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 = 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. [05 marks] 2. Is it optimal for Pierre to supply 0.75 units of labour? [05 marks] 3. What is Pierre's optimal choice of consumption and leisure. Illustrate with a graph. [15 marks] 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? [10 marks] 5. Explain your results in Question 3) in terms on income and substitution effects. Which effect is the strongest in the present case?