1. Short-Run Phillips Curve Assume that an economy is governed by the Phillips curve: 71' = E7r â€” 0.5(u â€” 0.06), where 71' is the inï¬‚ation rate, E7r is the expected inï¬‚ation rate, and the natural rate of unemployment is 6%. Also, note from Okunâ€™s law that 1 percentage point of unemployment translates into 2 percentage points of lost output. Suppose that today, 71' = 0.05 and E7r = 0.05. The government wants to lower inï¬‚ation to 2%. Assume that people have adaptive expectations. (a) How much cyclical unemployment does the economy have to experience to have inï¬‚ation rate of 2%? (b) What is the sacriï¬ce ratio? Assume that the government announced its plans to lower inï¬‚ation before the workers and ï¬rms form their expectations. The workers and ï¬rms form their expected inï¬‚ation by the following rule: E7r = 0471'â€œ + (1 â€” a)7r_1, where 7T_1 is the inï¬‚ation rate in the previous period, 71'â€œ is the announced inï¬‚ation, and a E [0, 1] is the weight workers and ï¬rms put on the announcement (credibility of the government). (c) Suppose that households and ï¬rms fully trust the government, and thus a = 1. How much cyclical unemployment does the economy have to experience to have inï¬‚ation rate of 2%? (d) Suppose a = 0.5. How much cyclical unemployment does the economy have to experiâ€” ence to have inï¬‚ation rate of 2%? What is the sacriï¬ce ratio? (e) How does or affect the sacriï¬ce ratio?
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