Question I [40 marks] Pierre values consuming goods [C] and enjoying leisure {i}. Pierre has it = 1 units of time to divide between working and enjoying leisure. For each hour worked. he receives at = 1 units of the consumption good. Suppose that Pierre's preferences are described the utility function we, a} = 2 111(0) +1n{l]|. Pierre also owns shares in a factory which give him an additional 11' = {1.125 units of income. The government in this economy taxes labour income only and using the proceeds to buy con- sumption 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 maximise 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. lustrate with a graph. [15 marks] 4. Suppose that1 in order to increase government spending. the government increases the tax rate to 45%. How are Pierre's optimal decisions affected by this change? [ll] marks] 5. Explain your results in Question 3} in terms on income and substitution effects. Which effect is the strongest in the present cme? [[15 marks]