Consider the model of Kydland and Prescott studying the dynamic inconsistency of low inflation monetary policy. The aggregate supply of the economy is given by y = y + b( e ), b > 0, y = ln Y, y = ln Y , where Y is output and Y is its flexible-price level. The inflation rate of the economy is , and the inflation expectation of the public is e . The policymaker of the economy chooses the inflation rate, , to minimize the social welfare loss, L, caused by output gap and inflation. L = 1 2 (y y ) 2 + 1 2 a( ) 2 , a > 0, y = ln Y . The social optimal level of output, Y , is assumed to be higher than Y , that is, y > y. In addition, inflation is assumed to be costly if it is different from the level .

1. Determine the equilibrium levels of output and inflation if the policymaker can follow a monetary rule (making a binding commitment about what inflation will be before expected inflation is determined)