The next four questions are based on the following labor-taxes model: Rodolfo has a lifetime utility...
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The next four questions are based on the following labor-taxes model: Rodolfo has a lifetime utility given by: (1-4) 7 B 1-0 1-o I 1-0 where co, C₁ is consumption of both periods of life, and lo is labor in the first period (so 1-lo is leisure). The wage in the first period is wo. He does not work in the second period. Risk aversion is a>0 and the utility of labor is such that < 1. (a) (5 points) If the interest rate per period is r, and Rodolfo's initial assets are do, what is Rodolfo's lifetime budget constraint? (b) (5 points) Set up the Lagrangian and derive the first order conditions with respect to all three choice variables (co, C₁, lo). Express lo and e, in terms of co (c) (5 points) Assume r= 0.25. For what value of 3 is consumption constant over Rodolfo's life cycle (that is co=C₁). (d) (5 points) Now assume 3 = 0, ao = 0, wo = 1, a= 2 and y=-1. Use the first order conditions and the budget constraint to determine the optimal choice of co, c and lo. Explain intuitively your results. The next four questions are based on the following labor-taxes model: Rodolfo has a lifetime utility given by: (1-4) 7 B 1-0 1-o I 1-0 where co, C₁ is consumption of both periods of life, and lo is labor in the first period (so 1-lo is leisure). The wage in the first period is wo. He does not work in the second period. Risk aversion is a>0 and the utility of labor is such that < 1. (a) (5 points) If the interest rate per period is r, and Rodolfo's initial assets are do, what is Rodolfo's lifetime budget constraint? (b) (5 points) Set up the Lagrangian and derive the first order conditions with respect to all three choice variables (co, C₁, lo). Express lo and e, in terms of co (c) (5 points) Assume r= 0.25. For what value of 3 is consumption constant over Rodolfo's life cycle (that is co=C₁). (d) (5 points) Now assume 3 = 0, ao = 0, wo = 1, a= 2 and y=-1. Use the first order conditions and the budget constraint to determine the optimal choice of co, c and lo. Explain intuitively your results.
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a The lifetime budget constraint is given by do r1 lo c0 c1 where lo is labor in the first period ... View the full answer
Related Book For
Intermediate Accounting
ISBN: 978-0077400163
6th edition
Authors: J. David Spiceland, James Sepe, Mark Nelson
Posted Date:
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