this model

In this model, the redundant equation is hs = hh. We make the assumption that the central bank fixes the interest rate rt = 0.03 and the government spends gt = 50 at all periods. Assumptions = 0.2, 1 = 0.6, 2 = 0.4, 0 = 0.635, 1 = 5 and 2 = 0.01. 2a) In a steady state, what is the level of GDP yt and consumption ct? What is the debt-to-GDP? 2b) In a steady state, what is the total amount of interest paid by the government? What is the amount interest paid to the household sector by the government? 2c) Define the Governments effective interest rate as the ratio of interest charges paid to households by the government on the governments TOTAL debt. Calculate the effective interest rate of the government. Is it higher or lower than the interest rate determined by the central bank? 2d) Find now the level of GDP, consumption and debt-to-GDP ratio by assuming that 1 = 0.8 and 2 = 0.2. Is your answer different from that found in 2a)? For the rest of the question, assume that 1 = 10 rt 1. 2 2e) Let us assume initially that 10 = 0.75 and = 5 and that 2 = 0.4. What is the value of 1 in the state stationary?

(9) (10) (11) (12) (13) (14) bd.t Yt = (t + gt ydt = yt +rt-ibh.t-1 - tt tt = (Yt + Tt-1bh,t-1) Vt = 0+-1 + yd: - Ct = Q1. ydy + 02.0t-1 hn,t = V- but yde E do +1.1t - 12 ve vi v = vt-1+ ydi bn,t = bd.t bs,t = bs,t-1 + (9+ + rt-1bs,t-1) (t+ + rt-1bcb,t-1) hs,t = hs,t-1 + bcb,t - bcb.t-1 bcb,t = bs,t - bd,t yd = ydt-1 (15) - CE (16) (17) (18) (19) (20) (21) = (9) (10) (11) (12) (13) (14) bd.t Yt = (t + gt ydt = yt +rt-ibh.t-1 - tt tt = (Yt + Tt-1bh,t-1) Vt = 0+-1 + yd: - Ct = Q1. ydy + 02.0t-1 hn,t = V- but yde E do +1.1t - 12 ve vi v = vt-1+ ydi bn,t = bd.t bs,t = bs,t-1 + (9+ + rt-1bs,t-1) (t+ + rt-1bcb,t-1) hs,t = hs,t-1 + bcb,t - bcb.t-1 bcb,t = bs,t - bd,t yd = ydt-1 (15) - CE (16) (17) (18) (19) (20) (21) =