A typical household aims to maximize its expected discounted lifetime utility function defined over consumption ct and labor nt given by: = 2:016 tale; \"t) - .~- rJ1 .1 knl+w era , _ '3: \"_I_ The period utility is UTE: ' t) 10- 21\" .and the discount factor '6: 151"? "fa denotes the rate of time preference and o is the coefcient of relative risk aversion discussed in class. Both labor parameters 2 and ti are positive and constant. The household is endowed with one unit of time that can be used for leisure It and labor nt. Cine unit of labor time earns the average wage rate wt . In each period. the household consumes ct and saves in physical capital kt. Let capital's depreciation rate 5 equal D and rt denote the rate of return to physical capital. The household pays a proportional tax Tn only on earnings from work. A representative rm hires x. capital kt at rental rate rt and labor at wage rate wt to produce output ytbe Fa":t -" \"1)- . The production kaht). = Akf'ntb\" function is given by: , where parameter A denotes total factor prod uctivitv. The {gt}: government finances its expenditure stream using tax revenue