Of course, even if there is a constant saving rate, an increase in income will result in an increase in the supply of saving. If the demand for investment is unchanging, then the result is a lower natural interest rate.
The response regarding the saving rate is really an implicit claim that the demand for investment should also rise in proportion to current real income. If that is true, then growing real income and equal saving and investment rates results in the supply of saving and demand for investment increasing in proportion. The natural interest rate would remain unchanged and the amount saved and invested grow together. Spending on consumer goods and capital goods grow in proportion. (I must admit that this is the way I think of dynamic equilibrium.)
And so, this line of criticism naturally suggests that the failure of investment demand to grow at the same rate as real income is characterized as a "decrease" in the demand for investment. With saving supply growing with income and investment demand growing more slowly than real income, the natural interest rate falls.
Interestingly, while the amount saved and invested rise together with income in this scenario, the slower growth in investment drags down the realized saving rate. Both saving and investment become a smaller proportion of real income and real output if the growth of investment demand slows.
Simplifying the analysis by assuming a given level of real income, an increase in the supply of saving combined with a decrease in the demand for investment results in a lower natural interest rate and the amount saved and invested ambiguous. It is, of course, possible that they exactly offset, leaving the amount saved and invested unchanged. (If this is all treated as fractions of real income and real output, then the savings and investment "rates" are unchanged, with both the amount saved and invested growing in proportion to real income and output. However, the natural interest rate is lower.)
If consumer goods and capital goods are each homogeneous, then there is no change in the allocation of resources. The demand for consumer goods and capital goods are unchanged (or are growing in proportion.)
However, capital and consumer goods are not homogeneous. Goods with relatively high interest elasticities of demand (both capital and consumer goods) should expand relative to goods with relatively low interest elasticities of demand (again both capital and consumer goods.) If these conditions are expected to persist, then all sorts of specific capital goods might be constructed whose profitability depend on this particular pattern of demands.
Suppose that rapid growth in one part of the world economy leads to rapid increases in real incomes both in that area and in aggregate. While the consumption of those reaping these gains increases remarkably, it rises less than their incomes. Their savings rates are high, and this pushes up the world saving rate.
Other things being equal, this lowers the natural interest rate. One of the normal effects of this would be a decrease in the quantity of saving supplied as a response to lower interest rate. While this may just dampen the rise in saving by those receiving the large increases in income, it may, and really "should," be expected to lower savings rates in the rest of the world. It becomes cheaper to finance the purchases of new cars, microwaves, pools, porches, home computers, and any number of things.
If this was the entire story, then the world saving rate rises. The lower natural interest rate also stimulates expanded investment expenditure. The production of new capital goods rises, which will allow for increased production of consumer goods in the future--when those who have been socking away these savings finally begin to use them to fund more consumption.
However, suppose that at the same time, wildly optimistic estimates of the benefits of computer technology in enhancing factor productivity are dashed. The demand for investment, especially computer equipment and software, falls off. This decrease in investment demand lowers the natural interest rate even more and at least partially offsets the impact of the greater savings supply.
While the lower natural interest rate may at least partly dampen the enthusiasm for saving by those with the rapidly growing incomes, it should be expected to also further reduce the saving of everyone else. Financing consumer durables is even more attractive.
As for investment, the lower interest rate should partly dampen the decrease in demand for computer equipment and software, but it will also tend to expand the demand for other sorts of capital goods. If purchases of new single family homes are counted as "residential investment," then the lower natural interest rate should be expected to raise both the prices and the production of new single family homes.
If this pattern of demand is expected to persist, it could result in the construction of a variety of specific capital goods aimed at better accommodating the pattern of production to this pattern of demand. If those expectations are wrong, then slower growth in saving supply and more rapid growth in investment demand could result in substantial structural unemployment and losses on specific capital goods.
Yes, it is a "just so" story. I call it "history." There is no reason why saving supply cannot rise at the same time investment demand falls. And there may be historic episodes where both happen to grow rapidly, both more slowly, or investment demand grows more rapidly while saving supply grows more slowly.
Finally, suppose this new "low natural interest rate" pattern of demand and allocation of resources is faced with a new increase in the demand for investment. Sadly, the increase in investment demand is created by an illusion--a speculative bubble, where foolish investors myopically project past increases in housing prices into the future.
I don't want to deny that the Federal Reserve could keep the market interest rate above the natural interest rate. It is almost certain that by creating monetary disequilibrium and falling or slower growth in cash expenditures, the Fed could deter entrepreneurs from making investments that will turn out to be mistakes. But why focus on interest sensitive demand? An entrepreneur who thinks that he has a great idea for a soft drink might be protected from actually carrying out the project only to discover that no one likes the beverage. If it weren't for the Fed causing a recession, he would have sunk a lot of money into a failed project. Specialized nasty tasting beverage production equipment would have been a waste of resources.
My view is that total cash expenditure--Final Sales of Domestic Product--should be kept on a 3 percent growth path and the market should determine interest rates. I have little doubt that temporary changes in market interest rates, and even speculative bubbles, could still lead entrepreneurial error. But those are just one of many possible sources of structural unemployment and losses on specific capital goods. The notion that fixing the level or growth path of some measure of the quantity of money, or worse, manipulation of market interest rates by central banks to prevent or "pop" bubbles, are appropriate policies to avoid these sorts of problems is a mistake.