For the following questions, consider a consumer who earns income y each month. She has to spend c each month on essential goods, such as food and shelter. She has no access to reliable savings, so she must spend her entire income each month. The consumer is interested in taking a loan to finance a large purchase. The cost of capital for banks is fixed at k each month and the monthly interest rate charged to borrowers is r. Both K and r are equal to one plus the interest rate as we are used to seeing it - e.g., if a loan charges 5% monthly interest, then r = 1.05.

(1) What is the largest nonessential purchase that the consumer can make each month without borrowing? Express it as a function of y and c.

(2) Under the zero profit condition for lenders (i.e. banks), what will the interest rate r charged to borrowers be? Assume there is no risk of default and no fixed costs and express it as a function of k, y and c.

Now, assume that the borrower must repay the loan in a single payment before the end of the month (i.e. before they earn more income). The borrower can only use one month's income for repayment, since they are unable to save.

(3) What is the borrower's monthly disposable income (exclusive of essential purchases) with a loan, under the assumptions mentioned above? Express your answer as a function of y, c, k, and the loan amount L.

Please be careful to put ^"*^" between mathematical expressions if you intend them to be a product. ex: put "A*x" instead of "Ax"

(4) Would the borrower take out a one month loan under the assumptions sketched out above (i.e. the loan needs to be paid back in a single payment before the end of the month, with only one month's income used for repayment)?

oIt depends

oNo

oYes

Now assume the borrower can take a two month loan. For a tow month loan:

A loan of size L is made.

First month interest is calculated on the total amount L using the monthly interest rate.

The first repayment is subtracted from the total repayment burden (including second month interest) in the first month.

Second month interest (again using the monthly rate) is calculated on what's left of the loan and interest AFTER the first payment.

The second repayment should equal whatever is left to be repaid (including second month interest) in the second month.

(5) Assume the borrower repays the same amount m in both months. Express the payment amount m in terms of L and K. Remember to use an asterisk * between two terms that you are multiplying. For instance, m multiplied by r would need to be inputted as m*r.

(6) Under the same set up, what is the largest m that the borrower can afford to pay back each month? Do not include the loan itself in your answer and express it as a function of y and c.

(7) Using your answers to questions 5 and 6, what is the largest loan L that the borrower can afford to take out under this set up? Remember to use an asterisk * between two terms that you are multiplying. For instance, m multiplied by r would need to be inputted as m*r.

(8) Under this set up, does a loan increase disposable income for the first period?

oIt depends

oNo

oYes

(9) Will allowing a borrower who likes to smooth consumption to take out a longer term loan encourage or discourage borrowing for a given loan size?

oDiscourage

oEncourage