1. Short-Run Phillips Curve Assume that an economy is governed by the Phillips curve:

π = Eπ - 0.5(u - 0.06),

where π is the inflation rate, Eπ is the expected inflation rate, and the natural rate of unemployment is 6%. Also, note from Okun's law that 1 percentage point of unemployment translates into 2 percentage points of lost output.

Suppose that today, π = 0.05 and Eπ = 0.05. The government wants to lower inflation to 2%.

Assume that people have adaptive expectations.

(a) How much cyclical unemployment does the economy have to experience to have inflation rate of 2%?

(b) What is the sacrifice ratio?

Assume that the government announced its plans to lower inflation before the workers and firms form their expectations. The workers and firms form their expected inflation by the following rule:

Eπ = απ^a + (1 - α)π-1,

where π-1 is the inflation rate in the previous period, πa is the announced inflation, and α ∈ [0, 1] is the weight workers and firms put on the announcement (credibility of the government).

(c) Suppose that households and firms fully trust the government, and thus α = 1. How much cyclical unemployment does the economy have to experience to have inflation rate of 2%?

(d) Suppose α = 0.5. How much cyclical unemployment does the economy have to experience to have inflation rate of 2%? What is the sacrifice ratio?

(e) How does α affect the sacrifice ratio? 

2. Short-Run Phillips Curve How does an adverse supply shock change the short-run tradeoff between inflation and unemployment? Illustrate how Phillips curve shifts with an adverse supply shock.

3. Small Open Economy Consider a small open economy described by the following equations.

Y = C + I + G + NX
Y = 5000
G = 1000
T = 1000
C = 250 + 0.75(Y - T)
I = 1000 - 50r
NX = 500 - 500ε
r = r* = 5

(a) In this economy, solve for national saving, investment, the trade balance, and the equilibrium exchange rate.

(b) Suppose now that G rises to 1250. Solve for national saving, investment, the trade balance, and the equilibrium exchange rate. Explain what you find.

(c) Now suppose that the world interest rate rises from 5 to 10 percent (with G 1000). Solve for national saving, investment, the trade balance, and the equilibrium exchange rate. Explain what you find.