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Question 6 Consider the following sequence problem V(do, who) = max (18) s.t (19) 1=0 Wi+1 = (1 -6)w + owt (20) (i) For which value of 6 does (20) converge to a unique fixed point? What is the value of this fixed point? (ii) Define a = >(ats - wits) (21) 8=0 Use this definition to show that the problem above has a recursive representation. No formal proof is necessary, but explain the logic behind your result clearly. What interest rate do the "bonds" a, pay? (ini) In a deterministic economy, such as the one above, it appears as if a one period bond is sufficient to allocate resources efficiently. Is this also true in a stochastic economy? Why or why not?Question 5 Consider an infinitely lived individual born in time zero, endowed with a cake of size ro. The cake is storable (without depreciation) and infinitely divisible. The agent derives contemporary utility from (cake) consumption through u(c ), and has as her ultimate objective to maximize her infinitely discounted sum of utility streams. Her discount rate is, as usual, given by B. (i) Formulate the mathematical problem corresponding to the above description (i.e formulate the Sequence Problem). (ii) Provide a recursive formulation and show that its solution also solves SP in (i) (i.e Theorem 2). 2 (ini) Let u(c) = In(c). Derive both the value function, v(2), and the policy function, r' = g(x).Question 1 Consider the following (real valued) sequence {r:}72, defined by: ro = 1, "=lta, x,=ltata', I, = 1tata'+... + a" and so on. Prove that if |a|