Let T and there is consumption only at T = 1. (a) Let wealth at time...

 

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Let T and there is consumption only at T = 1. (a) Let wealth at time 0 be w = 62 AUD and endowment at time 1 be w = 0. Formulate the budget set with prices p = 1 and p 1 and p = (2, 1, 2). Specify an endowment w with w=0 that gives the same budget set. .Draw the budget set. (b) Compute the gradient for 1 4 In In [00] U(x) = { Inx + 1 x + x3 - x 2 10 10 Is it (= U) continuous? Is it strictly increasing? Is it smooth? Is it concave? Explain the second equality in [oo]. = = E [In(x)] Give a short formal argument for each answer. (c) Take part a. and b.: formulate the corresponding maximization (2, 1, 2) and solve it. Also formulate the problem with with p optimal solution as a lottery. (d) Compute the certainty equivalent of the optimal solution and draw an illustrating picture with the risk premium. (e) Compute and plot the Absolute Risk Aversion of the present util- ity index as a function of wealth. Let T and there is consumption only at T = 1. (a) Let wealth at time 0 be w = 62 AUD and endowment at time 1 be w = 0. Formulate the budget set with prices p = 1 and p 1 and p = (2, 1, 2). Specify an endowment w with w=0 that gives the same budget set. .Draw the budget set. (b) Compute the gradient for 1 4 In In [00] U(x) = { Inx + 1 x + x3 - x 2 10 10 Is it (= U) continuous? Is it strictly increasing? Is it smooth? Is it concave? Explain the second equality in [oo]. = = E [In(x)] Give a short formal argument for each answer. (c) Take part a. and b.: formulate the corresponding maximization (2, 1, 2) and solve it. Also formulate the problem with with p optimal solution as a lottery. (d) Compute the certainty equivalent of the optimal solution and draw an illustrating picture with the risk premium. (e) Compute and plot the Absolute Risk Aversion of the present util- ity index as a function of wealth.

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a The budget set is defined by the total wealth and the prices of the goods Given that the wealth at time 0 is w 612 AUD and the prices at time 1 are p1 2 1 2 the budget set is defined by the inequali... View the full answer