[3) [24 points] Consumption Theories Suppose the representative households Inter-temporal utility function in a taro-period model is given by l U = . (cute) 2Fl+1+ hie21 where p is the subjective discount rate. The budget constraint is given by at + e: = on, where tel is the labor income at time t = 1. Assume that there is no initial nancial asset in the rst perlod. (s) [6 points] List at least three di'emnoes between the Keynesian consumption function and the consumption function implied by the model above. {b} [6 points] Write an equation describing the household's optimal consumption decision, and interpret the optimality condition. {c} [6 points} Is the real rate of interest procyclical; that is, higher on average when economic activityr is expanding than when activity is contracting? Explain. (d) [6 points] Does this household increase the consumption in period 1 if the real rate of interest rises