let a countrys stochastic sas curve be given by y

Question

Let a country's stochastic SAS curve be given by Y = Y* + Π - Π^e + σ, where σ equals 5 in 50% of the cases and -5 in the other 50%. The society's indifference curves are ellipse shaped in a Y/ Π space, centred in (Y^d, 0). A moderately conservative central bank is in charge of setting output and inflation optimally. Whenever σ = 5 set inflation at -2%; when σ =-5 inflation is set at 6%.

(a) What is the rationally expected inflation rate?

- the answer to this point is functional to better understand the next ones: (b) and (c)

- state clearly/describe the formula and the assumptions you are using

- compute the mathematical result

(b) Let Y*=100. What are the income levels in periods of positive supply shocks and in periods of negative supply shocks, respectively?

- the answer to this point is functional to better understand the next one: (c)

- state clearly/describe the formula and the assumptions you are using

- compute the mathematical result

(c) Represent graphically the reaction function for the moderately conservative central bank and derive its slope

- Here you should use a graph, where you summarise all the information gathered from previous answers (a) and (b)

- state clearly/describe the curves you are using in the graph

- compute the mathematical result by using the information appearing in the graph

Imagine that the society decides to evaluate the replacement of the moderately conservative central bank with an ultra-conservative central bank.

(d) which one of the two monetary authorities should be preferred by the society? Discuss.

- The only way you have to explain this formally is to exploit the graphical analysis of point (c);

- If you think the question does not provide enough details in order to reach a clear-cut answer you can introduce some standard elements that allow you to do so, eventually (before doing that, make sure you can effectively answer with the elements originally at hand and that the elements you introduce do not conflict with the original setup of the question);

- Check whether the theory, the real world or the common sense suggest a different answer than the clear-cut answer, in order to refine your judgement