There is an infinite-lived representative consumer with preferences given by [BIC Y t=0 where 0 0, he is the human capital of the representative consumer, and ut is time spent by the consumer in the production of consumption goods. The consumer spends vt units of time in each period working for the government, with production of government-consumed goods given by &t = nhtvt, where n > 0. The government sets vt = v, a constant, for t = 0,1,2,.. Human capital is produced according to ht+1 = Shtxt, where 8 >0 and xt is the quantity of time devoted to human capital accumulation. x = 1 -ut - v a. Determine the paths followed by consumption and human capital and determine how the consumer allocates time to the production of consumption goods and human capital accumulation in each period. b. How are the growth rates of consumption and human capital, and the allocation of the consumer's time affected by a change in v? Explain your results.