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ECON7150 Assignment

Creation date：2024-06-18 16:41:56

Belonging category：经济Economics

Tag ECON7150

Assignment

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ECON7150

Assignment
Instructions:
• All answers to the assignment must be neatly hand written. This can be done on paper or
directly onto a file using a tablet.
• Save your assignment as one pdf document. If it is written on paper, you should scan it
into a single file. If you do not have access to a flatbed scanner you can use a phone app such
as “Adobe Scan” or “Microsoft Office Lens”.
• Submit your assignment on Blackboard through Turnitin.
• Make sure you show all steps, key formulae, and workings clearly. Final solutions should
be simplified as much as possible and either highlighted or circled. Round to the nearest
hundredth if necessary.
• 100 Marks - 30% of overall assessment
1. (15 marks) Suppose that a decision maker has $100. They need to choose how many kilos of
chocolate (c) and vegetables (v) they will purchase. Chocolate costs $2 per kilo and vegetables
cost $1 per kilo. They are choosing c and v to maximise the utility function
U(c, v) =
5
α
cα +
1
α
vα
where α is a constant and 0 < α < 1.
a) (5 marks) Formally write down the decision maker’s optimisation problem and the asso-
1
2ciated Lagrangian.
b) (5 marks) Write down the first order conditions and find the values of c and v that satisfy
those conditions. Your answer should be a function of α.
c) (5 marks) Check the second order conditions for the solution(s) you found in part (b). Do
these values of c and v solve the decision maker’s problem?
2. (16 marks) Define A =

5 w 1
w −1 3
−2 −3 4
, B =

−1 2x y
y − x 4 1
3y − 1 1 5
, C =

1 0 z − 2
3 −1 z
7 3 2

a) (4 marks) For what value(s) of w is the matrix A singular?
b) (4 marks) Treating x and y as constants, find the determinant of the matrix B.
c) (8 marks) Treating z as a constant, find the inverse of the matrix C. [Hint: check your
answer by plugging in simple values for z and making sure that the product of C and its
inverse is the identify matrix.]
3. (12 marks) Consider the function f(x, y) = (y − 3)ey2−4x2 .
a) (6 marks) Find all stationary points of f(x, y).
b) (6 marks) Classify any points you found in part a) as either saddle points, local maxima,
or local minima.
4. (15 marks) A firm produces q1 units of good 1 and q2 units of good 2. The firm is a price
taker and faces prices $100 per unit of good 1 and $50 per unit of good 2. The firm’s cost of
producing q1 and q2 in dollars is
C(q1, q2) = 5q
2
1 + 2q1q2 + 4q
2
2
a) (3 marks) Write down the firm’s profit maximization problem in terms of x and y.
b) (6 marks) Use the first order conditions and find the values of x and y that solve the firm’s
problem. [Note: For this problem, we are not assuming that the quantities need to be a
whole numbers. They can be any positive real number.]
c) (6 marks) Use the second order conditions to show that the solution from part b) is a
maximum.
5. (18 marks) Consider the problem
max − 3x+ 4y
subject to 5x2 + 2y2 = 10
(a) (3 marks) Write down the Lagrangian for this problem.
3(b) (9 marks) Write down the first order conditions for the optimisation problem and find
all values of x and y that satisfy those first order conditions.
(c) (6 marks) Check the second order conditions to classify the solution(s) you found in part
(b). Do these values of x and y solve the problem?

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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 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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 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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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