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Suppose an individual is truly an exponential discounter but perceives a 70% chance getting a future reward and a 100% chance of receiving an immediate reward. In other words, they are completely sure that an immediate reward will be paid but they are only 70% sure that the researcher will pay them a future reward. (14 points total) a. What do their observed discount factors look like for t=0, t=1, and t=2? (Hint: ifI think there is a 50% chance of being paid $100, how much money do I expect to be paid? If there is a 50% chance of being paid $100 and I participate in this experiment a large number of times, how much do I get paid on average?) (5 points) b. Dene the marginal discount rate,pi',;+1 to be the marginal amount that utility is discounted between time periods t= and t=i+1 for all i 2 0. What are the observed marginal discount rates, p04, p12, and p23? (Hint: the true marginal discount rates for an exponential discounter are {(1/ 5)1, (1/ 5)1, (1/ 5)1, ...} and assume that the researcher cannot infer this individual's perceived probabilities of receiving the future reward.) (5 points) 0. What do you conclude about the effects of uncertainty in a future reward when the uncertainty is constant for all time periods? (4 points)