Hello, im looking for help on a particular question..

Samuelson Multiplier-Accelerator Interaction Model: Let y_t, c_t, and I_t denote income, consumption and investment at time t respectively. Suppose that investment, It, and consumption, c_t, are characterized by following equations

I_t = (c_t c_t1), 0 < < 1 &

c_t = by_t1, 0 < < 1. is known as accelerator or acceleration coecient. National account identity is

y_t = c_t + I_t + G where G is constant government expenditure.

(a.) What is the interpretation of b?

(b.) Convert the system of equations in the second order dierence equation in income, y_t.

(c.) Derive characteristic roots.

(d.) Derive the steady state solution.

(e.) Is the steady-state stable? Distinguish among dierent types of characteristic roots.