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Pierre values consuming goods (C) and enjoying leisure (l). Pierre has h = 1 units of...

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 by the the utility function U(C, l) = C 2/3 l 1/3 . Pierre also owns shares in a factory which gives him an additional π = 0.125 units of income. The government in this economy taxes labour income only and uses the proceeds to buy consumption goods that are given to the army. Pierre pays a lump sump tax equal to 0.35.

1. Write down Pierre’s budget constraint.

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 the government increases the tax to 0.45. How are Pierre’s optimal decisions affected by this change?

5. Suppose that w decreases to 0.8 with the taxes still being 0.35. How are Pierre’s optimal decisions affected by this change.

6. Explain your results in Question 5) in terms on income and substitution effects. Which effect is the strongest in the present case?

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Answer #1

I have answered the first 4 parts. The notations are explained in the answers.UL. B Labour seapplies het l be the amount of leisure (l)alt – e wage from t t Lant of Labous = L unit comumph good . BudgetUtility Cuwe 10 0.775 * ВС 20. Jor ut 1 0.775 4) If tax = 0.45 BC: +0.125 - 0.45 = c. 20.325 = re. = 0.675 -C til 20- U=ceB =

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