Questions
SP25 ECON 312 001 Homework #7 (Introduction to the Short Run)
Numerical
Suppose the economy is currently producing at potential and the actual output is $22 trillion. The inflation rate is 4.5%. The slope of the Phillips curve is 1 2 . In response to a macroeconomic shock that does not affect actual output but raises potential output from $22 trillion to $22.5 trillion, you know that based on the Phillips Curve the inflation rate in the economy will change to ________ percent. Recall that πt=πt−1+Δπt. Round your answer to the nearest tenth of a percent.
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Step-by-Step Analysis
Opening thought: the problem mixes a Phillips-curve relationship with a shift in potential output and a stable actual output, so the key is to track the output gap and apply the given slope.
Option exploration (no choices to pick from yet): we know the economy starts at Y = 22 trillion with inflation π = 4.5%. The slope of the Phillips curve is given as 1/2, which typically means a one-period change in inflation (Δπ) is half a percentage point per unit of output gap (depending on units), or alternatively Δπ = α (Y − Yp) with α = 0.5 if......Login to view full explanationLog in for full answers
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An open economy is fully characterized by the following IS curve, monetary policy rule, and Phillips curve: IS: 𝑌 ~ 𝑡 = 𝑎 ¯ − ( 𝑏 ¯ 𝑖 + 𝑏 ¯ 𝑛 𝑥 ) ( 𝑅 𝑡 − 𝑟 ¯ ) + 𝑏 ¯ 𝑛 𝑥 ( 𝑅 𝑡 ∗ − 𝑟 ¯ ) , where 𝑅 𝑡 ∗ is the real interest abroad, 𝑎 ¯ = 𝑎 ¯ 𝑐 + 𝑎 ¯ 𝑖 + 𝑎 ¯ 𝑔 + 𝑎 ¯ 𝑛 𝑥 − 1 , and 𝑎 ¯ 𝑛 𝑥 = 𝑎 ¯ 𝑒 𝑥 − 𝑎 ¯ 𝑖 𝑚 . Monetary policy rule: 𝑅 𝑡 − 𝑟 ¯ = 𝑚 ¯ ( 𝜋 𝑡 − 𝜋 ¯ ) Phillips curve: 𝜋 𝑡 = 𝜋 𝑡 − 1 + 𝑣 ¯ 𝑌 ~ 𝑡 + 𝑜 ¯ 𝑡 Assume that 𝑎 ¯ = 0 , 𝑎 ¯ 𝑛 𝑥 = 0 , 𝑏 ¯ 𝑖 = 𝑏 ¯ 𝑛 𝑥 = 0.2 , 𝑣 ¯ = 0.5 , 𝑅 𝑡 ∗ = 0.04 , 𝑟 ¯ = 0.03 , 𝜋 𝑡 − 1 = 𝜋 ¯ = 0.02 , 𝑚 ¯ = 1 , and 𝑜 ¯ 𝑡 = 0.025 . Calculate 𝜋 𝑡 = ______ percent. Round your answer to the nearest tenth of a percent. Note: Calculate your answers for this one and the next three questions in a spreadsheet application. Enter rounded numbers in the answer box for each question. Do not, however, round your intermediate answers in the spreadsheet.
An open economy is fully characterized by the following IS curve, monetary policy rule, and Phillips curve: IS: 𝑌 ~ 𝑡 = 𝑎 ¯ − ( 𝑏 ¯ 𝑖 + 𝑏 ¯ 𝑛 𝑥 ) ( 𝑅 𝑡 − 𝑟 ¯ ) + 𝑏 ¯ 𝑛 𝑥 ( 𝑅 𝑡 ∗ − 𝑟 ¯ ) , where 𝑅 𝑡 ∗ is the real interest abroad, 𝑎 ¯ = 𝑎 ¯ 𝑐 + 𝑎 ¯ 𝑖 + 𝑎 ¯ 𝑔 + 𝑎 ¯ 𝑛 𝑥 − 1 , and 𝑎 ¯ 𝑛 𝑥 = 𝑎 ¯ 𝑒 𝑥 − 𝑎 ¯ 𝑖 𝑚 . Monetary policy rule: 𝑅 𝑡 − 𝑟 ¯ = 𝑚 ¯ ( 𝜋 𝑡 − 𝜋 ¯ ) Phillips curve: 𝜋 𝑡 = 𝜋 𝑡 − 1 + 𝑣 ¯ 𝑌 ~ 𝑡 + 𝑜 ¯ 𝑡 Assume that 𝑎 ¯ = 0 , 𝑎 ¯ 𝑛 𝑥 = 0 , 𝑏 ¯ 𝑖 = 𝑏 ¯ 𝑛 𝑥 = 0.2 , 𝑣 ¯ = 0.5 , 𝑅 𝑡 ∗ = 0.04 , 𝑟 ¯ = 0.03 , 𝜋 𝑡 − 1 = 𝜋 ¯ = 0.02 , 𝑚 ¯ = 1 , and 𝑜 ¯ 𝑡 = 0.045 . Calculate 𝜋 𝑡 = ______ percent. Round your answer to the nearest tenth of a percent. Note: Calculate your answers for this one and the next three questions in a spreadsheet application. Enter rounded numbers in the answer box for each question. Do not, however, round your intermediate answers in the spreadsheet.
Suppose the Federal Reserve decreases interest rates from 4% to 3%, which shifts aggregate demand and increases short-run output to 5.0%. If there are no other shocks to the economy, and the resulting change in inflation is 2.0 percentage points, what is the value of the parameter 𝜈 ¯ ? Round your answer to the nearest tenth.
Suppose the Federal Reserve decreases interest rates from 4% to 3%, which shifts aggregate demand and increases short-run output to 3.0%. If there are no other shocks to the economy, and the resulting change in inflation is 1.5 percentage point, what is the value of the parameter 𝜈 ¯ ? Round your answer to the nearest tenth.
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