(a) Optimal bundle = (25,3)

Please solve for (b), (c), and (d), thank you! I will give you a good rate.

The photo of the entire question of (b), (c), and (d) is posted.

3 (35%) Suppose good 1 is alcohol and good 2 is cigarettes. The two goods are perfectly divisible. The prices of alcohol and cigarettes are pi = 1 and p = 5 respectively. Takashi's budget on the goods is given by m = 40. Takashi's preference over the two goods is quasilinear. It can be represented by U(31,12)=251 + 12. (a) (5%) Find out Takashi's optimal bundle X Hint: To answer questions (b)-(a), you will make use of the properties of Takashi's preference. Depicting how the circumstance changes in a graph may help. Numerical examples are also helpful. (b) (10%) Before Takashi makes his purchase, his business partner calls and offersen units of alcohol as a gift. After Takashi accepts the gift, he will NEVER resell the gift in the market. He will keep the bottles of alcohol forever even if he is not going to drink it. Find out Takashi's optimal bundle after he accepts the gift. Note that is the quantity consumed. For example, if Takashi buys 5 units of alcohol and consumes 15 units, then t = 15. Draw both the budget set and the optimal bundle with and without the gift in the same graph. Make sure your graph is consistent with your answer. Takashi's wife, Lily, is worrying about his health. She turns down the gift for Takashi, Now suppose the government is introducing an ad volarem tax 7>on the ALCO- HOL. For simplicity, we assume the prices of the goods remain the same. Takashi will pay $(1 + 7) for each unit of alcohol. Lily is not sure whether the alcohol tax will improve Takashi's health. (c) (10%) Lily comments that " With the tax on the alcohol, Takashi will drink less. If the tax rate is set at a prohibitively high level, Takashi will quit drinking." Do you agree with Lily ? Explain your answer with the aid of relevant mathe- matical conditions or graphs. You are expected to provide a concise answer with fewer than 150 words. (d) (10%) Lily comments that with the tax on the alcohol, cigarettes become relatively cheaper. Takashi will substitute cigarettes for alcohol. He will end up smoking more, and his health will deteriorate." 10 3 (35%) Suppose good 1 is alcohol and good 2 is cigarettes. The two goods are perfectly divisible. The prices of alcohol and cigarettes are pi = 1 and p = 5 respectively. Takashi's budget on the goods is given by m = 40. Takashi's preference over the two goods is quasilinear. It can be represented by U(31,12)=251 + 12. (a) (5%) Find out Takashi's optimal bundle X Hint: To answer questions (b)-(a), you will make use of the properties of Takashi's preference. Depicting how the circumstance changes in a graph may help. Numerical examples are also helpful. (b) (10%) Before Takashi makes his purchase, his business partner calls and offersen units of alcohol as a gift. After Takashi accepts the gift, he will NEVER resell the gift in the market. He will keep the bottles of alcohol forever even if he is not going to drink it. Find out Takashi's optimal bundle after he accepts the gift. Note that is the quantity consumed. For example, if Takashi buys 5 units of alcohol and consumes 15 units, then t = 15. Draw both the budget set and the optimal bundle with and without the gift in the same graph. Make sure your graph is consistent with your answer. Takashi's wife, Lily, is worrying about his health. She turns down the gift for Takashi, Now suppose the government is introducing an ad volarem tax 7>on the ALCO- HOL. For simplicity, we assume the prices of the goods remain the same. Takashi will pay $(1 + 7) for each unit of alcohol. Lily is not sure whether the alcohol tax will improve Takashi's health. (c) (10%) Lily comments that " With the tax on the alcohol, Takashi will drink less. If the tax rate is set at a prohibitively high level, Takashi will quit drinking." Do you agree with Lily ? Explain your answer with the aid of relevant mathe- matical conditions or graphs. You are expected to provide a concise answer with fewer than 150 words. (d) (10%) Lily comments that with the tax on the alcohol, cigarettes become relatively cheaper. Takashi will substitute cigarettes for alcohol. He will end up smoking more, and his health will deteriorate." 10