Economics 576

Macroeconomic Theory & Policy

Model & Multiplier Summary

Model I Two Sector

Y = C + I No Government

C = C_o + C₁Y No Taxes No Foreign Trade

I = I_o Autonomous Investment

Ye = 1 (C_o + I_o)

1 - C₁

dY ₌ 1___

dI 1 - C₁

Model II Three Sector

Y = C + I + G No Foreign Trade

C = C_o + C₁Y_d Autonomous Investment

Y_d = Y - T_x No Tax Function (Flat Dollar Tax)

I = I_o

G = G_o

T_x = Tx_o

Ye = 1 (C_o - C₁Tx + I_o + G_o)

1 - C₁

d Y = 1 d Y = 1 d Y = -C₁

d I 1-C₁ d G 1-C₁ d T_x 1-C₁

Model III Four Sector

Y = C + I + G + X - M Autonomous Investment

C = C_o + C₁Y_d No Tax Function

Y_d = Y - T_x

I = I_o

G = G_o

Tx = Tx_o

X = X_o

M = M_o + M₁Y

Note M₁ = MPM = d M

d Y

Ye = 1 (C_o - C₁T_x + I_o + G_o + X_o - M_o)

1-C₁+M₁

d Y = d Y = d Y = 1___

d I d G d X 1-C₁+M₁

d Y = -C₁___{__}

d Tx 1-C₁+M₁

Model IV Three Sector

Y = C + I + G No Foreign Trade

C = C_o + C₁Y_d Investment Function

Y_d = Y - T_x Flat Dollar Tax

I = I_o + I₁Y

I₁ = MPI = d I

d Y

G = G_o

Tx = Tx_o

Ye = 1 (C_o - C₁T_x + I_o + G_o)

1-C₁-I₁

d Y = 1_____

d I_o 1 - C₁ - I₁

d Y = 1___

d G 1-C₁-I₁

d Y = -C₁__

d T_x 1-C₁-I₁

Model V Three Sector

Y = C + I + G No Foreign Trade

C = C₀ + C₁Y_d No Investment Function

Y_d = Y - T_x Tax Function

I = I_o

G = G_o

T_x = T_o + T₁Y

T₁ = d Tx = MPTx

d Y

Ye = 1 _ (C_o - C₁T_o + I_o + G_o)

1-C₁+C₁T₁

d Y ₌ 1___

d I 1-C₁+C₁T₁

d Y = ____1___

d G 1-C₁+C₁T₁

d Y ₌ -C₁____{______}

d T_o 1-C₁+C₁T₁

Model VI Three Sector Model

Y = C + I + G Tax Function

C = C_o + C₁Y_d Investment Function

I = I_o + I₁Y

G = G_o

T_x = T_o + T₁Y

Ye = 1 __ (C_o - C₁T_o + I_o + G_o)

1-C₁+C₁T₁-I₁

d Y = ?

d I_o

d Y = ?

d G

d Y = ?

d T_o

Model VII Four Sector - Full

Y = C + I + G + X - M

C = C_o + C₁Y_d

I = I_o + I₁Y

G = G_o

X = X_o

M = M_o + M₁Y

T_x = T_o + T₁Y

Ye = 1______ (C_o - C₁T_o + I_o + G_o + X_o - M_o)

1-C₁+C₁T₁I₁+M₁

d Y = ?

d G

d Y = ?

d T_o