Joe can allocate his time between working
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Joe can allocate his time
between working (H – hours worked) and leisure (L – hours spent in leisure),
and spends all 24 hours per day doing one or the other. He earns a wage of w
dollars per hour, which he spends entirely on consumption of all other goods
(not including leisure time); he has no other source of income. Since we assume
all goods are measured in dollar amounts, consuming Y dollars’ worth of goods
is at a price of $1 – it costs $1 to buy $1 worth of all goods.
His utility function is U= 3LY where Y
is his total income. His M???????? = 3???? and his M???????? = 3L.
·
[3 points] What levels of H and L does
he choose in optimal? [Hint: optimality has to ensure 3 conditions here: budget
constraint, time constraint and the tangency condition]
·
[4 points] Now suppose Joe’s industry
goes into a rough phase and his boss has to slash Joe’s wages to μ. Draw a
diagram with leisure on the horizontal axis and all other goods on the vertical
axis and the usual downward sloping indifference curve. Show i) the
budget lines and the optimal choices for the two cases of before and after the
wage cut (2 points) ii) the substitution effect and income effect following the
wage cut (2 points). [Hint: the expression from part b should tell you where
the optimal point will be on the new budget line]
·
[2 points] Briefly explain the
substitution effect and income effect situation from part b with special
reference to the income elasticity of leisure demand and the price elasticity
of leisure demand.
·
[1 point] Draw Joe’s labour supply curve using the information from parts a a
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