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ECON 457 Computational Economics
Creation date：2024-04-27 16:27:43
Belonging category：经济Economics
Computational Economics

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ECON 457 - A01

Computational Economics*
UVIC - Department of Economics
Spring Term 2021/22
Assignment 3
Due on Brightspace before 11pm March 10th 2022
Please create and submit a pdf file, making sure that it’s readable and unlocked.
The file name has to follow this template: 457 PS3 Surname Name StudentNumber.pdf
You can cooperate with other students, but no group submissions will be accepted
If you do cooperate, please list the other students’ names in the cover page
No “Photocopy”answers will be accepted
No late submissions will be accepted
NOTE: YOU MUST INCLUDE THE ASSIGNMENT COVER PAGE
(Failure to do so will entail a 5-point deduction from the grade received)
Remarks: Your answers have to be submitted in a “report” format. Relying on Jupyter is the easiest
option. The codes you developed have to be included as well in the pdf file. Devote some time to give the
graphs, plots and tables a format easy to understand. Also the way you present your answers matters for
the final grade. Even if a question is mainly technical, briefly explain what you are doing, stressing the
economic meaning of the various steps whenever possible. Being able to convey your thoughts effectively is
an asset also in real life.
Question 1: Systems of Non-Linear Equations (40 Marks)
Consider the vector-valued function f : R2 → R2 defined byf1(x, y)
f2(x, y)
 =
100x(y − x2)− x+ 1
150(x2 − y)

(a) Rather than writing the code in terms of x and y, we want to use a more compact, and often more
powerful, way of thinking about these problems. In particular, we are going to rely on vectors and matrices.
Write two Python functions, say “nlfun” and “nljac”. The two Python functions should take as an input
a column vector xvec of dimension 2. This vector stores the current values of the variables x and y as the
entries xvec[0] and xvec[1], respectively.
The two Python functions should return as their respective output: i) for “nlfun”: a column vector fval
of dimension 2 that contains the value of f(.) at xvec; ii) for “nljac”: a 2-by-2 matrix fjac that contains the
Jacobian of f(.) at xvec.
Note: in “nlfun” you may want to write two formulas that compute the two entries in the vector storing
the two dependent variables (fval[0] and fval[1]); in “nljac” you may want to write four formulas, namely
the four partial derivatives that represent the Jacobian (fjac[0, 0], fjac[0, 1]...). All formulas should be
expressed in terms of the entries of the vector xvec, i.e. xvec[0] and xvec[1].
(b) Compute numerically the root of f(.) with Newton’s method. As the basis for your code, you may
want to use the “mynewton” function included in the Python notebook I distributed.
The code should have a for-loop. Inside the loop, at each iteration the code should be calling the two
Python functions you developed,“nlfun” and “nljac”, to compute the value of the function and its Jacobian.
The last operations performed in the loop should be the update of the guess, and the convergence check.
Use as initial guess the value xvec = [1.5, 1.5]. Note: please write the code without using the scipy.optimize
library, but feel free to use it to check that you are getting the right answer. This library needs two user-
specified functions that evaluate the values of f(.) and its Jacobian for the current guess. To achieve this
goal, you could use the functions “nlfun” and “nljac” that you have already developed.
*The material contained in this document is copyrighted ©, property of the University of Victoria, meant exclusively for
the use of students enrolled in ECON 457, and it cannot be shared without the author’s explicit consent.
Question 2: General Equilibrium (60 Marks)
Consider a simple endowment economy with four agents and two goods. Agent i is initially endowed
with eij units of good j and maximizes the following utility function:
Ui(x) =
2∏
j=1
x
aij
ij (1)
subject to the budget constraint
2∑
j=1
pjxij =
2∑
j=1
pjeij . (2)
Here, xij is the amount of good j consumed by agent i, pj is the market price of good j, and aij > 0 are
preference parameters.
A competitive general equilibrium for the endowment economy is a pair of relative prices, p1 and p2,
normalized to sum to one, such that all the goods markets clear and each agent maximizes utility subject to
their budget constraints.
(a) Write a Python code to compute the competitive general equilibrium for the following parameters:
(i, j) aij eij
(1,1) 0.50 2.0
(1,2) 0.50 3.0
(2,1) 0.75 1.0
(2,2) 0.25 2.0
(3,1) 0.80 4.0
(3,2) 0.20 0.0
(4,1) 0.25 0.0
(4,2) 0.75 2.0
Comment on your findings.
(b) Compute the competitive general equilibrium with these new parameters (all the others are kept the
same as in part a):
(i, j) aij eij
(4,2) 0.75 5.0
Comment on your findings.
(c) Compute the competitive general equilibrium with these new parameters (all the others are kept the
same as in part a):
(i, j) aij eij
(1,2) 0.50 0.0
(3,2) 0.20 3.0
Comment on your findings.
(d) Consider the general equilibrium allocations you have obtained in parts (a) and (c). Compute the
related utilities of the four agents. The change in endowments can be considered as a public intervention,
taxing individual 1 and redistributing the revenues to individual 3. Is this a Pareto improvement? Consider
the effect on individuals 2 and 4: are they better off or worse off, and why?
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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 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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 MGMTMFE 405 25579 1ECE 273 M122 COMP4434 1ELEC ELEC5620M STAT0010 BFF2401 MXB361 MATH3811 CS330 CMT307 FIT1033 CptS 583 UP 431 MATH6005 AF5343 CS2435 ECOM30002 ES50061 CS 2506 ECMT6002 CODE 00099F MT4539 ESSAY ICM317 MATH1231 MFIT5010 BMA547 MATH334 CIVL2201 MATH39032 T-04 CIVE97119 EMESTER CAB302 CAB301 59PM STAT802 ISYS3412 RM3 COSC 2123 AcF 311 MATH2022 1FINAL 4CCS1PHC ICM 142 ENVS3023 Math 4023 I1 ACSE8 FIN B385F CS-275 STA 4109-01 A31021 EE140 MT1 EE124 ECO-6004B Inf2-IADS CS126 IS2184 UL18 MATH5092 ECOM009 COMP 6211 ELEC202 MKT3019 IAB230 FIT5046 584-S21 COMP3210 CO250 A29401 MATH 136 MGT6174 ECMT6007 DATA2001 MAT 443 MATH10222 PHDE0071 ELE00123M COSC1295 MAT00045H MATH32032 1004GRC MAS223 COMP10001 DATA3404 CIVL2110 STAT2008 FNCE10002 EEE6431 COM6515 COMP9120 NBS8185 ECTE942 ECON 405 MATH314301 STAT 2011 COMPSCI 350 COMP20007 CMPSC-132 ECON5002 STA 35 MTH6108 FIT5147 MTH6150 100C FINA 5260 DESC9115 ECON4998 NBS8257 GMM ECON 6070 BSA2 ECE599 STATS 102B STA120 INFS601 BFC3241 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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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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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