2. The economy is populated by infinitely-lived consumers with preferences given by {log (c) + Blog ht} t=0 where ct and

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2 The Economy Is Populated By Infinitely Lived Consumers With Preferences Given By Log C Blog Ht T 0 Where Ct And 1 (83.92 KiB) Viewed 16 times

2. The economy is populated by infinitely-lived consumers with preferences given by {log (c) + Blog ht} t=0 where ct and h, are individual's consumption and leisure. The parameter B> 0 reflects the value of leisure relative to the utility from consumption. The time discount factor = 1+ where p > 0 is the time preference rate. The consumer has one unit of time which can be supplied as labor (4) and earns wage rate w, per unit of hour. The consumer has an access to a financial market where he can save or borrow at real interest rate r. The representative firm has a technology for producing consumption goods, given by Yt = nt where yt is output and n,is the labor input. In this economy, there is an election every odd period and government spending increases in the election year. That is, there is a cycle in government spending: gt = gL where t is even (t = 0, 2, 4, 6,) and gt = 9H > 9L when t is odd (t = 1,3,5,-). Government finances these purchases through lump-sum tax T or by issuing bonds bt. The government's budget constraint is as follows and bo = 0: 9₁ + (1+r₁) b₁ = T₁+b₁+1 (a) Write down the problem of the consumer and explain the optimality condition(s). (b) Determine the consumption, leisure, and output for each period. Show that these variables exhibit two-period cycles.