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CONSUMPTION-SAVINGS
创建日期：2024-05-22 17:01:20
所属分类：金融Finance
标签： CONSUMPTION
CONSUMPTION-SAVINGS

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CONSUMPTION-SAVINGS

FRAMEWORK
CHAPTER 3
2BASICS
Introduction
 Consumption-Savings Framework – provides foundation for
 Goods-market demand function (again…but w/different interpretation)
 Financial-market supply function
 Two time periods
 Important: all analysis will be conducted from the perspective of the very
beginning of period 1…
 …so a “future” (period 2) for which to save
 Dynamic models are the staple of modern macroeconomic analysis
 An explicit accounting of time
 Two periods are sufficient to illustrate the basic principles
 Soon will extend beyond two periods (Chapter 8)
3BASICS
Introduction
 Timeline of events
 Notation
 c1: consumption in period 1
 c2: consumption in period 2
 P1: nominal price of consumption in period 1
 P2: nominal price of consumption in period 2
 Y1: nominal income in period 1 (“falls from the sky”)
 Y2: nominal income in period 2 (“falls from the sky”)
 A0: nominal wealth at the beginning of period 1/end of period 0
 A1: nominal wealth at the beginning of period 2/end of period 1
 A2: nominal wealth at the beginning of period 3/end of period 2
 i: nominal interest rate between periods
 r: real interest rate between periods
 π2: net inflation rate between period 1 and period 2
 y1: real income in period 1 ( = Y1/P1)
 y2: real income in period 2 ( = Y2/P2)
2 1 2
2
1 1
1
P P P
P P

 
   
 
Period 1 Period 2
A0 A2Economic events during
period 1: income,
consumption, savings
A1 Economic events during
period 2: income,
consumption, savings
Start of the
world
End of the
worldStart of economic
planning horizon
End of economic
planning horizon
4STOCKS VS. FLOWS
Macro Fundamentals
 Stock variables, aka accumulation variables
 Quantity variables whose natural measurement occurs at a particular
moment in time
 Checking account balance
 Credit card indebtedness
 Mortgage loan payoff
 Flow variables
 Quantity variables whose natural measurement occurs over the course
of a given interval of time
 Income
 Consumption
 Savings
 The two broad categories of income
 Labor income
 Asset income (generated by interest rate(s) on (components of)
wealth)
Economic
examples
Economic
examples
Interpret A in our framework as net
wealth ( = total assets – total debts)
All income is a
FLOW
regardless of
source
5BASICS
Macro Fundamentals
 Building blocks of consumption-savings framework
 Utility
 Describes the benefits of engaging in financial market (and other)
activities
 Budget constraint
 Describes the costs of engaging in financial market (and other)
activities
 Utility and budgets two DISTINCT concepts
 As in basic consumer analysis (Chapter 1)
 Only after describing utility and budgets separately do we bring
the two together to obtain predictions from the framework
6UTILITY
Model Structure
 Preferences u(c1, c2) with all the “usual properties”
 Lifetime utility function
 Strictly increasing in c1
 Strictly increasing in c2
 Diminishing marginal utility in c1
 Diminishing marginal utility in c2
 Plotted as indifference curves
 Utility side of consumption-savings
framework identical to Chapter 1
framework
c1
u(c1,c2)
c2
u(c1,c2)
c2
c1
7BUDGET CONSTRAINT(S)
Model Structure
 Suppose again Y “falls from the sky”
 Y1 in period 1, Y2 in period 2
 Need two budget constraints to describe economic opportunities
and possibilities
 One for each period
 Period-1 budget constraint
 Period-2 budget constraint
1 1 1 1 0(1 )Pc A Y i A   
Total expenditure in period 1:
period-1 consumption +
wealth to carry into period 2
Total income in period 1:
period-1 Y + income from
wealth carried into period 1
(inclusive of interest)
2 2 2 2 1(1 )Pc A Y i A   
Total expenditure in period 2:
period-2 consumption +
wealth to carry into period 3
Total income in period 2:
period-2 Y + income from
wealth carried into period 2
(inclusive of interest)
1 1 1 0 1 0Pc A A Y iA   
2 2 2 1 2 1Pc A A Y iA   
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)
DEFINITION: A consumer’s savings
during a given period is the change in
his wealth during that period
can rewrite as
can rewrite as
8BUDGET 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 budget constraint
 Period-2 budget constraint
1 1 1 1 0(1 )Pc A Y i A   
2 2 2 2 1(1 )Pc A Y i A   
9BUDGET 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 budget constraint
 Period-2 budget constraint
1 1 1 1 0(1 )Pc A Y i A   
Asset position at end of
period 1/beginning of
period 2 the key link
- will think further about
this soon…2 2 2 2 1(1 )Pc A Y i A   
Assume = 0 (no bankruptcies + strictly increasing utility)
10
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 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 1 0(1 )Pc A Y i A   
Asset position at end of
period 1/beginning of
period 2 the key link
- will think further about
this soon…2 2 2 2 1(1 )Pc A Y i A   
2 2 2
1 1 1 0(1 )
1 1
Pc Y
Pc Y i A
i i
    
 
Present discounted
value (PDV) of all
lifetime expenditure
Present discounted value (PDV)
of all lifetime income
Assume = 0 (no bankruptcies + strictly increasing utility)
11
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 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 1 0(1 )Pc A Y i A   
Asset position at end of
period 1/beginning of
period 2 the key link
- will think further about
this soon…2 2 2 2 1(1 )Pc A Y i A   
2 2 2
1 1 1 0(1 )
1 1
Pc Y
Pc Y i A
i i
    
 
Present discounted
value (PDV) of all
lifetime expenditure
Present discounted value (PDV)
of all lifetime income
For graphical simplicity, will often assume A0 = 0 (i.e., consumer begins planning horizon with zero net wealth).
Note this is a different assumption than A2 = 0.
Assume = 0 (no bankruptcies + strictly increasing utility)
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ACCOUNTING BUSS1040 CHEM 181 MAT136H1 GY 6183 COMP3170 AGRI90089 PHYSICS 1002 ECON10003 IEOR E4004 ACS61012 MATH 40550 MKTG2113 TELE4653 ENSC1004 ECE 232E MK726 MTRX2700 SHEET 3 CSCA08 COMP30027 Math 2XX3 statistic MMAN3200 BISM7213 ECMM109 ECON 2022 FNCE 20005 GR5067 CSCB09 ME 3017 CS 5100 PHYS 2903 COMS 4771 COMP222 COMP 1046 CSC148H1 ISYS2038 FINS2615 OT5206 COMP2048 A6 MECH5770M MA826/20 CMPT 726 STA457 INFS6071 INFS588 integral ECON 216 IRDR 0017 MA323 PA 15213 PSYC2001 ENV222 Statistics ACCT5930 ACCT12 LAND2121 ME 5405 COMM1180 TELE3113 A7 ECE 568 ACCT2019 INFS1200 ENGG1340 CS 1400 ASST3 FINM7409 SWEN30006 INFO2222 FIN20150 SOSS1000 CSSE7231 FINS5513 COMS3200 CECN 702 ECON4060H MN3515 HW2 PSYA02H3 ECON 2112 COMP90051 CS 1652 MA30059 AF1605 MKTG7501 ECO-6003B COM4521 CTM ECON3350 COMP 3804 ELEC9762 BISM 7255 ST22 MATH20014 MNE3122 COMP343 MATH5165 ELE7029 ENGR30002 SEEM3500 ECON7350 RISK5002 FINM7405 COMP90059 MOS 3320B STAT 431 BISM7221 MATH3014 MTH783P EBA 35302 ACS133 BUS2206 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