The Person-Swenson model. (Person and Swenson, 1989.) Suppose there are two periods. Government policy will be controlled by different policymakers in the two periods. The objective function of the period-t policymaker is 0020 where U is citizens’ utility from their private consumption; αt is the weight that the period-t policymaker puts on public consumption; Gt is public consumption in period t; and V(•) satis  . Private utility, U, is given by

 

 where W is the endowment; Tt is taxes in period t; and C (•), the cost of raising revenue, satisfies C  (•) ≥ 1, C (•) > 0. All government debt must be paid off at the end of period 2. This implies T₂ = G₂+D, where D = G₁− T₁ is the amount of government debt issued in period 1 and where the interest rate is assumed to equal zero.

 

(a) Find the first-order condition for the period^-2 policymaker’s choice of G₂ given D. (Note: Throughout, assume that the solutions to the policymakers’ maximization problems are interior.)

 

(b) How does a change in D affect G₂? (c) Think of the period-1 policymaker as choosing G₁ and D. Find the first order condition for his or her choice of D. (d) Show that if α1 is less than α₂, the equilibrium involves inefficiently low taxation in period 1 relative to tax-smoothing (that is, that it has T₁ <>₂). Explain intuitively why this occurs. (e) Does the result in part (d) imply that if α₁ is less than α₂, the period-1 policymaker necessarily runs a deficit? Explain.