4. This problem asks you to trace out the adjustment of inflation when the economy starts with an output gap. Suppose that the economy’s aggregate demand curve is Y = 1,000 − 1,000π, where Y is short-run equilibrium output and π is the inflation rate, measured as a decimal. Potential output Y* equals 950, and the initial inflation rate is 10 percent (π = 0.10). (LO2) a. Find output for this economy in short-run equilibrium and inflation in long-run equilibrium.

b. Suppose that, each quarter, inflation adjusts according to the following rule: This quarter’s Last quarter’s  inflation =  inflation − 0.0004(Y* − Y). Starting from the initial value of 10 percent for inflation, find the value of inflation for each of the next five quarters. Remember, Y will continuously change as the current inflation rate change according to the given relationship Y = 1,000 − 1,000π. Does inflation come close to its long-run value