Exercise 1) Truth or false. Explain your answer.

A) Tobin's q-theory for the housing market says that investors will choose to build new houses if and only if the housing prices in the next period are expected to exceed the housing prices for this period.

B) The expectations hypothesis "adaptive changes" states that economic operators will create the expectation x_t^e for an economic size x_t in period t, as a weighted average of the last to observed values of the same size. Accordingly x_t^e = ∅x_(t-1) + (1-Ø)x_(t-2), where Ø is a parameter 0 < Ø < 1.

Exercise 2) Monetary and fiscal policy in a closed economy

π_t^e describes economic operators expectations for inflation in period t-1 until t. π_(t+1)^e describes economic operators as well as the central banks expectations to inflation in period t until period t+1.

The four equations of the economy:

y_t - y ¯= v_t + α₁(g_t - g ¯ ) - α₂(r_t - r ¯) (IS)

r_t = i_t - π_(t+1)^e (RR)

i_t = r ¯+π_(t+1)^e + h(π_t - π^*) + b (y_t - y ¯) (MP)

π_t = π_t^e + μ(y_t - y ¯) (AS)

y_t, r_t, i_t, π_t are all endogenous variables.

α₁, α₂, h, b and μ are all strict positive parameters.

y ¯, g ¯, r ¯ and π^*are all exogenous variables.

1) Show that π_(t+1)^e can be eliminated from the two equations (RR) and (MP) which then means: r_t = r ¯+ h(π_t -π^*) + b(y_t - y ¯) (MP')

2) Show that (IS) and (MP') implies the AD curve:

y_t - y ¯ = z_t - a(π_t - π^*) (AD)

Where z_t = (v_t + α₁ (g_{t-g ¯}))/(1+α₂ b) and a=(α₂h)/(1+α₂b) > 0 (1)

Briefly explain this.

3) Show that (AS) and (AD) for a given expectation π_t^e implies

y_t = y ¯+(z_t-a(π_t^e-π^*))/(1+aμ) (2)

π_t = π^*+ (π_t^e - π^* + μz_t)/(1+aμ) (3)

4) In the following the reduced system will be consisting of (AS) and (AD) and it is a long run equilibrium in period 0, where y₀ = y ¯, π₀ = π^*, g₀ = g ¯ and v₀ = z₀ = 0.

Illustrate AD and AS in the long run equilibrium in period 0 with y_t at x-axis and π_t at the y-axis.

5) In the following a temporary shock hits the fiscal policy, where public spendings raises to g₁ > g ¯ in period 1. Afterwards g_t returns to the long run level g ¯ from period 2 and onwards.

Expectations are static at: x_t^e = π_(t-1) (SE)

The model then consists of (AS), (AD), (SE) and x_t^e is an endogenous variable for each period t.

Explain why x_t^e = π^*. Explain and illustrate the effects of the shock to the fiscal policy only for period 1. Describe and explain what the parameters h & b means to these effect.

6) Illustrate (in a diagram with y_t at x-axis and π_t at the y-axis) how things will change for the forthcoming periods 2, 3, ... and so on.

7) Now the same fiscal policy shock are considered under a different market assumption, where private operators have confidence in the central banks inflations goals π_t^e = π^* (WRE)

The model now consists of (AS), (AD), (WRE), x_t^e is an endogenous variable for each period t.

From equations (2) and (3) show the stochastic processes for y_t and π_t under WRE. Explain and illustrate for period 1 and the following periods. Compare the results from questions 5 and 6, and explain the differences.

8) For the remaining three exercises a negative demand shock (v_t < 0) have created so negative output and inflation gaps that the nominal interest rate in accordance with (MP) have declined past it's lower limit (which would be expected to be 0). The economy is in a liquidity trap and (MP) is replaced with i_t = 0 (MP')

In the first fase the economy will still have the current wage contract, from before the negative shock hit the economy. Therefore expected inflation until the considered period t is x_t^e =π^*. For the forthcoming expected inflation x_(t+1)^e stochastic expectations will be assumed again.

x_(t+1)^e = π_t (SE)

Show that with these assumptions the model will be reduced to

y_t - y ¯= v_t + α₁ (g_t - g ¯ ) - α₂ (-π_t - r ¯) (AD')

π_t = π^*+ μ(y_t - y ¯ ) + s_t (AS')

9) It is assumed that 1/α₂ > μ

Illustrate and explain the effects of expansive fiscal policy g_t > g ¯ in a period t where the model consists of AD' and AS'. Remember that a negative shock has hit output and inflation below the long run limits.

10) Now assume that expected inflation will no longer be at π_t^e = π^* but rather x_t^e = π_(t-1) (Therefore π^*in AS' is replaced by π_(t-1). Illustrate what this means over time for the economy, and comment on the result.

Attachment:- Assignment File.rar