consider a consumer who earns incomeeach month. She has to spendeach 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 ateach month and the monthly interest rate charged to borrowers is . Bothandare 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

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

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

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 k(capital), 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 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.

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

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