Sep 1, 2016 - Course Description: Surveys foundational concepts of lifespan development psychology, such as sensitive periods, developmental stages and transitions, and trajectories of change across the lifespan. Text: Berger, K.S., & Chuang, S.S. (2
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Assignment 3 Econ 506 Total Marks - 100
Due Date - 8th Nov.
Question 1 Fisher Model, Chapter 2, Lecture Note, pp. 14-17. a Suppose that non-policy shock, vt follows first-order autoregressive process vt = ρvt−1 + ξt . Derive the optimal monetary policy rule. Marks 10 b Suppose that aggregate demand is given by yt = mt − pt + vt where vt is non-policy shock to the aggregate demand. Derive the path of yt . Now suppose that money supply process is given by mt = m∗t where m∗t is the money supply chosen by the central bank and non-policy shock follows random walk vt = vt−1 + ξt Derive the optimal policy rule. (Hint: You might find it helpful to define a variable m ˆ t = mt + vt and express yt in terms of m ˆ t .) Marks 15 Question 2 Taylor Model, Chapter 2, Lecture Note, pp. 17-19. Derive equation (4.22). Marks 15 Question 3: Consider example 1 in Lecture 2. Suppose that agents can buy and sell only two types of assets (other than money) : one-period nominal bond (short bond) and two period nominal bond (long bond). One period nominal bond pays 1$ next period, while two period nominal bond pays 1$ after two periods. Derive the expression for prices for one and two period nominal bonds in terms of exogenous variables. Derive the relationship between prices and thus rates of return of one and two period bonds. Hint: If an agent buys two-period bond at time t, he/she cannot redeem it at time t + 1. However, he/she can sell it at time t + 1. What will be the price of two-period bond bought at time t in period t + 1? It will be equal to the price of one-period nominal bond at time t + 1. Marks 35 1
Question 4: Consider Money in Utility function model of Example 2 lecture note 3. Define real money balance as xt = mpt+1 . Suppose that the period utility function is given t by U (ct , xt ) = w(ct ) + v(xt ) where v(xt ) = xt (B − D ln xt ). B & D are positive parameters. Rest of the environment remains the same. (a) Derive the money demand function. 0
(b) Define α = wD(c) . Derive an expression for the welfare cost of inflation. How does welfare cost depend on α? Marks 25