. Consider the following version of the Barro-Gordon model. Let the Central Bank's (CB) welfare function be 𝑊 = 𝑌 − 𝜃𝜋 2

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. Consider the following version of the Barro-Gordon model. Letthe Central Bank's (CB) welfare function be 𝑊 = 𝑌 − 𝜃𝜋 2 with𝜃>1. The CB maximizes this social welfare function subject tothe Phillips curve constraint: 𝑌 = 𝑌 ∗ + λ(π − π 𝑒 ) where0<λ<1. The CB chooses the optimal inflation given the privatesector's expectation (π 𝑒 ) about inflation. Assume that therelative PPP condition holds. (i) Derive the CB's welfaremaximizing inflation rate and show how this depends on the expectedrate of inflation (π 𝑒 )? (20 marks) (ii) Draw the CB'sindifference curves in an output-inflation plane and showgraphically the CB's optimal inflation and output. (20 marks) (iii)Now suppose the private sector has rational expectation aboutinflation. What is the Nash equilibrium pair of inflation andoutput? (20 marks) (iv) What is the Nash equilibrium rate ofdepreciation of the home currency? (20 marks) (v) What implicationdoes this model have for a currency crisis? (20 marks)