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2. (24 marks) Consider a Lucas type overlapping generations model, where individuals live on three spatially separated islands. The total population / is constant over time. From the old, = N live on each of the three islands. The number of young on an island N' is a random variable with the three possible outcomes for Ni being {{ N, N, 3N). The monetary policy captured by the growth rate of the money supply z, is also a random variable with the three possible outcomes for z, being { 1, 2, 3}. Individuals only observe the price on their island p;. Except for the number of possible outcomes the structure of the model and the assumptions are the same as in the standard Lucas model. In particular, an individual faces the following budget constraints over their lifetime, Ci,f + 4 = ci,t + vim; = y C2,1+ 1 = Ultim; + atti = Ut+ 1 vi where " is the real rate of return to work. Pi+1 (a) (6 marks) Using the market clearing condition for money on an island solve for the prices under each possible combination (N', zt). (Hint: construct a matrix with the possible combinations of (zt, N'), and denote these combinations by a, b, c, d, ...). (b) (6 marks) Order the possible prices from lowest to highest for a given 4. How many prices are not unique? What will a young individual choose to do, in terms of output, if they observe a non-unique price and why? (c) (6 marks) Compute aggregate output for this economy, when the monetary policy is 2 = 1, when it is at = 2, and when it is z = 3. With which policy is aggregate output the highest and with which is it lowest