macro economics homework. ( do not message me if you do not know about econ)

Instructions:

Answer ALL of the following questions.

1. Consider the labor market represented by the wage-setting (WS) and price-setting (PS) relations. Answer the following four questions:

a. Discuss how changes in real wages and employment can be understood according to collective bargaining theories and efficiency wage theories. (7 points)

b. Derive the WS equation; and discuss the main assumptions used to derive it. (6 points)

c. Derive the PS equation; and discuss the main assumptions used to derive it. (6 points)

d. Derive the general representation of the equilibrium in the labor market according to the WS and PS equations; and represent graphically the latter. (6 points)

2. Consider a linear representation of the WS equation, 𝑊𝑡 = 𝑃𝐸[𝐵 + 𝛼(𝑦𝑡 − 𝑦𝑒) + 𝑧𝑤], where 𝑊𝑡 denotes nominal wages, 𝑃𝐸 is the expected price level, 𝐵 is a constant that incorporates any unemployment benefits and the disutility of work, 𝛼 is a sensitivity parameter, 𝑦𝑡 is the equilibrium level of output in the short-run, 𝑦𝑒 is the equilibrium level of output in the medium run, and 𝑧𝑤 is and exogenous catch-all variable that contains wage-push variables. Assume that 𝑃𝐸 = 𝑃𝑡−1. Answer the following four questions:

a. Derive the following representation of the Phillips curve: 𝜋𝑡 = 𝜋𝑡−1 + 𝛼(𝑦𝑡 − 𝑦𝑒), where 𝜋𝑡 is the inflation rate; and discuss the main assumptions used to derive it. (7 points)

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b. Given your answer to (2a), what happens to the change in the inflation rate, 𝜋𝑡 −

𝜋𝑡−1, when 𝑦𝑡 = 𝑦𝑒 ? What does this mean? (6 points)

c. Given your answer to (2a), what happens to the change in the inflation rate, 𝜋𝑡 −

𝜋𝑡−1, when 𝑦𝑡 > 𝑦𝑒 ? What does this mean? (6 points)

d. Given your answer to (2a), what happens to the change in the inflation rate, 𝜋𝑡 −

𝜋𝑡−1, when 𝑦𝑡 < 𝑦𝑒 ? What does this mean? (6 points)

3. Answer the following two questions:

a. Discuss the main assumptions and principles of the inflation targeting monetary policy regime. (8 points)

b. Consider the following Central Bank (CB)’s loss function: 𝐿𝑡 = (𝑦𝑡 − 𝑦𝑒 )2 +

𝛽(𝜋𝑡 − 𝜋𝑇)2, where, in addition to the variables previously defined in (2), 𝜋𝑇 is the inflation target and 𝛽 is a sensitivity parameter. Answer the following two questions:

i. Assume that 𝛽 = 1, 𝛽 > 1 and 𝛽 < 1. Discuss the implications for the CB’s loss function for each value of 𝛽; and represent graphically the respective loss functions. (8 points)

ii. Derive the Monetary Rule for an inflation targeting CB: 𝑦𝑡 − 𝑦𝑒 =

−𝛼𝛽(𝜋𝑡 − 𝜋𝑇); and discuss the main assumptions used to derive it. (9 points)

4. Consider the three-equation model, depicted by a Dynamic 𝐼𝑆 curve; a Phillips curve (under the assumption of adaptive expectations); and the Monetary Rule derived in (3bii). For each of the following shocks, discuss the respective propagation mechanisms and the response of the CB. Also, represent graphically the changes in the economy.

a. A positive temporary aggregate demand shock. (6 points)

b. A positive permanent aggregate demand shock. (6 points)

c. A negative permanent aggregate demand shock that leads the economy to a deflation trap. (7 points)

d. A positive aggregate supply shock. (6 points)