Barro-Gordon model

1. The output in an economy follows the following expectationsaugmented Phillips curve: yt=+(7rt7r), where longrun level of output is equal to 0.2, Le, 37 = 0.2. Policy makers want to minimize the following loss function: 1 L: = i [4 (7T: 77*)2 + (y: 31*)2] a where \"I\" is the targeted level of ination and 71'\" = 0, and y* is the targeted level of output and y\" = 237. (a) Graphically draw the expectations-augmented Phillips curve when the expected rate of ination is equal to 0 (7r: = 0). (1)) Calculate the optimal rate of ination and the resulting output and loss when 7r? = 0. Compare these results with the option of maintaining ination equal to 0. (c) If the private sector has rational expectations and therefore adjusts ination ex- pectations to be equal to the rate set by policy makers, calculate the rate of ination, output, and the loss to society when policy makers set an optimal pol icy rule versus when they commit to zero ination