10 marks Find the equilibrium values of inflation and the output gap and the

10 marks find the equilibrium values of inflation and

This preview shows page 1 - 2 out of 2 pages.

[10 marks] Find the equilibrium values of inflation, 𝜋 𝑡 , and the output gap, 𝑥 𝑡 , and the nominal interest rate, 𝑖 𝑡 , needed to implement the optimal policy. (c) [10 marks] Explain intuitively why inflation and the output gap move in opposite directions following a cost-push shock, ? 𝑡 , but do not respond at all to the demand shock, ? 𝑡 . (d) [10 marks] In the remainder of the question, assume ? 𝑡 = 0 for simplicity. Now suppose the central bank is worried about excessive interest rate fluctuations. It chooses to minimize the new loss function: 𝐿 = 1 2 (𝜋 𝑡 2 + 𝑖 𝑡 2 ) By using the IS curve equation, eliminate 𝑖 𝑡 from the loss function to write it in terms of 𝜋 𝑡 and 𝑥 𝑡 . Now repeat part (a), and sketch a diagram plotting the new first-
Image of page 1
2 order condition together with the Phillips curve. What now happens to 𝜋 𝑡 and 𝑥 𝑡 following a shock to demand, ? 𝑡 ? Explain your answer. (e) [10 marks] Suppose the central bank uses the original loss function involving 𝜋 𝑡 and 𝑥 𝑡 , but now the interest rate directly affects firms’ costs, so that the Phillips curve becomes: 𝜋 𝑡 = β𝐸 𝑡 [𝜋 𝑡+1 ] + 2𝑥 𝑡 + 𝑖 𝑡 . Using the IS curve, eliminate 𝑖 𝑡 from the Phillips curve to write it in terms of only 𝜋 𝑡 and 𝑥 𝑡 . What will happen to 𝜋 𝑡 and 𝑥 𝑡 after a demand shock, ? 𝑡 ? Explain your answer. 2. Optimal monetary policy Consider the following New Keynesian model: 𝜋 𝑡 = 𝐸 𝑡 [𝜋 𝑡+1 ] + 𝑥 𝑡 + ? 𝑡 𝑥 𝑡 = 𝐸 𝑡 [𝑥 𝑡+1 ] – (𝑖 𝑡 – 𝐸 𝑡 [𝜋 𝑡+1 ]) + ?
Image of page 2

You've reached the end of your free preview.

Want to read both pages?

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Stuck? We have tutors online 24/7 who can help you get unstuck.
A+ icon
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes
A+ icon
Ask Expert Tutors