Question

Consider the following structural model,

C_t=a_o+a₁Y_t

I_t=b_o+b₁Y_t+b₂Y_t-1

Y_t=C_t+I_t+G_t

Find the reduced form of the model, Consumption (C) and Income (Y)

Answer 1

$$I_1=Y_1-C_1-G_1$$

$$Y=\frac{b_0-4+a_0+G_1}{1-b_1-b_2-a_1}$$

$$C=a_0+a_1Y$$

$$C=a_0+a_1\frac {b_0+a_0+G_1-4}{1-b_1-b_2-a_1}$$