be negative in principle). Set up the representative agent's maximization problem. Show that Delta1 = delta 1 - q1 delta 2 and Delta 2 = delta2 + A. Show that the present value of taxes must be unchanged (for given bond prices), i.e., Delta - q0Delta 1 - q0q1 Delta 2 = 0.

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