For this question, use the two-period New Keynesian model discussed in Topic 2 (weeks 7-11). The central bank minimises the following loss function 1 L = - 2 ( y Ye) + 10 (p = p), 2 K (4) using the nominal interest rate as an instrument and subject to the following Phillips Curve p-pe=k(y- Yn). (5) Derive the central bank's inflation targeting policy, showing all your workings. Suppose that a dry year hits the New Zealand economy in the short run, lowering productivity due to electricity outages (since New Zealand primarily relies on hydro power). The drought is believed to be temporary. Explain in detail, using mathematical equations where appropriate, how the electricity outages cause the economy to transition from an initial equilibrium to a new equilibrium in the short run. Graphically demonstrate how the central bank responds to the effects of the dry year based on its flexible inflation targeting policy. Explain your reasoning. [10 marks]