GOVERNMENT AND FISCAL POLICY IN
THE CONSUMPTION-SAVINGS MODEL
CHAPTER 7
2A DYNAMIC MODEL OF THE GOVERNMENT
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
3A DYNAMIC MODEL OF THE GOVERNMENT
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
 g1: real government spending in period 1
 g2: real government spending in period 2
 b0: government asset position at beginning of period 1/end of period 0
 b1: government asset position at beginning of period 2/end of period 1
 b2: government asset position at beginning of period 3/end of period 2
 r: real interest rate between periods
Period 1 Period 2
b0 b2
Government activities
during period 1:
government spending
and tax collection
b1
Government activities
during period 2:
government spending
and tax collection
Start of the
world
End of the
world
Start of economic
planning horizon
End of economic
planning horizon
4A DYNAMIC MODEL OF THE GOVERNMENT
Model Structure
 Economic activities/actions described by period budget constraints
 Period-1 government budget constraint
 Period-2 government budget constraint
 Definition: A government’s savings during a given period is the
change in its wealth during that period
 “Fiscal surplus” if government savings is positive
 “Fiscal deficit” if government savings is negative
1 1 0 1(1 )g b r b t   
2 2 1 2(1 )g b r b t   
Total expenditure in period 1:
period-1 spending + wealth to
carry into period 2
Total income in period 1:
period-1 tax collections +
income from wealth carried into
period 1 (inclusive of interest)
Total expenditure in period 2:
period-2 spending + wealth to
carry into period 3
Total income in period 2:
period-2 tax collections +
income from wealth carried into
period 2 (inclusive of interest)
1 1 0 1 0g b b t rb   
2 2 1 2 1g b b t rb   
Savings during
period 1 (a flow)
Savings during
period 2 (a flow)
Asset income
during period 1 (a
flow)
Asset income
during period 2 (a
flow)
can rewrite as
can rewrite as
Surplus/deficit is
a flow measure
5GOVERNMENT BUDGET CONSTRAINT(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 b1…
 …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
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 b0 = 0 (i.e., government begins life with zero net wealth).
Note this is a different assumption than b2 = 0.
IMPORTANT: Government
must balance budget over its
lifetime, not necessarily in
each period
6CONSUMER BUDGET CONSTRAINT(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 a1…
 …and substitute into period-1 budget constraint
1 1 1 0 1 0c t a a y ra    
2 2 2 1 2 1c t a a y ra    
2 2 2
1 1 1 0(1 )
1 1
c y t
c y t r a
r r

     
 
Present discounted
value (PDV) of all
lifetime expenditure
Present discounted value (PDV)
of all lifetime disposable income
(i.e., after-tax income)
7ECONOMY-WIDE RESOURCE FRONTIER
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
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

      
 
8ECONOMY-WIDE RESOURCE FRONTIER
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
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

      
 
Suppose = 0 for
graphical simplicity
c1
c2
slope = -(1+r)
y2 - g2
y1 - g1 An important theoretical result for the analysis of
tax policy.
Resource Frontier
THEOREM (intermediate micro): If taxes are lump-
sum, then consumer optimal choices can be
analyzed using either the consumer LBC or the
economy-wide resource frontier (superimpose
indifference map), and either approach will yield the
same predictions.
IMPORTANT: taxes do
not directly appear in
the resource frontier…
9NATIONAL SAVINGS
Macro Fundamentals
 National savings = savings by consumers + savings by government
+ savings by firms
 No firms in our model (yet..), so



1 1 1 1
privs y t c  
1 1 1
govts t g 
1 11 11 11 1 1 11
govpriv tnat s y t ccss t y gg        
1 0
firms 
10
EFFECTS OF TAX POLICY
Fiscal Policy and National Savings
 National savings = savings by consumers + savings by government
+ savings by firms
 No firms in our model (yet..), so



