Exercise 1: Consumer Choice Application Labor-Leisure Choice Barbie has preferences over bundles of leisure time (x), measured as fraction of total time (i.e. x=1 corre- sponds to 100% of time - or 168 hours per week- spent on leisure) and money for consumption (y). She has an endowment consisting of both time and a dividend payment, d = 40, that she receives independent of her choice to work. Barbie's endowment is E= (xo, yo) = (1, 40) and her utility function is - u(x, y) = x - Y Assume that she is absolutely free to choose the number of hours she works per week, (1-x). 168 € [0, 168]. 1. For fixed wage rate w> 0 (per 168 hours) (that is, if she chooses x = 0 her labor income is w, resulting in total income w+ d), find Barbie's budget constraint. 2. Under what conditions would Barbie choose not to work? That is, find the threshold wage w such that Barbie's optimal choice is (x*(w), y* (w)) = E= (1, 40) for all w< w? 3. Now assume w>w, what is Barbie's optimal consumption bundle as a function of the wage rate (x* (w), y* (w))?

Exercise 1: Consumer Choice Application Labor-Leisure Choice Barbie has preferences over bundles of leisure time (x), measured as fraction of total time (i.e. x=1 corre- sponds to 100% of time - or 168 hours per week- spent on leisure) and money for consumption (y). She has an endowment consisting of both time and a dividend payment, d = 40, that she receives independent of her choice to work. Barbie's endowment is E= (xo, yo) = (1, 40) and her utility function is - u(x, y) = x - Y Assume that she is absolutely free to choose the number of hours she works per week, (1-x). 168 € [0, 168]. 1. For fixed wage rate w> 0 (per 168 hours) (that is, if she chooses x = 0 her labor income is w, resulting in total income w+ d), find Barbie's budget constraint. 2. Under what conditions would Barbie choose not to work? That is, find the threshold wage w such that Barbie's optimal choice is (x(w), y (w)) = E= (1, 40) for all w< w? 3. Now assume w>w, what is Barbie's optimal consumption bundle as a function of the wage rate (x* (w), y* (w))?

Economics (MindTap Course List)

13th Edition

ISBN:9781337617383

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter29: Interest, Rent, And Profit

Section: Chapter Questions

Problem 1QP

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