Johnny is an impoverished college student who works at a bakery full time while attending school. After spending money on rent, tuition, and books, he only has $80/month left over to spend on food. The good thing about his job is that he gets to take home all the stale bread he wants. He only has to buy peanut butter and jelly in order to make sandwiches. The price of a jar of jelly is $1.60 and the price of a jar of peanut butter is $2.00. He likes to consume both subject to the utility function U=P1/2J1/2, where P is the number of jars of Peanut Butter and J is the number of jars of Jelly purchased per month. a. Find the number of each good purchased. b. Find the utility received from this per month. c. Suppose that the price of jelly rises to $2.50 per jar. With the original level of income, what is the consumption bundle with the new prices? d. Further, he is considering working a part time job on the weekends that will increase his income. What is the level of income necessary to give Johnny the same utility as he had before the price change? e. With the level of income in d, what is the consumption bundle with the new prices? f. What is the total change in quantity of jelly due to the price increase? How much of that change is due to the income effect, and how much is due to the substitution effect? g. Graph these income and substitution effects. (Show the optimal bundle before and after the price change, and illustrate the income and substitution effects)