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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This is a mathematical error. The PIPO case is the building block for all capital theory, from which its other familiar formulae are derived by summation. Discounted cash flow, sinking fund, compounded cash flow, installment plan factors, capitalization in perpetuity, internal rate of return ... all can be derived, jointly or separately, as summations of geometrical progressions of PIPO cases. What is true for the basic element is likely to hold also for the summations. Above (Section III.C), I pointed out how Faustmann's formula, ostensibly dealing with timber growth, can be adapted to deal with all capital assets, with any time-patterns of inputs and outputs whatsoever.

To respond to the error of isolating the PIPO case, the writer has published a set of models showing how to replicate Wicksell's grape-juice model with depreciating assets, or with a constant-valued asset of finite lifespan (Gaffney 1976). The last, the "cow-sow model," is the easiest to grasp and requires little mathematics or capital theory. A cow is assumed to yield a constant milk flow over 10 years, then suddenly be slaughtered for the hide and meat, which are sold for exactly the original cost of birthing and weaning. There is a herd of cows whose ages are staggered. Cut the lifespan to five years, and the ratio of cows (capital) to the costs of slaughter and birthing (labor) is halved. Let each cow require a fixed complement of land, and the ratio of land to labor is likewise halved.

The "clean sock" model is even simpler, more homely and intuitive. To have a clean pair of socks every morning, I can have one pair of socks and wash them by hand every night. (Some can recall that situation, as soldiers or students.) If I choose to save labor by washing once a week, I will need seven pairs of socks, with added storage space, a hamper, a washer, and so on. Baumol (1965) makes a similar point, mutatis mutandis, with his cash flow model.

Perhaps Gaffney, like Faustmann, published in the wrong place at the wrong time, for his findings went unnoticed by the macro economists of his day. Or perhaps Gaffney got it wrong: That is for others to judge.

VI

Henry George

GEORGE ON CAPITAL THEORY is best forgotten. He is best known for his observations on land ([1879] 1938). The gist of Progress and Poverty is that land markets function badly, keeping the best lands from their highest uses and creating an artificial scarcity. He likens this to a universal cartel. George's goal is to break the cartel, thus creating jobs, raising wage rates, and raising production and living standards.

We find in Progress and Poverty three major reasons why land markets (absent land-value taxation) perform badly. One is "land speculation," conceived as "holding for the rise" and, by strong implication, as a "store of value" without regard to current use. A second is the appetite of the rich for land as an item of consumption for recreation, for amenity, and for show, as exemplified then by English noblemen's "deer parks," and today by the vast manorial holdings of rich Americans in once-rural counties, marina space for their mega yachts, airspace for their private planes, urban land for grounds around their mansions, trophy golf courses and polo fields, hunting clubs, and so on. A third is that our Solons base taxes on using and improving land, with hardly any on just holding land. The "excess burden" of such taxation takes the form of underusing land. Gaffney (2006) has undertaken to show this excess burden in terms of the capital theory that George lacked.