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 AD curve is:

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 per cent (π = 0.10). LO 11.5 HARD a)Find output and inflation for this economy in short-run equilibrium and in long-run equilibrium. b)Suppose that, each quarter, inflation adjusts according to the following rule: This quarter’s inflation = last quarter’s inflation − 0.0004 (Y* − Y) Starting from the initial value of 10 per cent for inflation, find the value of inflation for each of the next five quarters. Does inflation come close to its long-run value?