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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).
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
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?