Question

Consider the following dynamic IS-LM model:

E_t = C_t + I_t (Total expenditure)

C_t = C₀ + cY_t, C₀ > 0, 0 < c < 1 (Consumption function)

I_t = I₀ − δ_it, I₀> 0, δ > 0 (Investment)

L_t = kY_t − hi_t, h, k > 0 (Money demand)

M_t = ￣M (Money supply) (￣M) is M bar.

where i_t represents the nominal interest rate at time t.

The output and the interest rate adjust following ways:

ΔY_t = α(E_t − Y_t), α > 0

Δi_t = β(L_t −M_t), β > 0

a. Drive the system of difference equations in terms of Y_t and i_t.

b. Find a steady state, and draw the phase diagram.

c. Suppose that initial level of money supply is given by ￣M = M₀. Now central bank increases money supply to M₁. Explain the dynamic and steady state effects of monetary expansion on output and interest rate.

Answer 1

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