Consider a version of the economic model with the associated assumptions of Chapter 6, in which the money growth rate is a random variable. Let the probability be 4/5 that *zt *= 1 and the probability be 1/5 that *zt *= 2. The realization of the monetary policy (the realized value of *zt *) is kept secret from the young until all purchases have occurred - that is, people do not learn *Mt *until period *t *is over. Prices are only thing directly observable by the young. Let ????(????????????)=5+0.2???????????? in island i at time t.

- (a) Solve for ???????????? using the market clearing condition. (5 marks)
- (b) Can the worker make use of this price level as an indicator of the unknown monetary policy? (5 marks)
- (c) How can the workers make use of the price obtained in part a to decide on their work decision? (5 marks)

**Show all your steps and explain your answers to avoid grade penalty. **