Growth Modeling: The Asymptotic Decline of Output

From The Solow Growth Model (PDF, 10 pages), unattributed, but the URL leads to Ana Sayfa of Dokuz Eylül University in Turkey:

The Solow Growth Model is a model of capital accumulation in a pure production economy: there are no prices because we are strictly interested in output = real income. Everyone works all the time, so there is no labor/leisure choice. In fact, there is no choice at all: the consumer always saves a fixed portion of income, always works, and owns the firm so collects all “wage” income and profit in the form of all output...

This model, then, is a model that captures the pure impact savings = investment has on the long run standard of living...

Ingredients: Consumers and Firms. All consumers own the firms, so consumers receive all output, and therefore all profit and rent.

Since there is no government (no taxes), there are no imports/exports (no trade), consumers receive everything from the firms, and there are no financial markets, savings is simply investment (the only place consumers can put their “money”, which is actually output, is simply back into the firm)…

Let's take this model that captures the pure impact that "savings = investment" has on the long run standard of living, let's take it and tweak it a tad. Let's NOT suppose there are no financial markets.

Just suppose.

That means there is a little less productive investment than there is savings, so financial savings accumulate. And total spending (consumption plus productive investment) is less than total income. Right away you can see an asymptotic decline because, if we always spend a little less than we receive, then the amount we spend and receive must eventually approach zero. (Factors like inflation and population growth disguise this trend but do not alter it.)

We continue to define spending and income as defined in the Solow model: "Spending" is spending on the production and consumption of output; and "income" is the income generated by the production and consumption of output.

Because financial markets exist, total spending is less than total income. The difference is the interest that accrues to accumulated savings. This difference, this interest, is income to financial markets. To productive markets, it is a cost.


The assumption that financial markets exist has two effects on the Solow Growth Model: It makes growth slower and costs higher. The rate of growth is reduced, because productive investment is reduced. And productive sector costs increase, because income accrues to savings.

Growth is slower and costs are higher, because financial markets exist. Sounds like a stagflation problem, don't you think?. Lucky for us, this is only a model.