For all questions, if necessary, make appropriate assumptions. 1. Consider the following economy where consumers have identical preferences given by [ Bt [log at + Blog le] where a is consumption, 4 is leisure, B > 0, and B e (0, 1). Each consumer has an endowment of one unit of time. The consumer has an access to a financial market where he can save or borrow by purchasing or issuing bonds. The asset he held from the previous period yields r this period. Thus, the consumer j's budget constraint at time t is Cj,t + Sjit+ 1 = Wt (1 - l j,t ) + (1 + rt) sj,t where s;t is the asset holdings by consumer j at time t. Consumers face the common interest rate and wage. But, each consumer may have different asset holdings. If sit > 0, he is a lender (saver). If sit 1. Show that output, consumption, and real interst rate exihit a two-period cycle. (d) In which period the real interest rate high? Explain