Tuesday, June 17, 2008

Intertemporal Consumption and Savings with Interest Rates Not 0

Intertemporal consumption and Savings with Interest Rates Not Zero, or that Intermediation performed by banking is not Zero costs...

This was in response to one of my assignments in Developing Finance class and wanted to at least post the graphs for other stuff.

This is response to a question you raised on my first assignment.

A side point I want to make is: when interest rates rise this will lead some creditors to become debtors. But considering that the transaction cost whether on the supply side or the demand side is greater than zero then the slope of the interest rate line (-(1+r))should be ‘kinked’. Illustrate?

The above diagram is an approximate drawing of the A. Debtor on page 11, unit 1 in handbook. Let me try to label the points in words. The left indifference curve is if the person did not borrow or save and consumed what his endowment was at present horizontal axis and future of the vertical axis. The right indifference curve is what he desires to be at if allowed to borrow at r rate of interest. The left indifference curve should be left and below the right one even if it does not show that way. If the debtor decides to consume less than his present endowment then the line of (-(1+r)) is correct to the left of the left indifference curve. But if the debtor decides to borrow and thus change his consumption to the right indifference curve and we assume he has a transaction cost even if just in time, then the slope would be the same but shifted to the left as illustrated.

In the above I assumed that there was no transaction cost for being a creditor. But if we loosened that theory then the creditors may be facing a disjointed interest rate line also. This is by either transaction costs in savings at least with regard to time and bonuses for becoming savors with one time gifts such as toasters.

Above I am showing a kinked interest rate line for a creditor. As the creditor saves more and more of his present endowment he receives a higher rate of interest.



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