An individual has a vNM utility function over money of u(x) Vx, where x is final wealth. She currently has $8 and can choose among the following three lotteries. Which lottery will she choose? • Lottery 1: Give up her $8 and face the gamble (0.1, 0.5, 0.4) over final wealth levels ($1, $8, $27). • Lottery 2: Keep her $8. • Lottery 3: Give up her $8 and face the gamble (0.2, 0.8,0.0) over final wealth levels ($1, $8, $27) O Lottery 1 O Lottery 2 O Lottery 3 O They are indifferent between lotteries 1 and 2 O They are indifferent between lotteries 2 and 3 O They are indifferent between lotteries 1 and 3 O They are indifferent between all three lotteris

A pirate is about to set sail on a 2-period journey (trip). He has 100 bags of barley (food). He must decide how much to consume in period 1 and how much to consume in period 2: (C1, c2). He gets all the barley in period 1 and none in period 2. Unfortunately, rats will eat 50% of any barley that he saves to consume in period 2. If the pirate's utility function is U(C1, C2) = C1C2, what levels of consumption does he choose in each period? (Hint: The "price" of barley in each period can be assumed to be 1.)

At a company, 20 employees are making contributions for a retirement gift. Each of the 20 employees is choosing how many dollars to contribute from the interval [0,20]. The manager of these 20 employees announces that she will contribute dd dollars for every dollar that an employee contributes. The payoff to employee ii who makes contribution of xixi​ dollars is bi(1+d)xi−xi, where bi>0.bi​(1+d)xi​−xi​, where bi​>0. Assume that d=4d=4, bi=0.25bi​=0.25 for i=1,2,…,10i=1,2,…,10, andbi=0.5bi​=0.5 for i=11,12,…,20i=11,12,…,20 What is the best contribution level of any employee ii for i=1,2,…,10i=1,2,…,10.   At a company, 20 employees are making contributions for a retirement gift. Each of the 20 employees is choosing how many dollars to contribute from the interval [0,20]. The manager of these 20 employees announces that she will contribute dd dollars for every dollar that an employee contributes. The payoff to employee ii who makes contribution of xixi​ dollars is bi(1+d)xi−xi,…

Mr Usu has an expected utility function with u(x) = x0.5. He is analyzing an investment opportunity that promises to pay out $1,160 with prob. 0.6 and $2,800 with prob. 0.4. What is the expected utility of this opportunity?

1 Q1. Jerry has wealth of $60 and derives utility from this according to the utility function U(w) = 1 - Where w is his wealth. Jerry now finds a lottery ticket (the drawing takes place the next day) that offers a 50% chance of winning $5. W a) What is the expected value of Jerry if he takes the lottery ticket? (pay attention, it's not jerry's wealth) b) What is the minimum amount for which Jerry would be willing-to-sell the ticket? (Hint: sets a price of p, and at the minimum amount, the expected utility of selling and not selling should be the same) c) Which is bigger, your answer to (a) or (b), and suggest whether Jerry is a risk averse person based on the previous conclusion? d) If he does not sell the ticket, what is Jerry's cost of risk? (The cost of risk is the difference between the expected wealth and the certainty equivalence)