Thursday, December 17, 2009

The effect of loans in my alternative money supply model

As outlined in the previous post, the flow of money through the economy has a complex structure that can be described as two large cycles with a limited number of flows between the two. That description is obviously a simple one, and in this and possibly later posts I will flesh this idea out with more detailed descriptions of phenomena occurring within these cycles. This post will focus on loans made to wage earners.

Consumers typically hold their wealth in bank accounts. The bank accounts are highly secure, allowing the consumer to claim with certainty that the money they have deposited will remain available to them unless it is spent, even though the bank will loan out the vast majority of its deposits. A bank with a large pool of depositors combines the statistical predictability of withdrawals, FDIC insurance, and simple rules limiting withdrawal to ensure that sufficient funds are always on hand to to meet the withdrawal demands. Moreover, Federal rules require an even larger reserve be kept than what banks would probably prefer.

Of any given paycheck received by a wage earner, that wage earner is likely to deposit the majority of the check at the beginning of the month. By the end of the month, the wage earner will have spent most of what was earned, perhaps even all or more than what was earned. Thus, the wage earner who deposits money seems to treat this money as part of his "budget" for goods in that time frame. Other individuals who receive a portion of the original paycheck are likely to deal with the same or a different bank and deposit what was just withdrawn. As the aggregate of all banking activity is large, this creates a space in which banks and their clients interact in a way that is best described as the rearrangement of funds from one account to another.

Those funds which are deposited are available to the bank to lend out to other entities for various purposes. The way the loan interacts with the rest of the money supply depends on what the loan is spent on, but all loans also have common properties. It should be noted that because of the certainty of withdrawal outlined above, funds used to create loans do not alter the behavior of the many small consumer accounts from which the loan money is drawn. The money in the account may not actually be there, but because of the certainty described above, the consumer acts as if the money is still there.

All loans alter the behavior of the individuals receiving them in two key ways. First, it allows large purchases to occur in the absence of large savings accounts. Therefore, the demand for these goods is increased by the existence of loans. These demand increases will tend to increase prices as well, especially in markets that are naturally scarce (such as real estate). Second, loans have a repayment requirement, which places a long term debt burden on the borrower. This burden is expressed through a reduction in available income. As these loans are taken by consumers, the drag that repayment creates on purchasing power reduces G (see my previous post for a definition of G).

Loans can be differentiated into two categories based on the type of good that was purchased with the loan. A purchase of real property with money from a bank represents an injection from one part of the financial services sector to another. A purchase of some consumer good or capital equipment represents an injection from the financial services sector into the wage sector. When loans are available for these purchases, they also occur earlier and with greater frequency.

Take LC as loans for capital or large consumer purchases, G as the change in flow from the financial services sector to the wage sector, and IL as the total of payments on loans outstanding. In a given time period the following relationship holds:

LC = IL + G

Absent is the amount in loans for purchasing of real estate, LR. Because this quantity of money does not cross sector, it is not represented. However, the volume of these loans still contribute to the interest paid function.

A salient question is then to ask the question: Under what conditions is LC greater than IL?

For sake of simplicity, I'll treat each loan as a fixed interest rate (i) loan with the same number of total payments (n) and not compound interest. In a given period, t, the new obligations for repayment are given as (1 + i)(LC + LR). Thus, assuming for accounting purposes that the first payment is taken immediately, we can see the total obligations represented by IR as the sum of term payments on all loans still outstanding:

[1 + i(t)] * [LC(t) + LR(t)] / n + [1 + i(t-1)] * [LC(t-1) + LR(t-1)] / n + ... + [1 + i(t-n+1)] * [LC(t-n+1) + LR(t-n+1)] / n = IL

(This function counts from 0 to n-1, but I could just as easily set it up to be from 1 to n. At this juncture I haven't found any compelling reason for either).

The two factors that determine whether IL is greater than LC are the rate of growth of total loans and the ratio of LC to LR. At any given loan growth rate, there exists a corresponding ratio of LC to LR that gives IL = LC. From this point, if LC/LR increases, LC exceeds IL; if LC/LR decreases, IL exceeds LC. Similarly, a higher rate of loan growth will push LC above IL.

In order to conjecture as to the extent that loans are beneficial to the society, the above results can be analyzed in the context of the business disincentive/shortage spectrum outlined previously. Loans only contribute to G so long as the quantity of lending is increasing. Even when the lending quantity is increasing, G can be negative when the LC/LR ratio is low. Therefore, in a system experiencing shortage, LR should be encouraged and/or the quantity of lending should be decreased or braked. Similarly, in a system experiencing disincentive, LC should be encouraged and/or the quantity of lending should be increased or accelerated.

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