Question

6) In the macroeconomic model below, Y is aggregate output, C is aggregate consump- tion, I. 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 en- dogenous, Go, Io, and t are exogenous, and a, b, and k are parameters. Express this system of equations in a matrix form, clearly writing out and labeling each of the matrices. Y = C + Io + Go C = a + b(Y – T) (a > 0,5 € (0, 1)) T = k + tY (k > 0,5 € (0,1))

Answer 1

Y = Y-C c + = Io + Go Io + Go c = a + bey-T) c = a + by- bT c+bT-by = a -by te + b = a T = ktty T-tY = K. - ty t T = k from equ. lis, in 8 ciiis Y-c = Iot - by+c+bT = - ty + 7 = Go a x The matrix formulation can be written as of above equations. Io + Go ь - р I-t т o с IT K where the variabler Y, C, I are endogenous.