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))?
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![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
1
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))?
4. Based on your previous answers determine Barbie's labor supply curve s(w). That is, find the function
wage rate w into the percentage of time she works, 1 - x* (w).
that maps
the
Is her labor supply curve s(w) = 1- x* (w), increasing in w?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10f13288-371b-4dde-8ecd-eccecfaaefe3%2F9a38e3ef-637d-4594-8a09-875e882c5caa%2Fccvd1e_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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
1
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))?
4. Based on your previous answers determine Barbie's labor supply curve s(w). That is, find the function
wage rate w into the percentage of time she works, 1 - x* (w).
that maps
the
Is her labor supply curve s(w) = 1- x* (w), increasing in w?
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