 Policy Experiment: Is national savings affected by a decrease in t1?
 Suppose g1 and g2 do not change
 Question 1: Effect on t2?
 t2 must rise (examine government lifetime budget constraint)
 Question 2: Effect of tax changes on consumers’ optimal choice of
period-1 consumption?
 Using intermediate micro theorem, NO EFFECT ON optimal c1
 Taxes are lump sum (will define/discuss next time…)
 Economy-wide resource constraint does not depend on taxes  optimal choice of c1
unaffected by the change in tax policy
 Question 3: Effect of tax changes on period-1 national savings?
 NONE – because neither g1 nor c1 changed
1 1 1 1
privs y t c  
1 1 1
govts t g 
1 11 11 11 1 1 11
govpriv tnat s y t ccss t y gg        
1 0
firms 
Crucial logic
Analyzing effects of changes in
tax policy on optimal
consumption choices is the key
11
RICARDIAN EQUIVALENCE
Fiscal Policy and National Savings
 Ricardian Equivalence Theorem: For a given PDV of government
spending, neither consumption nor national savings is affected by
the precise timing of lump-sum taxes
 A benchmark result/concept in the theory of macroeconomic policy
 Economic Interpretation: Rational consumers understand that a
tax cut today means a tax increase in the future (because total
government spending is unchanged)
 Thus entire tax cut is saved by consumers in order to pay higher taxes
in the future
 Private savings and government savings move in exactly offsetting
ways
1 1 1 1
privs y t c  
1 1 1
govts t g 
Rises when t1 decreases, GIVEN that we have
CONCLUDED that c1 does not change
Decreases when t1 decreases
12
RICARDIAN EQUIVALENCE
Fiscal Policy and National Savings
 Ricardian Equivalence Theorem: For a given PDV of government
spending, neither consumption nor national savings is affected by
the precise timing of lump-sum taxes
 A benchmark result/concept in the theory of macroeconomic policy
 Economic Interpretation: Rational consumers understand that a
tax cut today means a tax increase in the future (because total
government spending is unchanged)
 Thus entire tax cut is saved by consumers in order to pay higher taxes
in the future
 Private savings and government savings move in exactly offsetting
ways
 Ricardian Equivalence is to tax theory what perfect competition is
to standard economic theory
 Prediction relies crucially on lump-sum taxes
13
NATURE OF TAXATION
Macro Fundamentals
 Lump-Sum Tax
 A tax whose total incidence (i.e., total amount paid) does not depend in
any way on any decisions/choices an individual makes
 Real-world examples: ?…
 Taxes in our two-period framework so far
 Lump-sum! Total amounts t1 and t2 paid by consumer are independent
of any of their decisions/choices
 Proportional (aka distortionary) Tax
 A tax whose total incidence depends on decisions/choices an individual
makes
 In simple two-period framework: consumers only make consumption
choices c1 and c2
1 1 1 0 1 0c t a a y ra     2 2 2 1 2 1c t a a y ra    
Period-1 budget constraint Period-2 budget constraint
1 1 0 11 0(1 )c a a y ra     2 2 1 22 1(1 )c a a y ra    
Period-1 budget constraint Period-2 budget constraintτ is consumption
tax rate (aka sales
tax rate)
14
PROPORTIONAL TAXATION
Fiscal Policy and National Savings
 Combine into consumer LBC
 Slope is
 Non-lump-sum taxes: optimal consumption choices must be
determined using consumer LBC, not economy’s resource frontier
(i.e., intermediate micro theorem does not apply)
 Changes in tax rates do affect optimal consumption choices
because they change slope of consumer LBC
 Ricardian Equivalence Theorem does not apply
 Changes in tax rates do affect national savings
1 1 0 11 0(1 )c a a y ra     2 2 1 22 1(1 )c a a y ra    
Period-1 budget constraint Period-2 budget constraintτ is consumption
tax rate (aka sales
tax rate)
2 2
1 1 0
2
1
(1 )
(1 ) (1 )
1 1
c y
c y r a
r r



     
 
1
2
1
(1 )
1
r


 
  
 