A central bank has the following loss function: [ begin{equation*} L=-left(y_{t}-y_{e} ight)+betaleft(pi_{t}-pi^{top} ight)^{2} tag{13.7} end{equation*} ] Use

A central bank has the following loss function:

\[ \begin{equation*} L=-\left(y_{t}-y_{e}\right)+\beta\left(\pi_{t}-\pi^{\top}\right)^{2} \tag{13.7} \end{equation*} \]

Use the information in this chapter to answer the following questions:

(a) What can we interpret about the central bank's preferences from this loss function (Equation 13.7)?

(b) Briefly explain how this loss function compares to the standard loss function and a loss function with \(y^{\top}>y_{e}\).

(c) Find the inflation bias for a central bank with this loss function (Equation 13.7). [Hint: see Section 4.6 in Chapter 4].