4. (30 points) Leah and Bob work for the same company and earn the same amount of money: y = 230 and y' 140. They pay the same taxes: t = 30 and t' = 8. The market real rate of return is ten percent. a. Plot Leah and Bob's budget constraint, making sure to carefully calculate and label all appropriate points and the slope. Please make the graph large (at least half a page), since you'll be adding more lines to it. b. Leah's utility function is given by In(c) + 3ln(c'). Calculate her optimal consumption point (c, c*) and mark it on the graph above. Is Leah a borrower or a lender? Calculate her savings. c. Bob's utility function is given by 3ln(c) + ln(c'). Calculate his optimal consumption point (CB, CE*) and mark it on the graph above. Is Bob a borrower or a lender? Calculate his savings. d. Due to a recent string of mortgage defaults, Leah and Bob's local bank is increasing the interest rate on borrowing to twenty percent; the lending interest rate remains the same at 10 percent. Update the budget constraint graph to reflect this change (preferably, and for ease of understanding, in a different color). e. Does the change in the bank's interest rate schedule interfere with Leah's ability to get to her optimal consumption point? Explain. If your answer is yes, calculate her new optimal point. (Hint: you can use the same FOC you derived in part b, but plug in the updated values for we and r.) Discuss the difference between the optimal points before and after the interest rate change using the concepts of income and substitution effects in the table format. f. Does the change in the bank's interest rate schedule interfere with Bob's ability to get to his optimal consumption point? Explain. If your answer is yes, calculate his new optimal point. (Hint: you can use the same FOC you derived in part c, but plug in the updated values for we and r.) Discuss the difference between the optimal points before and after the interest rate change using the concepts of income and substitution effects in the table format. 4. (30 points) Leah and Bob work for the same company and earn the same amount of money: y = 230 and y' 140. They pay the same taxes: t = 30 and t' = 8. The market real rate of return is ten percent. a. Plot Leah and Bob's budget constraint, making sure to carefully calculate and label all appropriate points and the slope. Please make the graph large (at least half a page), since you'll be adding more lines to it. b. Leah's utility function is given by In(c) + 3ln(c'). Calculate her optimal consumption point (c, c*) and mark it on the graph above. Is Leah a borrower or a lender? Calculate her savings. c. Bob's utility function is given by 3ln(c) + ln(c'). Calculate his optimal consumption point (CB, CE*) and mark it on the graph above. Is Bob a borrower or a lender? Calculate his savings. d. Due to a recent string of mortgage defaults, Leah and Bob's local bank is increasing the interest rate on borrowing to twenty percent; the lending interest rate remains the same at 10 percent. Update the budget constraint graph to reflect this change (preferably, and for ease of understanding, in a different color). e. Does the change in the bank's interest rate schedule interfere with Leah's ability to get to her optimal consumption point? Explain. If your answer is yes, calculate her new optimal point. (Hint: you can use the same FOC you derived in part b, but plug in the updated values for we and r.) Discuss the difference between the optimal points before and after the interest rate change using the concepts of income and substitution effects in the table format. f. Does the change in the bank's interest rate schedule interfere with Bob's ability to get to his optimal consumption point? Explain. If your answer is yes, calculate his new optimal point. (Hint: you can use the same FOC you derived in part c, but plug in the updated values for we and r.) Discuss the difference between the optimal points before and after the interest rate change using the concepts of income and substitution effects in the table format