Keeping land in capital theory: Ricardo, Faustmann, Wicksell and George

American Journal of Economics and Sociology, The,  Jan, 2008  by Mason Gaffney

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C. Site Rent Rises as Interest Rates Fall

This is a most important result, one that is flouted daily in the business press, in academic literature, and in pleas to redistribute wealth and income from rich to poor by lowering interest rates. In the two-factor world of neoclassical economists, land is just another form of capital; by implication, rents and interest rates must move in sympathy. This has become the working assumption behind many public policies, some introduced from the "left" and some from the "right," but equally mistaken.

When interest rates rise, site rents fall. Equation (2) tells us there are two reasons for this. The more obvious reason is that P, the initial planting cost, is compounded forward to year n, using a market rate of interest, before being subtracted from S (stumpage) in year n.

The second reason is less obvious, but equally weighty and general: The SFF is also a decreasing function of i. This is not obvious because. both the numerator and denominator of the SFF are increasing functions of i. Both approach zero as i approaches zero, so we cannot demonstrate the point by the easy reductio ad extremum of letting i equal zero. Rather, we can tabulate values of the SFF to show how it varies with i. It approaches a limit of 1/n as i [right arrow] 0. I begin with very low values of i, so the top row of Table 2 makes the point. (1) Note that the values are rounded.

D. When to Terminate Investment Cycles

The best forest sites, the ones that are "warm, wet, and fiat," are where timber grows fastest, and where succeeding crops may be replanted soonest. Faustmann therefore focused on finding the optimal harvest time, to maximize site rent. This turns out to be the year when the value of timber's current annual growth just covers the sum of interest on the stumpage (S) and the site rent (B). (Gaffney 1957 covers the interesting problem of simultaneously finding the highest and best value of B while also using it to determine itself.)

From Table 2, when n = 50 and i= 5 percent or more, the SFF is negligible compared with interest on S. Practical foresters often just ignore it. However, when n = 10 and i = 5 percent, the SFF is 8 percent, and plays a larger role than i in determining harvest dates. A great deal of timber now matures in less than 20 years, especially in the southeastern United States, where sites are "warm, wet, and flat," and the Southern yellow pine thrives.

When the interest rate falls, easing the pressure to harvest mature timber, site rent rises, partially offsetting and tempering the first effect. So the net effect of interest rates on harvest times is much weaker than the simpler analysis, still found in textbooks, would indicate.

But replacement analysis concerns much more than timber. The greater practical role of site rent is in determining when to clear aged buildings and renew the site. Here there is no salvage value, but only a weak and dying cash flow or service flow. Ratcliff (1949) and Gaffney (1964, 1969) have addressed this case.