Find

(a) the reduced form,

(b) the numerical value of Ye, and

(c) the effect on the multiplier when a lump-sum tax is added to the model and consumption becomes a function of disposable income (Yd), given

where C0 = 100, b = 0.6, I0 = 40, and T = 50.

(a)

Or substituting in (4.51),

(c) As seen in part (a), incorporation of a lump-sum tax into the model does not change the value of the multiplier. It remains 1/(1 – b). Only the aggregate value of the exogenous variables is changed by an amount equal to −bT. Incorporation of other autonomous variables such as G0, X0, or Z0 will not affect the value of the multiplier.

Transcribed Image Text:

Y = C +1 C = Co+bYd I = Ya=Y-T