Pierre values consuming goods (C) and enjoying leisure (l). Pierre hash= 1 units of time to divide between working and enjoying leisure. For each hour worked, he receivesw= 1 units of the consumption good. Suppose that Pierre's preferences are described by the the utility function

2/3 1/3U(C,l)=C l .

Pierre also owns shares in a factory which gives him an additional= 0.125 units of income. The government in this economy taxes labour income only and uses the proceeds to buy consump- tion goods that are given to the army. Pierre pays a lump sump tax equal to 0.35.

1. What is Pierre's optimal choice of consumption and leisure. Illustrate with a graph?
2. Suppose the government increases the tax to 0.45. How are Pierre's optimal decisions affected by this change?
3. Suppose thatwdecreases to 0.8 with the taxes still being 0.35. How are Pierre's optimal decisions affected by this change.
4. Explain your results in Question 4) in terms on income and substitution effects. Which effect is the strongest in the present case?

I found the budget constraint to be C=0.775