Briefly explain each equation and find the equilibrium for

Question

Question 1. In the following model, Π (Π^e) is inflation (expected inflation), u is the rate of unemployment, and m is the rate of growth of the money supply:

Π_t = α - β (u_t) + Π_t^e

ΔΠ_t^e = λ(Π_t-1 - Π_t-1^e)

α, β, δ, λ. are all positive and λ is less than 1

a. Briefly explain each equation.

b. Find the equilibrium for inflation and unemployment.

c. Find the characteristic equation and comment briefly on its properties.

(d) When inflation is high and must be reduced, comment on the implications for policy if this is the appropriate model of the economy.

Question 2. In the following model, m is the log of the money supply, p the log of the price level, y the log of output, and E_t-1x_t is the rational expectation of x, formed with information on period t -1 data:

m_t = p_t + δy_t - α(E_t-1P_t+1 - E_t-1P_t)

y_t = y* + 0.33β[(p_t - E_t-1p_t )] + (p_t - E_t-2p_t) + (p_t - E_t-3P_t)] + λ(y_t-1 - y*)

y* and m are constants; it, an i, i, d error term. All the parameters are positive

(a) Briefly explain each equation.

(b) What are the solutions for output and the price level?

(a) Is monetary feedback policy effective in stabilising output in this model? Briefly explain your answer.

(d) When inflation is high and must be reduced, comment on the implications for policy if this is the appropriate model of the economy; compare your answer with that for Q1(d).