Question

Find (a) the reduced form. (b) the numerical value of 𝑌𝑒 , and (c) the effect on the multiplier if a proportional income tax (t) is incorporated into the model. 𝑌 = 𝐶 + 𝐼, 𝐶 = 𝐶𝑂 + 𝑏𝑌 𝑑 , 𝑇 = 𝑇𝑂 + 𝑡𝑌, 𝑌 𝑑 = 𝑌 − 𝑇 where 𝐼 = 𝐼𝑂 = 30, 𝐶𝑂 = 85, 𝑏 = 0.75, 𝑡 = 0.2, and 𝑇𝑂 = 20

Answer 1

(a) $T=To+tY$

$C=Co+mpc(Y-tY)$

$Y=AE=C+I+G$

$Y=Co+mpc(Y-tY)+I+G$

$Y+mpctY-mpcY=C+I+G$

$Co+MPC(Y-tY)$

$Y=\frac{1}{1-mpc(1-t)}(C+I+G)$

($Y=\frac{1}{1-mpc(1-t)}(C+I)$

(b)$Y=\frac{1}{1-mpc(1-t)}(C+I)$

$Y=\frac{1}{1-0.75(1-0.2)}(85+30)$

$Y=\frac{1}{1-0.75(1-0.2)}(85+30)$

Y=575

(c)$\frac{1}{1-mpc(1-t)}$

the multiplier increases if a proportional income tax is included in the model