2. (A Twist on Barro-Gordon) Suppose that an economy is described by the following equations: y = b(x - T' ) +u L= (y - y)? + a(m - ?' )?

For intermediate macroeconomics, please help with all parts, thank you!

2. (A Twist on Barro-Gordon) Suppose that an economy is described by the following equations:y = b(x - T' ) +uL= (y - y")? + a(m - ?' )?y" =y+c . uU ~ (0, oz)a > 0, b > 0and note that u is an i.i.d. supply shock to y with mean 0 and variance of.ECON402 Winter 2019Due April 5, 2019(a) Solve for the optimal inflation response by the central bank(b) Describe how u affects .(c) Suppose the public believes in the central bank policy, i.e. at = a*. Write down acondition that describes when we observe inflationary bias.WHUILIVI WHIGU UCOLLIUCS WHICH WC VUSCI VC HILLOLIVIaLy DIGS.(d) Now assume that y = 0, c = 1, and consumers have rational expectations. Calculateoutput, average output, inflation, and average inflation. In one sentence, explain theoptimal governmental policy y" and z*.