Suppose the representative consumer's preferences are given by the utility function, U(C, I) = aln C + (l- or.) In! Where C is consumption and I is leisure, with a utility function that is increasing both the arguments and strictly quiescence, and twice differentiable. A. The total quantity of time available to the consumer is h. The consumer earns w real wage from working in the market, receives endowment 71: from hisr'her parents, and pays the T lump-sum tax on the endowment. Setup the consumer's optimization problem where hefshe chooses C and I to maximize U(C, 1). Obtain and interpret the optimization conditions and optimum consumption bundle for the consumer. (I point) B.Consider that consumption and leisure are normal goods. Show the effects of an increase in endowment TE and real wage w on consumption and leisure. (1 point) C.Now suppose, the government imposes a proportional income tax on the representative consumer's real wage. How will be the consumer's budget constraint changed? What effects does the income tax have on consumption and leisure? Explain your results in terms of income and substitution effects using a diagram. (2 points)