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CONSUMPTION-SAVINGS
Creation date：2024-05-22 17:01:20
Belonging category：金融Finance
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)
Case category
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关键词一 关键词二 关键词三 关键词四 关键词五 和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 EMESTER1 MAS8383 ECO 512 STAT 8310 CMN3102 MA577 CMPT 225 COMP0045 Methods Equations MATH 113 Math 3283W ICS-33 EN4302/ENT603 BIA B350F MA318 MTHM506 MECH 5315M ECONOMICS MAS8382 COM 2004 PX3142 XJEL 3662 STAT 231 MGT B399F PX4131 COM2108 30AM MSCI521 ECONM1015 ACFI304 GR5241 MATH10101 ECON 2070 COMS31900 EFIM20011 CSE 250B ACSE-5 STAT4207 SOFT2412 ELEC 331 AY2020 MSIN0209 FIT2094 CS 241L ST404 CS 411 3D CA3 INF4002 COMP3506 SIT718 CS 188 CS 170 MATH 138 CSE 251A CMT118 DATA5207 CMPT307 CMPT459 T1 PGEE11108 COSC 3P32 ME 163 MATH96007 7QQMM203 EE6227 BA 574 STA 4234 ECO206Y1Y ECO2008 MT2300 MATH 11158 CS 527 MACM 316 CSE474 2DI70 ISE 525 COMP3411 EMAT30007 7CCSMBDT MFIN704 MFIN704W21 MfIB ECE 438 CS 436 F36 CS5344 FE 621A FE621 TBA 612 ECM3151 ECMM422 MF1 MSIN0107 ESSMENT CS 5854 MFIT 5008 MIPS R4000 ENG5274 BU52018 ENG2079 BIOA02 STA2570 F0 INF553 STAT 440 STAT3008 COMP9417 COMP6451 6COM1042 BU52006 ST303 HW-1 CISC-235 CS 510 MATH3161 ECN 140 ECE391 Comp 3613 CVEN 9625 PRG455 UESTION 1 EARN 5 FE 825 IERG 5130 STAT 8178 EE161 ADS2 G54FUZ CS326 113B ECN 226 QBUS6860 ELEC3202 COMP9334 MGT11B MET CS 777 STA238 00099F Python SMM306 CMT206 EC116 SP MAST90084 CS480/680 BCPM0091 CMPT 300 ECON2209 FY20 STAT 432 CVEN9625 MATH1712 CMP9771M CMP3750M CIS 325 AI506 MAT344H1S MGT7180 PSTAT 160B CSYS5010 1D STAT 453/558 ME152B STA304H1F CSCI-128 ME428 CO3002 FINE 7640 COMP3234 ECSE 223 EE497 – 3D MATH5905 ECS648U ENG5009 MATH10242 EC665 A CPI221 ISOM5220 MACE40402 MGT B456F COMP9315 AFM 113 STAT 778 CS 564 MA231 CS 230 CS 124 COMP5511 CSC317 ITEC1010 ELEC207 INFT 3019 7CCMFM06 EE 161 5G ECLT5810 MATH 7349 CS526 O2 COMP90054 ELE00063M ACCT5034 ARC1015 CSCI 40 CSCI E40 FIN 524B CS 462 389COM CMT309 MFIN703 COMP4250 STA304 STA304H1S STA 1003 FIN 448 BUFN 732 CS520 CVEN3701 ECMT6006 PHAS0100 CSIT314 MDIA 5028 CSCI 2134 MAT 451 CMPT 459 STAT 457 INFO20003 COMP4141 IELE8066 F540 ECM9 CSE 6321 FIN 430 MATH3911 BFC5916 COMP1011 EEE 6209 STATS 240 CW3 COMP206 COMP1003 4331W ISE 530 CMPT 295 MATH 239 QF5203 INFR08010 IT114105 FIT2093 ECON3124 ECON1195 MATH 337 STAT 3006 COMP202 COMP3130 MATH3609 COMP 250 CS6140 IEEE ELE00041I FIN40090 CIV 5899 MATH3066 IGNMENT MATH 2009 STAT3405 HIST 101 MATH 3281 CEGE0042 ICT532 LAB 7 LAB 5 MCO455 CSIT214 Q4 IFB104 A1 ECO220Y5Y DA5020 CMPSC473 FIN9007 DSCI553 MSCI534 COMP3308 CSE-112 CMPT 310 EE104 F 2C P20 ALY2010 BUSM060 STA258 ECO00030M R BIOSTAT 274 COS6012-B FIT3155 CMPUT 340 EC421 INFS4205 ECOM135 NATS 1740 COMP809 MBE 6005 STA465 CSSE2310 