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This is final exam of VNUIS, Exams of Mathematical finance

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2021/2022

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FINAL ASSIGNMENT
Code: 2
Program: IB, AC, MIS, BDA
Course Code: MAT 1092
Course Title: Advanced Mathematics
Time allowed: 03 hours
Date: 21/8/2021
Starting at 15:30, 21/8/2021
Ending at 18:30, 21/8/2021
Lecturer’s Signature
Asso. Prof. Nguyễn Hải Thanh
Date: 01/8/2021
Department’s Signature
Date: 02/8/2021
Instructions to students:
1. At 15:30, 21/8/2021, each student is assigned a final assignment with code number that is identical to the tens digit of his / her student code (for example: if
a student code is 17071365 then the tens digit is 6, and he / she must choose to do Final Assignment MAT1092 Code 6).
2. Final assignment consists of 5 problems, students should write the answers by hand to these problems in 10 pages. Solution of problem 1 is written in pages
1-2, problem 2 in pages 3-4, problem 3 in pages 5-6, problem 4 in pages 7-8, problem 5 in pages 9-10. Each page is numbered clearly by hand writing in the right-top
corner. Some pages not used are left with blank space. Students should write clearly his / her full name, student code and class course in the first row of the first page
(for example: Nguyễn Văn Thao, 17007365, MAT109201).
3. To submit the final assignment, students use CamScanner to scan all the above 10 pages and save them to a pdf file, starting from page 1, then page 2, 3, 4,
5, 6, 7, 8, 9 and 10.
4. Students should finish submitting the final assignment / the pdf file with the file name: student’s full name.student code.class course (for example:
Nguyen Van Thao.17007365.MAT109201) in due time through MS Teams Assignment (do not be late in submitting the final assignment in due time, 18:30,
21/8/2021).
5. Any violation of the above instructions can CAUSE ZERO MARK for the final assignment.
Problem 1 (2 points): The values of nominal prices of a good at the end of each year between 2016 and 2019 (with 2016 being the b ase year) are
listed in the table which also shows the annual rates of inflation:
Year 2016 2017 2018 2019
Price 150 158 170 179
Inflation 5% x% y% z%
where x, y, z are the last three digits of your student code (for example: if a student code is 17071435 then x = 4, y = 3, z = 5).
a/ If the index number of the real price for 2020 is 105 and the rate of inflation for this year is 6%, work out the value of nominal price in 2020;
b/ If the index number of the nominal price for 2015 is 90, work out the value of real price in 2015.
Problem 2 (2 points): The demand function for a firm’s domestic and foreign markets are:
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FINAL ASSIGNMENT

Code: 2 Program: IB, AC, MIS, BDA Course Code: MAT 1092 Course Title: Advanced Mathematics Time allowed: 03 hours Date: 21/8/ Starting at 15:30, 21/8/ Ending at 18:30, 21/8/ Lecturer’s Signature Asso. Prof. Nguyễn Hải Thanh Date: 01/8/ Department’s Signature Date: 02/8/ Instructions to students:

At 15:30, 21/8/2021 , each student is assigned a final assignment with code number that is identical to the tens digit of his / her student code (for example: if a student code is 17071365 then the tens digit is 6, and he / she must choose to do Final Assignment MAT1092 Code 6).

  1. (^) Final assignment consists of 5 problems, students should write the answers by hand to these problems in 10 pages. Solution of problem 1 is written in pages 1-2, problem 2 in pages 3-4, problem 3 in pages 5-6, problem 4 in pages 7-8, problem 5 in pages 9-10. Each page is numbered clearly by hand writing in the right-top corner. Some pages not used are left with blank space. Students should write clearly his / her full name, student code and class course in the first row of the first page (for example: Nguyễn Văn Thao, 17007365, MAT109201 ).
  2. (^) To submit the final assignment, students use CamScanner to scan all the above 10 pages and save them to a pdf file, starting from page 1, then page 2, 3, 4, 5, 6, 7, 8, 9 and 10.
  3. (^) Students should finish submitting the final assignment / the pdf file with the file name: student’s full name.student code.class course (for example: Nguyen Van Thao.17007365.MAT109201 ) in due time through MS Teams Assignment (do not be late in submitting the final assignment in due time, 18:30, 21/8/2021 ).
  4. (^) Any violation of the above instructions can CAUSE ZERO MARK for the final assignment. Problem 1 (2 points): The values of nominal prices of a good at the end of each year between 2016 and 2019 (with 2016 being the base year) are listed in the table which also shows the annual rates of inflation: Year 2016 2017 2018 2019 Price 150 158 170 179 Inflation 5%^ x%^ y%^ z% where x, y, z are the last three digits of your student code (for example: if a student code is 17071435 then x = 4, y = 3, z = 5). a/ If the index number of the real price for 2020 is 105 and the rate of inflation for this year is 6%, work out the value of nominal price in 2020; b/ If the index number of the nominal price for 2015 is 90, work out the value of real price in 2015. Problem 2 (2 points): The demand function for a firm’s domestic and foreign markets are:

P 1 = 25 – 2.5Q 1

P 2 = 15 – 2Q 2

and the total cost function is: TC = 25 + 5Q, where Q = Q 1 + Q 2. a/ Determine the prices needed to maximize profit with and without price discrimination; b/ Find the maximum profit values in these two cases and give your comment. Problem 3 (2 points) Given the demand function P = - QD

  • 4QD + 64, and the supply function P = QS

– 4QS + 14.

a/Assuming pure competition, find the consumer’s surplus and the producer’s surplus; b/ Explain the meaning of values of the surpluses as found in question a/. Problem 4 (2 points): Consider the macroeconomic model defined by National income: Y = C + I + G* (G* > 0) Consumption: C = aY + b (0 < a < 1, b > 0) Investment: I = cr + d (c < 0, d > 0) Money supply: MS* = k 1 Y + k 2 r (k 1 > 0, k 2 < 0, MS* > 0) Show that this system can be written as Ax = b, where a/ Use Cramer’s rule to find I; b/ Write down the government expenditure multiplier for I and deduce its meaning. Problem 5 (2 points): Consider the supply and demand equations: QSt = 0.4Pt-1 - 5 QDt = - 0.8Pt + 55 a/ Assuming that the equilibrium conditions prevail, find an expression for Pt and Qt when P 0 = 75; b/ Is this system stable or unstable, explain why?