If you are unable to answer all parts. Simply do parts 1-3. Thanks

Question I [40 points] A representative consumer living in a Country A values consuming goods (C) and enjoys leisure (l). The (X)nsumer has h = 1 units of time to divide between working and enjoying leisure. For each hour worked, he receives w = 1.5 units of the consumption good. The consumer also owns shares in a factory which gives him an additional r = 0.55 units of income. The government in this economy taxes the (X.nsumer and uses the proceeds to buy cxmsumption goods that are given to the army. The consumer pays a lump sump tax T equal to 0.35. Suppose that the consumer's preferences are described by the the utility function = Cl/3 + 11/3 1. Write down and graph the consumer's budget constraint. [04 points] 2. Define and cmpute the MRS as a function of C and l. [04 points] 3. Is it optimal for the consumer to supply NS = 0.8 units of labour? [04 points] 4. Find the consumer's optimal choice of cx.nsumption and leisure. Illustrate with a graph. [08 points) 5. Suppose the government decreases the tax to 0.25. How are the consumer's optimal decisions affected by this change? (05 points] 6. Suppose that u,' increases to 1.2 with the taxes still being 0.35. How are consumer's optimal decisions affected by this change. (05 points) 7. Explain your results in Question 6) in terms on income and substitution effects. W"hich effect is the strongest in the present case? (05 points] 8. Now assume the consumer has an opportunity to move to a country B that offers u,' = 1.75, = 0.55, and T = 0.6. Should the consumer move to Country B? Explain. [05 points) Note: For this question, we assume that Country A offers the package u,' = 1.5, 0.55, and 0.25.