Addie's grandfather has left them a trust and the value of the money they receive depends on the age choose to collect this gift of money. Their options are given in the table below. Payoff at age 19 $17,000 0 0 Options Collect payment at age 19 Collect payment at age 20 Collect payment at age 21 Suppose Addie is an exponential discounter, and their utility function is u(x)=x. a. If Addie is indifferent between receiving $17,000 at age 19 and receiving $28,000 at age 21, what must their discount factor be? (Show your work). Payoff at age 20 0 Payoff at age 21 0 0 $28.000 $22,000 0 Suppose now that Addie is an exponential discounter with 6-0.9 and utility function u(x)=x. b. Show that Addie is time consistent when making the decision above (i.e., when to collect the gift). Suppose now that Addie is a hyperbolic discounter with 6-0.9 and p=0.8 and utility function u(x)=x. c. Under these conditions, demonstrate that Addie will behave impulsively (and that their preferences change over time).