There are two periods, this year and next year. John receives his income and und

Question

There are two periods, this year and next year. John receives his income and undertakes all his expenditures at the end of each year. Let Y1 denote his income at the end of this year and Y2 denote his income at the end of next year. And let E1 denote his expenditure at the end of this year and E2denote his expenditure at the end of next year. At the end of this year he will receive $100,000 in income, and at the end of next year, he will receive $105,000 in income. At the end of this year, he can lend money at a rate of interest of 5%, which is to be paid back at the end of next year, or he can borrow money at the rate of interest of 10%, which he must pay back by the end of next year. He starts this year with nothing in the bank and ends next year with nothing in the bank. Draw his budget constraint in E1 - E2 space. (Hint: He has the option of spending all of this year's income when he receives it, and all of next year's income when he receives it).

Explanation / Answer

If the required reserve ratio is 10 percent, then starting with new reserves of, say, $1,000, the most a bank can lend is $900, since it must keep $100 as reserves against the deposit it simultaneously sets up. When the borrower writes a check against this amount in his bank A, the payee deposits it in his bank B. Each new demand deposit that a bank receives creates an equal amount of new reserves. Bank B will now have additional reserves of $900, of which it must keep $90 in reserves, so it can lend out only $810. The total of new loans the banking system as a whole grants in this example will be ten times the initial amount of excess reserve, or $9,000: 900 + 810 + 729 + 656.1 + 590.5, and so on.

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