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325_Lecture9_Feb21

325_Lecture9_Feb21 - GOVERNMENT AND FISCAL POLICY IN THE...

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1 G OVERNMENT AND F ISCAL P OLICY IN THE C ONSUMPTION- S AVINGS M ODEL (CONTINUED) F EBRUARY 21, 2011 February 21, 2011 2 A D YNAMIC M ODEL OF THE G OVERNMENT A Government in the Two-Period Model So far only consumers in our two-period framework Introduce government in very simple form Exists for both periods Has spending in each period it needs to finance – can be financed via Taxes Issuing government debt/assets Notation g 1 : real government spending in period 1 g 2 : real government spending in period 2 b 0 : government asset position at beginning of period 1/end of period 0 b 1 : government asset position at beginning of period 2/end of period 1 b 2 : government asset position at beginning of period 3/end of period 2 r : real interest rate between periods
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2 February 21, 2011 3 G OVERNMENT B UDGET C ONSTRAINT(S) Model Structure Adopt a lifetime view of the budget constraint(s) All analysis conducted from perspective of beginning of period 1 Period-1 government budget constraint Period-2 government budget constraint Combine into lifetime budget constraint (LBC) Solve period-2 budget constraint for b 1 …and substitute into period-1 budget constraint 1 1 1 0 (1 ) g b t r b ± ± ± 2 2 2 1 (1 ) g b t r b ± ± ± Asset position at end of period 1/beginning of period 2 the key link Assume = 0 (fully-rational, informed, benevolent government) 2 2 1 1 0 (1 ) 1 1 g t g t r b r r ± ± ± ± ± ± Present discounted value (PDV) of all lifetime government expenditure Present discounted value (PDV) of all lifetime government income For graphical simplicity, will often assume b 0 = 0 (i.e., government begins life with zero net wealth). Note this is a different assumption than b 2 = 0. IMPORTANT : Government must balance its budget over its lifetime , not necessarily in each period February 21, 2011 4 C ONSUMER B UDGET C ONSTRAINT(S) Model Structure Introduce tax payments into consumer side of framework All in real terms for simplicity – can cast in nominal terms by multiplying by P Period-1 budget constraint Period-2 budget constraint Combine into lifetime budget constraint (LBC) Solve period-2 budget constraint for a 1 …and substitute into period-1 budget constraint 1 1 1 0 1 0 c t a a y ra ± ± ² ± 2 2 2 1 2 1 c t a a y ra ± ± ² ± 2 2 2 1 1 1 0 (1 ) 1 1 c y t c y t r a r r ² ± ² ± ± ± ± ± Present discounted value (PDV) of all lifetime expenditure Present discounted value (PDV) of all lifetime disposable income (i.e., after-tax income)
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3 February 21, 2011 5 E CONOMY- W IDE R ESOURCE F RONTIER Macro Fundamentals Consumer lifetime budget constraint Government lifetime budget constraint Summing the two yields economy-wide resource frontier aka “production possibilities frontier” (PPF) The GDP accounting equation in two-period form 2 2 2 1 1 1 0 (1 ) 1 1 c y t c y t r a r r ² ± ² ± ± ± ± ± 2 2 1 1 0 (1 ) 1 1 g t g t r b r r ± ± ± ± ± ± 2 2 2 1 1 1 0 0 (1 )( ) 1 1 c y g c y g r a b r r ² ± ² ± ± ± ± ± ± Suppose = 0 for graphical simplicity c 1 c 2 slope = -(1+ r ) y 2 - g 2 y 1 - g 1 IMPORTANT : taxes do not appear in the
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