Question

Consider the following extended classical economy (in which the misperceptions theory holds): AD Y=300+10(M/P) SRAS Y=Y+P-pe Full-employment output Y = 500 Natural unemployment rate u=0.06 a. Suppose that the money supply M = 1000 and that the expected price level Pe= 50. What are the short-run equilibrium values of output Y and the price level P? What are the long-run equilibrium values of these two variables? b. Now suppose that an unanticipated increase raises the nominal money supply to M = 1260. What are the new short-run equilibrium values of output Y and the price level P? What are the new long-run equilibrium values of these two variables? In gen- eral, are your results consistent with an expecta- tions-augmented Phillips curve?

Answer 1

a. Short-run equilibrium values of output Y and the price level P:To calculate the short-run equilibrium values of output Y and the price level P, first we have to calculate the value of M/P. Then the given AD and SRAS curves will be equated to find the value of Y and P.M/P = 1000/50 = 20AD Y = 300 + 10(M/P) = 300 + 10(20) = 500SRAS Y = Y + P - Pe = 500 + P - 50 = 450 + PEquating the two above expressions, we get:500 = 450 + P ⇒ P = 50Therefore, the short-run equilibrium values of output Y and the price level P are Y = 500 and P = 50.Long-run equilibrium values of output Y and the price level P:In the long-run, the economy moves towards the natural rate of unemployment and the full employment output. So, the natural rate of unemployment is given by u = 0.06.The full-employment output, Yf can be calculated as:Yf = 1/ (1-u) * Y = 1/ (1-0.06) * 500 = 532.56 (approx)So, the long-run equilibrium values of output Y and the price level P are Y = 532.56 and P = 50.b. Short-run equilibrium values of output Y and the price level P:Now, the money supply has increased to M = 1260. So, M/P = 1260/50 = 25AD Y = 300 + 10(M/P) = 300 + 10(25) = 550SRAS Y = Y + P - Pe = 500 + P - 50 = 450 + PEquating the two above expressions, we get:550 = 450 + P ⇒ P = 100Therefore, the short-run equilibrium values of output Y and the price level P are Y = 550 and P = 100.Long-run equilibrium values of output Y and the price level P:In the long-run, the economy moves towards the natural rate of unemployment and the full employment output. So, the natural rate of unemployment is given by u = 0.06.The full-employment output, Yf can be calculated as:Yf = 1/ (1-u) * Y = 1/ (1-0.06) * 500 = 532.56 (approx)The new expected price level will also rise due to the increase in money supply. We can calculate the new expected price level Pe as follows:Pe = Pe + α(P-Pe)Where α is the degree of adjustment and is equal to 0.1. So,Pe = 50 + 0.1(100-50) = 55Therefore, the long-run equilibrium values of output Y and the price level P are Y = 532.56 and P = 55.The result is not consistent with an expectations-augmented Phillips curve, because the Phillips curve predicts that there is a negative relationship between unemployment and inflation. But here, we see that when the money supply increases, both output and price level increase in the short-run, which is opposite to what Phillips curve predicts.