Consider a closed-economy aggregate expenditure model with the following function:

C_t= c₀+ c₁Y_D,t-1,

Y_D,t= Y_t- T_t,

I_t= I,

Z_t= C_t+ G_t+ I_t.

Equilibrium is given by Y_t= Z_t.

The parameters, c₀, I, and c₁, do not change over time; c₀= 200, I = 100, c₁= 0.5.

(a) Suppose G_t= T_t= 100, for all t < 10. Find the steady state (where all variables are time independent) level of output associated with these parameter values. Assume that the economy is at this steady state, for t < 10.

(b) At t = 10, suppose government spending increases to G_t= 108, and remains at this level forever. There is no change in taxation. Find the steady state output associated with this new level of government spending. Calculate the (equilibrium) values for Y_t, for t = 10, 11, 12, 13 (given that G_t= 100, for all t < 10).