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3) In the macroeconomic model below, Y is aggregate output, C is aggregate consump- tion, lo is aggregate investment, Go is government spending, T is the total amount of taxes collected by the government, and t is income tax rate. The variables Y, C, and T are endogenous, Go, lo, and t are exogenous, and a, b, and k are parameters. Y =C+ lo+Go C = a+b(Y - T) T =k+ tY (a > 0,6 € (0, 1)) (k > 0, t e (0, 1)) Calculate the determinant of the coefficient matrix A associated with this system of equations. The determinant of the coefficient matrix A is: a) JA = 1-6+ bt b) JA=1-b- bt +a c) JA =6+t d) JA| =1+a+b-t e) A| = Go +b+t f) JA| = lo-b+t g) |A = Go + lo+b-t %3D %3D

3) In the macroeconomic model below, Y is aggregate output, C is aggregate consump- tion, lo is aggregate investment, Go is government spending, T is the total amount of taxes collected by the government, and t is income tax rate. The variables Y, C, and T are endogenous, Go, lo, and t are exogenous, and a, b, and k are parameters. Y =C+ lo+Go C = a+b(Y - T) T =k+ tY (a > 0,6 € (0, 1)) (k > 0, t e (0, 1)) Calculate the determinant of the coefficient matrix A associated with this system of equations. The determinant of the coefficient matrix A is: a) JA = 1-6+ bt b) JA=1-b- bt +a c) JA =6+t d) JA| =1+a+b-t e) A| = Go +b+t f) JA| = lo-b+t g) |A = Go + lo+b-t %3D %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3) In the macroeconomic model below, Y is aggregate output, C is aggregate consump- tion, lo is aggregate investment, Go is government spending, T is the total amount of taxes collected by the government, and t is income tax rate. The variables Y, C, and T are endogenous, Go, Io, and t are exogenous, and a, b, and k are parameters. Y =C+lo+ Go C =a+b(Y-T) (a > 0,b e (0,1)) (k > 0,t € (0,1)) T =k+tY Calculate the determinant of the coefficient matrix A associated with this system of equations. The determinant of the coefficient matrix A is: a) |4 = 1-6+ bt b) JA| =1-b-bt + a c) JA = 6+t d) JA| = 1+a+b-t e) |A| = Go +b+t f) |A| = lo -b+t g) |A = Go + lo +b-t %3D 4) Use substitution to solve the macroeconomic model in problem 3) above, that is, find the equilibrium (Y,T", C"). Which of the following is true about the equilibrium of this model? a+t+blo+ kGo 1+a+b-t a - bk + Io + Go 1+a+b-t a- bk + b(1- t) (Io + Go) 1+a+b-t a) T = C" = ta +k- bk +t(Io+ Go) T = a- bk +Io+ Go C" 1-6+bt a- bk +b(1-t) (Io+Go) 1-6+ bt b) 1-6+ bt ba - ak - t(lo + Go+t) T 1+t-bt bk + (1+t) (Io-Go-a) C a + bk - Go c) Y = 1-6-bt+a 1-6-6t a- bk + lo+ Go b+t+lo abk + t(lo+ Go) C* lo + Go d) T = b+t+lo e) This model has infinitely many equilibria. f) This model has no equilibrium.
Transcribed Image Text:3) In the macroeconomic model below, Y is aggregate output, C is aggregate consump- tion, lo is aggregate investment, Go is government spending, T is the total amount of taxes collected by the government, and t is income tax rate. The variables Y, C, and T are endogenous, Go, Io, and t are exogenous, and a, b, and k are parameters. Y =C+lo+ Go C =a+b(Y-T) (a > 0,b e (0,1)) (k > 0,t € (0,1)) T =k+tY Calculate the determinant of the coefficient matrix A associated with this system of equations. The determinant of the coefficient matrix A is: a) |4 = 1-6+ bt b) JA| =1-b-bt + a c) JA = 6+t d) JA| = 1+a+b-t e) |A| = Go +b+t f) |A| = lo -b+t g) |A = Go + lo +b-t %3D 4) Use substitution to solve the macroeconomic model in problem 3) above, that is, find the equilibrium (Y,T", C"). Which of the following is true about the equilibrium of this model? a+t+blo+ kGo 1+a+b-t a - bk + Io + Go 1+a+b-t a- bk + b(1- t) (Io + Go) 1+a+b-t a) T = C" = ta +k- bk +t(Io+ Go) T = a- bk +Io+ Go C" 1-6+bt a- bk +b(1-t) (Io+Go) 1-6+ bt b) 1-6+ bt ba - ak - t(lo + Go+t) T 1+t-bt bk + (1+t) (Io-Go-a) C a + bk - Go c) Y = 1-6-bt+a 1-6-6t a- bk + lo+ Go b+t+lo abk + t(lo+ Go) C* lo + Go d) T = b+t+lo e) This model has infinitely many equilibria. f) This model has no equilibrium.
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