Lawrence must decide how to allocate his 24-hour day between non-wage activities, leisure, and wage activities, labor. For every hour of labor that he supplies he is paid by his employer $w. Lawrence can purchase bottles of wine (y) at a price of $20 per bottle (and wine is the only consumption good). Lawrence has non-wage income of $I and so his total income is equal to the sum of his wage income and his non-wage income. Finally assume that Lawrence’s preferences over leisure and wine can be represented by the following utility function: U(l ,y) =0.5 l + 10 ln (y) a) If Lawrence consumes 24 hours of leisure, then how many bottles of wine can he purchase? If Lawrence works 24 hours, then how many bottles of wine can he purchase. Illustrate his budget set in a diagram below and write the equation for his budget line. b) Find Lawrence’s demand, for leisure as a function of w and I. What is Lawrence’s supply of labor as a function of w and I? For parts (c) through (e) below set $I = $120. c) Given your answer to (b) what is Lawrence's supply curve of labor? Illustrate it. d) Suppose that Lawrence’s wage is $12. Given the demand functions that you found above what are Lawrence’s demands for leisure and wine at this wage? What is his supply of labor? Illustrate your answer in your diagram in part (a). Be sure to include an indifference curve through his best bundle. e) Suppose that Lawrence’s wage falls to $10. Given the demand functions that you found above what are Lawrence’s demands for leisure and wine at this wage? Illustrate in your indifference curve diagram the effect of the increase in wages on his optimal choice of leisure and wine. Given the slope of the labor supply curve which effect (the income or substitution) is larger on his demand for leisure?
Lawrence must decide how to allocate his 24-hour day between non-wage activities, leisure, and wage activities, labor. For every hour of labor that he supplies he is paid by his employer $w. Lawrence can purchase bottles of wine (y) at a price of $20 per bottle (and wine is the only consumption good).
Lawrence has non-wage income of $I and so his total income is equal to the sum of his wage income and his non-wage income. Finally assume that Lawrence’s preferences over leisure and wine can be represented by the following utility function: U(l ,y) =0.5 l + 10 ln (y)
a) If Lawrence consumes 24 hours of leisure, then how many bottles of wine can he purchase? If Lawrence works 24 hours, then how many bottles of wine can he purchase. Illustrate his budget set in a diagram below and write the equation for his budget line.
b) Find Lawrence’s demand, for leisure as a function of w and I. What is Lawrence’s supply of labor as a function of w and I?
For parts (c) through (e) below set $I = $120.
c) Given your answer to (b) what is Lawrence's supply curve of labor? Illustrate it.
d) Suppose that Lawrence’s wage is $12. Given the demand
e) Suppose that Lawrence’s wage falls to $10. Given the demand functions that you found above what are Lawrence’s demands for leisure and wine at this wage? Illustrate in your indifference curve diagram the effect of the increase in wages on his optimal choice of leisure and wine. Given the slope of the labor supply curve which effect (the income or substitution) is larger on his demand for leisure?
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