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Pierre values consuming goods (C) and enjoying leisure (l). Pierre has h = 1 units of time to divide between working and enjoying leisure. For each hour worked, he receives w = 1 units of the consumption good. Suppose that Pierre's preferences are described the utility function U(C, l) = 2 ln(C) + ln(l). Pierre also owns shares in a factory which give him an additional π = 0.125 units of income. The government in this economy taxes labour income only and using the proceeds to buy consumption goods are then thrown away. Pierre pays 35% of his labour earnings in income taxes
1. Write down Pierre's budget constraint. Explain how Pierre should determine consumption and leisure in order to maximize utility.
2. Is it optimal for Pierre to supply 0.75 units of labour?
3. What is Pierre's optimal choice of consumption and leisure. Illustrate with a graph.
4. Suppose that, in order to increase government spending, the government increases the tax rate to 45%. How are Pierre's optimal decisions affected by this change?
5. Explain your results in Question 3) in terms on income and substitution effects. Which effect is the strongest in the present case?
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