Suppose a version of the model economy in which the money growth rate is a random variable. Let the probability be 4/5 that z_t = 1 and the probability be 1/5 that z_t = 2. The realization of monetary policy (the realized value of z_t) is kept secret from the young until all purchases have occurred – that is, people do not learn M_t until period t is over. Prices are the only thing directly observable by the young. Let l(pⁱ_t) = 5 + 0.2 pⁱ_t.
a. Use Equation 6.11 to solve for the equilibrium price level on Island 1 and Island 2.