CIVL2700 DATA4700 CMPSC 473 ISE 529 CS5044 MAST30020 COMP2207 ENGG1001 COMP0046 FIT3165 STAT GR5241 MECH0007 vATHK1001 ANALYTIC ATHK1001 MATH352001 HW3 S1 BMAN 24662 COMP 636 Stat-461 STAT 302 STAT 2132 STAR534 ENG4137 CMP3752M CS3103 BISM3222 STA 135 ME155A IIMT3601 ECON3371 ECON 3371 HW4 FINA 5840 DT211C CTEC3902 MAT005 MATH2148 S261F Econ 332 MATH3734 MIS41270 7CCMFM13 SYST 664 CIS434 CENG10014 MT4111 MT4527 ECMM424 CMT219 Math 136 MATH 3120 COMP10002 MAST20009 MATH0058 BEEM117 ISYE 6420 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MOEC0021 STA 106 ENGG 1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A 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MAS316/414 ACCT2522 MSIN0181 ATMS 201 COMP3425 MATH7861 SOLA2060 MA 325 7CCEMCTH ECON 432 INFT2051 SOLA 2060 ECOS2002 Stats141XP BIOA02H3 S2022 MA4601 K5 COMP5329 EG 284 IB3A70 WECO1020 COMP3027 Energy ACS61011 MAST20026 STAT 533 MATA31 ENVS257 BEM2031 EC 486 COMP0172 CS3214 EECE5644 IB2B20 COSC2536 COSC1147 COMP6214 5CCM242A COMP0130 AMME2000 MTMG50: EG238 ACF6006 QBUS2810 COSC2391 ECON7560 MATH377 STA305 CS 486 COMP1117B EL648 ELEC3909 ECON 241 COMP 4901W BUSI4428 ENEN20002 ENGN4524 ELEC3115 CSC 413 PSYC 100B ECON1002 MATH256 ANSC20005 MTHS2008 MATH40082 COSC 2406 FIT3174 STA 238 CMT202 Differential Equations MTHM017 GARCH 101 MATH2069 CSC336S ACSC12 ETF2121 CEME 2001 DB B474F ARHT1001 EECS 3311 3220 STATS 786 CS 484 COMP20008 MATH4091 ECE 455 CSCI 204 BUS B200F BA 875 BU5562 COSC 1147 X11 GEOG 101 IMM250F CSE 584A MATH38172 LAB 4 ELEC5882M FINS5523 EE 430 COMP 465 6CCS3PRE 7CCSMNSE FINANCE ACMB02H3 ENGG2112 ELEC5616 SCM B371 CHEM3120 CS22 ECMT2130 MAST30011 ADSPBF706 CENG0013 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CMP7000A CMP-7038B Math 263 LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 ​COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 ​BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 ​LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ​ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 ​FINC5090 ​MATH1052 ​SciComp Elec4622 ​FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 ​MAT 237 BISM2201 EEE8099 Physics 11 ECE2238B Biostat 234 ​ECON30009 INF10025 CHEM252 CCMA4008 CIVE 3007 STAT0031 ELEC ENG 3108 MGMT90140 CHEM 252 STAT3016 MMM095 ​MMGT6016 Legal STAT 311 ELEC9764 COMP 370 TCS 3053 EECS 1021 FIT1051 C/C++ EE3C COMP2003J COM398 COMP51915 Simulator FIN42330 8PRO102 PGD ELEC5160 XJCO1921 COMP5123M INFS 2042 CHE1148H ECA5313 IN3329 Microsoft Modeling B15 2TT COMP3687 COMP2432 DMS2030 KAN4TSF CFKG CSE 5322 CSE 445 STATS 3DA3 CHC5223 COMP1048 EL3105 EECS 3221 CS231 ME 4434 ITP4510 ITP4501 CSCI 5708 Controller EECE 5699 CPEN 231L CPN programs CSC8016 MATU9D2 ENGN4213 2. SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum
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