Suppose the Multiplier Model Is

Essay

Suppose the multiplier model is
C = C₀ + cY_D
I = I₀
G = G₀
Y_D = Y + TR - tY
TR = TR₀
Y = C + I + G
where C₀ is autonomous consumption,c is the marginal propensity to expend,Y is income,C is consumption,Y_D is disposable income,I is investment,G is government expenditures,TR is transfer payments,and t is the income tax rate.Furthermore,C₀,I₀,G₀ and TR₀ are positive numbers and 0 < c < 1.In this version of the multiplier model,consumption spending is a function of disposable income (Y_D).Disposable income is defined as national income (Y)plus transfer payments (TR)and minus tax payments (tY).The tax rate is a constant,t,such that 0 < t < 1.Transfer payments are items like social security,Medicare,and welfare payments,and people who receive these payments can spend them like earned income.
(a)Derive the formula for equilibrium national income.
(b)Derive the multiplier for an increase in transfer payments from TR₀ to TR_1.