Consider an economy in a long-run equilibrium with Y = 40 and ? = 3. A demand shock in period one causes output to rise to 45 and inflation rises to 4

Then, the updating of expected inflation to equal 4 causes output in period two to decline to 43.85, and inflation to rise to 4.77. Assuming no further shocks, calculate the values of output and inflation for period three.

Moving from period one to period two, the change in expected inflation is 1, which causes output to decline by 1.15. Since the next change in expected inflation is 0.77, the resulting change in output will be 0.77 × 1.15 = 0.89, so output in period three is 42.96. Output is falling as the short-run aggregate supply curve shifts along the aggregate demand curve. Moving from period one to period two, a change in inflation of 0.77 caused output to decline by 1.15. Thus, a further output decline of 0.89 implies that inflation has increased by 0.89 × 0.77 ÷ 1.15 = 0.596. Inflation in period three is 5.36.