Joe can allocate his time between working
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Joe can allocate his time between working (H โ hours worked) and leisure (L โ 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 dollarsโ worth of goods is at a price of $1 โ it costs $1 to buy $1 worth of all goods.
His utility function is U= 3LY where Y is his total income. His ๐๐๐ฟ=3๐ and his ๐๐๐= 3๐ฟ.
a. [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]
b. [4 points] Now suppose Joeโs industry goes into a rough phase and his boss has to slash Joeโs wages to ฮผ. 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]
c. [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.
d. [1 point] Draw Joeโs labour supply curve using the information from parts a and c.
Please typewrite your answers. You should attempt to draw the graphs in MSWord or similar word processing software. Label your graphs. If you absolutely cannot draw graphs in software you can draw them by hand, ensure they are very clear, take a...