This is my queston, thank you!

Problem 1 (30 pts) Explain your answers! J the consumer consumes only two goods with quantities 2:1 and mg respectively. J's utility function is: n(x1.$g) = ln $1 + at; + 2. Let the prices be p1 = 1. pg 2 6 and Is income be in = 60. (a) 1What are J 's optimal quantities demanded of each good? Graph his budget line and label his optimal bundle as A. (Hint: You may want to derive J's optima}.r quantities demanded for any phpg, in and then just ping in the given trainee) Suppose now that the government puts a quantity tap that increases the price of good I to 103:2. (b) What are J 's optimal quantities demanded of each good after the tax is imposed? Plot his new budget line on the graph from (a) and denote his optimal bundle by C. (c) To how much must J 's income be adjusted after the tax is imposed so that he can just a'ord his optimal bundle from (a)? (d) \"that would J's optimal quantities demanded for each good be with the adjusted income as in (c) at the aftertax prices. Plot the budget line corresponding to this bundle on your graph and denote the optimal bundle by B . (e) Given your results nd the income and substitution effects of the change in p1 on J's consumption of each good. Explain briey the intuition for the results