ments with higher levels of risk that cannot be reduced by diversification have higher expected returns than less risky investments. Tax differences across jurisdictions, and other market frictions, can also generate differences in rates of return across places.

The expected rate of return also depends on consumer preferences, which determine the supply of savings. When the aggregate supply of savings increases, for example because in an older society more people hold substantial retirement savings, the demand for existing assets rises. This puts upward pressure on asset prices and lowers expected returns, thereby encouraging greater investment in physical capital. In the foregoing example of a machine, if the expected rate of return were to fall unexpectedly from 5 percent to 4.5 percent, then the price of existing machines would immediately increase from $200 to $222 (= $10/.045). The higher price would encourage additional investment in new machines, which would continue until the cost of producing them rose or the value of their output fell to the point where the expected return on an incremental investment or the purchase of an existing machine was 4.5 percent.

Population aging is a predictable process that is unlikely to cause sudden changes in asset prices, but it may affect the time pattern of returns that investors expect to earn in the future. Investors may, for example, expect to earn different rates of return in different years. Continuing with the previous example, imagine that investors expect the rate of return on the machine to be 5 percent per year for the next 5 years, then to fall to 4.5 percent annually for the 5 years after that, and then to stay at 4 percent for the indefinite future, reflecting the higher amounts of per capita savings held by the older population at that time. The price of the machine would rise each year during the first 10 years, so that the sum of the $10 profit from the machine’s production, plus the capital gain, would generate the return demanded by investors. It would reach $250 (= $10/.04) in year 10. Table 8-A-1 shows the price path that would provide investors with a total return—the combination of the $10 profit and the associated capital gain on owning the machine—that would equal their required return. In year 9, for example, when investors require a 4.5 percent return, the price would begin at $248.80, and the profit of $10, plus the $1.20 appreciation of the machine, would generate a return of 4.5 percent: [(10 + 1.20)/248.80 = .045]. Note that the price path rises gradually over time and levels off after year 10, at which point returns remain constant forever.



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