Matt and Ted each live for four periods, t = 1, 2, 3, 4. At the end

period 4, they retire and consume whatever wealth they have amassed. Their utility for wealth is given by u(w) = w. They do not consume in periods 1-3. At the beginning of period 1, both have $100 to invest for retirement.  Their money is currently in a checking account earning no return. However, at the beginning of each period, each has the option to put his money in one of two potential investments. Investment A earns a return of $2 in every period in which their wealth is invested in it, and money can be costlessly transferred from their checking account to Investment A. Investment B, meanwhile, earns a return of $10 every period, but requires a one-time immediate cost equal to $11 in order to transfer wealth from their checking account to Investment B (the high-return alternative investment takes effort to find). Suppose that wealth cannot be transferred between Investments A and B, and that once they decide to transfer their money, they transfer all of it.Matt is a naïve quasi-hyperbolic discounter with β = 1/2 and δ = 1. Ted is a sophisticated quasi-hyperbolic discounter with β = 1/2 and δ = 1. At the beginning of each period, including period 1, each decides(separately) whether to transfer his money out of his checking account, and if so, to which alternative investment. Money transferred at the beginning of period t earns the return of the new investment in period t. Note also that returns are earned in period 4 (if invested) before withdrawing money for retirement.Showing all of your work mathematically, and explaining the intuition as you go, answer the following.
(a) If Matt (a naïf) only has access to Investment A what will he do?
(b) If Matt (a naïf) has access to both Investment A and Investment B what will he do?
(c) If Ted (a sophisticate) only has access to Investment A what will he do?
(d) If Ted (a sophisticate) has access to both Investment A and Investment B what will he do?
(e) In 1-2 paragraphs, compare your answers in parts (a)-(d), highlighting any differences in behavior, how much money each agent has upon retiring in each scenario, and what we learn from this example.

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