NEED HELP WITH #2
1) Saving and borrowing: some other cases of budget constraints Tammy is a high school student. She babysits for her neighbors each Saturday evening, and this gives her a stable weekly income. Suppose she is planning ahead for the next 2 weeks and wants to decide how much to consume this week and how much next week. Assume she earns $40 each week, and that at the end of the 2nd week she doesn't want to have any remaining savings or loans. Draw her budget constraint under each of the following scenarios: a. Initially, Tammy is not able to borrow any money, but she can save some by hiding it in her room (what will be the interest rate?) b. Tammy can now borrow money from her parents at 0% interest rate. As before, she can also save at 0% interest rate. C. Now suppose that whenever Tammy saves any money, her brother inevitably finds it and takes it. d. Same case as before, but now her brother is starting to feel guilty, so he only takes half of any saved money he finds in Tammy's room. What is the "interest rate" Tammy will collect on her savings? e. Continuing with this case: suppose Tammy's parents decide to cap the loans they give her, so that they won't lend her more than $20 at any given time (the interest rate is still 0%) f. Now, let's say her brother only needs $10: if he finds her savings he will take half, but only up to $10, and he will leave the rest untouched. 2) Solving intertemporal optimization problems, non-standard budget constraints Next, let's see how we can solve the utility maximization problem for some of the scenarios listed in problem 1. Suppose that Tammy's utility function is U(C1,C2) = 15 Incz + c2 i. Take the graph from part Problem 1.e), and write the budget constraint equation on each relevant segment. Are there possible solutions on all segments? Help Tammy figure out how much to consume in each period in order to maximize her utility. Will she save or borrow any money? If so, how much? [If you are not sure what the budget constraint is at part (e), that's okay just solve the problem for the constraint you found, or for one of the earlier cases, or for some other scenario. Just be sure you draw clearly the budget constraint you are considering] ii. Same instructions, but this time for the situation from part (f) of problem 1. 1) Saving and borrowing: some other cases of budget constraints Tammy is a high school student. She babysits for her neighbors each Saturday evening, and this gives her a stable weekly income. Suppose she is planning ahead for the next 2 weeks and wants to decide how much to consume this week and how much next week. Assume she earns $40 each week, and that at the end of the 2nd week she doesn't want to have any remaining savings or loans. Draw her budget constraint under each of the following scenarios: a. Initially, Tammy is not able to borrow any money, but she can save some by hiding it in her room (what will be the interest rate?) b. Tammy can now borrow money from her parents at 0% interest rate. As before, she can also save at 0% interest rate. C. Now suppose that whenever Tammy saves any money, her brother inevitably finds it and takes it. d. Same case as before, but now her brother is starting to feel guilty, so he only takes half of any saved money he finds in Tammy's room. What is the "interest rate" Tammy will collect on her savings? e. Continuing with this case: suppose Tammy's parents decide to cap the loans they give her, so that they won't lend her more than $20 at any given time (the interest rate is still 0%) f. Now, let's say her brother only needs $10: if he finds her savings he will take half, but only up to $10, and he will leave the rest untouched. 2) Solving intertemporal optimization problems, non-standard budget constraints Next, let's see how we can solve the utility maximization problem for some of the scenarios listed in problem 1. Suppose that Tammy's utility function is U(C1,C2) = 15 Incz + c2 i. Take the graph from part Problem 1.e), and write the budget constraint equation on each relevant segment. Are there possible solutions on all segments? Help Tammy figure out how much to consume in each period in order to maximize her utility. Will she save or borrow any money? If so, how much? [If you are not sure what the budget constraint is at part (e), that's okay just solve the problem for the constraint you found, or for one of the earlier cases, or for some other scenario. Just be sure you draw clearly the budget constraint you are considering] ii. Same instructions, but this time for the situation from part (f) of problem 1
