Suppose that there are only 10 individuals In the economy each with the following utility function over present and future consumption: U (:31, oz) - o; + gag. where c1 is consumption today, and on Is consumption tomorrow. Consumption tomorrow is less valued because people are Impatient and prefer consuming now rather than later. Buying 1 unit of consumption today costs 51 today and buying 1 unit of consumption tomorrow costs 5! tomorrow. All individuals have in come of $10 dollars today and no income tomorrow (because they will be retired] but they can save atthe market interest rate r 2 0. What is the price today of one unit of consumption tomorrow? To verify that you have the correct answer. calculate the price today of one unit of consumption tomorrow if r = 0.05. P: David has an endowment of $10,000 that he wants to Invest in the stockmarket. which consist of two rms. A and B. Each rm's stock ls worth $100 today, and will be worth $140 In one year with probability .1; or will stay at $100 with probability 1}. Assume that the evolution of both stocks ls independent: that Is. the probability that stock A rises in value does not vary or depend on what has happened to stock B. and vice-versa. Finally, assume that David's utility function Is U (to) - JITJ, and Interest rate ls zero. What Is David's utlllty of not investing? [In this and the following questions. include the wealth endowment In your talcuations.) Uy=