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ECON4060H dynamic optimization
创建日期：2024-05-04 16:30:44
标签： ECON4060H
dynamic optimization

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ECON4060H Take‑Home Exam


DUE BY 8:00PM EASTERN TIME ON APRIL 20TH. UPLOAD YOUR ANSWERS TO BLACKBOARD.
Total points: 50.
Instructions
1. This exam is open‑book. References allowed include lecture slides, course handouts, personal
notes, and the reading list of the course.
2. Any form of collaboration or asking help from anyone is prohibited. Answers that appear very
close to each other will be inspected for possible collaboration.
3. If answers are hand written, writing must be legible.
4. You can use any programming languages. Python and/or R are recommended.
5. All computer programs must be submitted in their original formats that are used to obtain an‑
swers. Computer programs submitted in the PDF format or as images will be discarded and
result in zero marks. Original formats of programs can be plain text files with suffix .py or .R,
they can be also saved in Jupyter notebooks.
6. If there are multiple files to submit, please consider to compress them into one zip file for sub‑
mission.
7. Write your name and student ID number in all files you submit.
8. For full credit, show necessary steps and necessary explanation.
Question 1
Consider the intertemporal decisions of an individual. The individual is born in period 0, lives for +1
periods, and dies at the end of period . At the beginning of any period , the individual’s asset level
is , which is used for production. The amount of production is with 0 < < 1. Produced output
is used for consumption and for asset in the future. The budget constraint is
+ +1 = , for = 0, 1, 2,⋯ , .
The initial asset value 0 > 0 is given. When the individual dies, she/he leaves no bequest, that is,
+1 = 0.
The utility flow from consumption in period is given by () = ln(). The discount factor is with
0 < < 1.
1. (4 points) Formulate the individual’s dynamic optimization problem. You can use the Bellman
equation, but do not have to. Be thorough in describing the problemmathematically.
Shutao Cao 1
ECON4060H Take‑Home Exam, 2022 Winter 19 April 2022
2. (6 points) Suppose that the individual lives for 3 periods, i.e., = 2. Solve for the optimal
consumption in all periods. Do not use programming, solve the problemwith algebra using the
backward induction and optimal conditions. Show necessary steps.
3. (5 points) Suppose that the individual lives for 11 periods, i.e., = 10. Write a program to
numerically solve for the individual’s life‑cycle choices. Plot the optimal consumption and the
asset level over the life cycle. In doing so, you can use these values = 0.5, 0 = 1, = 0.7, or
set them to values of your own choice. Hint: you can either program by extending the pattern
displayed in the second part above, or solve for the value function with backward induction.

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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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