Question

in the macroeconomics model below matrix

In the macroeconomic model below, Y is aggregate output, C is aggregate consump- tion, Io 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, lo, and t are exogenous, and a, b, and k are parameters. Express this system of equations in a matrix form, clearly wrting out and labeling each of the matrices. Y=C+10 + Go C-bY-T) (a >0,b e (0,1)) Use substitution to solve the macroeconomic model in problem above, that is, find the equilibrium (Y*,TC)

Answer 1

C = a + b[Y - (k + tY)]

C = a + b[Y - k - tY]

C = a + bY - bk - btY

C = (a - bk) + [b x (1 - t)] x Y

In equilibrium, Y = C + I0 + G0

Y = (a - bk) + [b x (1 - t)] x Y + I0 + G0

[1 - {b x (1 - t)}] x Y = a - bk + I0 + G0

Y* = (a - bk + I0 + G0) / [1 - {b x (1 - t)}]

T* = k + tY = k + [t x (a - bk + I0 + G0)] / [1 - {b x (1 - t)}]

C* = (a - bk) + [b x (1 - t)] x (a - bk + I0 + G0) / [1 - {b x (1 - t)}]