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Question: i suppose that you satisfy the hypotheses of the discounted...

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I. Suppose that you satisfy the hypotheses of the discounted utility model, your yearly discount factor is dand your instantaneous utility function for money is given by u(m)-Vm (the same at every date t). You have been offered a job for three years, starting immediately. You have three options: (1) seniority compensation: you are paid Sw this year, S(w+s,) next year and S(w+s2) two years from now, (2) hiring bonus: you will be paid Sw all three years but you get an extra Sb this year as a sign- up bonus, (3) reverse seniority: you are paid Sz this year, S(e-s,) next year and Se -s2) two years from now For parts (a) and (b) assume that w S40,000 and$49,000 (a) If 60.9, b- $6,400, s 4,100, and s2-8,400 how do you rank the three options? (b) Suppose that you dont have a choice: seniority compensation is what the firm does and it implements it in such a way that every year your salary goes up by Ss (thus you get Sw the first year, S(w+s the second year and S(w+2s) the third year). You suggest to the manager the following: “I need more money this year than the next two years, because I am relocating; could we agree on my giving up the seniority increases (so that I get a flat salary of Sw each year), in exchange for a relocation bonus of Sb this year? The amount b that you suggested is that amount that makes you indifferent between seniority compensation (as just described) and the following: wb this year and w in each of the next two years. (b.1) Write an equation whose solution tells us the amount that you suggested if -0.75 and s -$8,000. No need to simplify or solve the equation.] (b.2) Write an equation whose solution tells us your discount factor if s-$8,000 and you suggested b- 12,000. No need to simplify or solve the equation.] (c) Assume that δ-05. Suppose now that you dont have a choice and the firm gives you the following deal: you will not be paid in the first two years and will be given $140,000 in the third year. Write down an equation whose solution gives an annual salary w that would make you indifferent between getting Sw every year and accepting the deal proposed by the firm. (d) Assume that δ-08. You are given a choice between a contract that pays a fixed salary of S40,000 every year and a contract that pays $46,000 the first year and $34,000 in the second and third year (d.1) [... points] Calculate your utility from the two contracts. (d.2) [... points] Calculate your utility from the two contracts for the case where you are a hyperbolic discounter with parameters 0.8 and B 0.5

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