consider a consumer who earns income each month. person has to spend each month on essential goods, such as food and personlter. person has no access to reliable savings, so person 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 each month and the monthly interest rate charged to borrowers is . Both and 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 = 1.05

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

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

A loan of size L is made. First month interest is calculated on the total amount L by use of the monthly interest rate. The first repayment is subtracted from the total repayment burden (including first month interest) in the first month. Second month interest (again using the monthly rate) is calculated on whats 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.

(Q) Assume the borrower repays the same amount m in both months. Express the payment amount m in terms of L and(capital k )

(Q)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"

(Q) Using your answers to the previus questions, what is the largest loan L that the borrower can afford to take out under this set up?