[Dynamic consistency] Consider a DM who is an exponential time discounter with discount factor . Let us consider a 3-period model in which the DM consumes ct in period t, for t=1,2,3. Instantaneous utility of consumption is given by a function u(c) = c. a. Write down an algebraic expression for total utility U(c1,c2,c3) in terms of . b. Consider the two consumption streams A = (3,0,0) and B = (0,4,0). For which values of does the DM prefer A over B? c. Consider the two consumption streams C = (0,3,0) and D = (0,0,4). If the DM is time- consistent and prefers A over B, what can you conclude about her preference between C and D? d. For which values of does the DM prefer C over D? e. Based on this example, what can you conclude about the relationship between exponential time discounting and time-consistency?