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# 代码代写｜Intermediate macro Assignment #1

### 代码代写｜Intermediate macro Assignment #1

The assignment is marked out of 25 points. The weight for each part is indicated following the question text.

Question 1 — Labor Market Model [8 points]

A model of the labor market. In this question, your task is to understand how the labor market responds to an economic downturn using the model we developed in Lecture 8. Suppose the matching function is given by

M(u, v) = A uv /(uη + vη)1,

where A governs the effiffifficiency of the matching process, u is the unemployment rate and v is the vacancy rate. Here, η is a parameter that governs the elasticity of the matching function. Assume each period in the model corresponds to a month. Parameter values are provided in Table 1.

Separate rate: 0.02 Matching effiffifficiency: A 1.0

Matching elasticity: η 0.5 Vacancy posting cost: 0.5

Match value: 4

Table 1: Parameter values for labor market model

(1) Using the parameter values in Table 1, calculate the steady-state values of labor market tightness θ, unemployment rate u and vacancy rate v. (2 points)

(2) Suppose the economy is initially in steady state (t = 0). At t = 1, a recession causes the value of fifilled jobs J to decrease to J = 2 for 15 months. Starting from the steady state, use the other parameter values in Table 1 and a spreadsheet/script to calculate and plot the time paths of market tightness, unemployment rate and vacancy rate for 15 months (t = 0, 1, …, 15) after the economy was hit by the recession. Describe how market tightness, unemployment rate and vacancy rate respond to the decrease in J. Has the economy settled to a new equilibrium by the end of 15 months? Explain your fifindings. (2 points)

(3) Some economists believe that the matching process becomes less effiffifficient in recessions, as indicated by the shifting out of the Beveridge curve. Suppose the economy is initially in steady state. At t = 1, a recession causes the matching effiffifficiency parameter A to decrease to A = 0.5 for 15 months. Starting from the steady state, use the other parameter values in Table 1 and a spreadsheet/script to calculate and plot the time paths of market tightness, unemployment rate and vacancy rate for 15 months (t = 0, 1, …, 15) after the economy was hit by the recession.

Describe how market tightness, unemployment rate and vacancy rate respond to the decrease in A. Has the economy settled to a new equilibrium by the end of 15 months? Explain your fifindings. (2 points)

(4) Recessions are associated with mass layoffffs, as indicated by a countercyclical job separation rate. Suppose the economy is initially in steady state. At t = 1, a recession causes separation rate s to increase to s = 0.04 for 15 months. Starting from the steady state, use the other parameter values in Table 1 and a spreadsheet/script to calculate and plot the time paths of market tightness, unemployment rate and vacancy rate for 15 months (t = 0, 1, …, 15) after the economy was hit by the recession. Describe how market tightness, unemployment rate and vacancy rate respond to the increase in s. Has the economy settled to a new equilibrium by the end of 15 months? Explain your fifindings. (2 points)

Question 2 — DAS-DAD Model [16 points]

Dynamic AS-AD model. The recession caused by the COVID-19 pandemic has reduced demand for Australian goods. Your task is to understand how this adverse aggregate demand shock affffects the Australian economy and the use of monetary policy in stabilizing the economy. You will use the Dynamic Aggregate Supply-Aggregate Demand model (developed in Lectures 10, 11 and 12) in your analysis.

For simplicity, suppose the natural level of output is constant. Each period in the model corresponds to a year. Interest rate and inflflation are expressed in percentage points. The parameter values of the model are provided in Table 2.

50 φ 0.60

π∗  2 θπ  1

ρ  2 θ0.30

α 1

Table 2: DAS-DAD model – Benchmark Parameter Values

(1) Using the parameter values in Table 2, calculate the long-run equilibrium values of inflflation,output, and the nominal and real interest rates. (1 point)

(2) Suppose the economy was initially in its long-run equilibrium. At year t = 1 the economy was hit by a persistent adverse aggregate demand shock (captured by ε < 0) that lasts for four years and then reverts to zero. In particular, the adverse aggregate demand shock takes the value εt = 2 for four years (t = 1, 2, 3, 4) before reverting back to zero at t = 5. Starting from the long-run equilibrium at t = 0, use the parameter values in Table 2 to calculate the magnitudes of the impact effffects at t = 1 on inflflation, output, nominal and real interest rates. Also explain how you can recover the values of inflflation, output, nominal and real interest rates from t = 2 onward. (3 points)

(3) Now use a spreadsheet/script to calculate and plot the time paths of inflflation, output, nominal and real interest rates for 50 years after the initial shock (t = 0, 1, … , 50). Describe inflflation,output, nominal and real interest rate dynamics associated with this adverse aggregate demand shock. Explain how monetary policy responds to the inflflation and output gaps. (3 points)

(4) Suppose the RBA decides to respond more aggressively to output gap by setting θπ = 0.3 and θY = 1. Keeping all other parameters as in Table 2, recompute the time paths of output, inflflation, nominal and real interest rates for 50 years after the initial shock (t = 0, 1, … , 50).

Explain how the policy change affffects the time paths of inflflation, output, nominal and real interest rate. Is there a policy tradeoffff between inflflation and output? Explain. (3 points)

For the remainder of this question consider the implications of a modifified version of the dynamic AS-AD model, where people’s inflflation expectations may be subject to random shocks.