How Deteriorating Highways Cause Deteriorating Wages: Musings on the Importance of Transaction Costs

Much of my work as an economist is built upon the insight of a book written in 1826 by Johann Heinrich von Thunen, called “Der Isolierte Staat”, which is translated, “The Isolated State”. In it, he presented a model of land use that suggested where various crops would need to be produced, given the cost of transportation of the crop to market.

Deteriorating roadAs I was thinking about von Thunen’s theory, it occurred to me that when used in conjunction with how the wage rate is set in a market economy — equal to the value of the marginal product of labor — it provided insight into how a deteriorating highway infrastructure — as we have in the United States — could explain in part the wage stagnation. My point in what follows is not that it explains all wage stagnation, or even a large part of wage stagnation, but only that it can be seen from a theoretical standpoint to explain some wage stagnation.

In a simple model, revenue, R, might be a function of the market price, p minus t, the transport cost, times a function of labor, L.

R = (p – t) f(L,z)

For simplicity, assume a Cobb-Douglas function, with a < 1 as the exponent on labor. R = (p - t) (L^a) The wage, given by the marginal cost of labor, which is the first derivative of the revenue function with respect to L, is given by w = (p - t) a (L^(1-a)) This shows that wages fall as transport costs rise. As an example, let t = 0.1p. A 10% rise in transport costs makes t = 0.11p, which means that wages have dropped from 0.9 p a (L^(1-a)) to 0.89 p a (L^(1-a)), which is a drop of 1.11%. But if t = 0.5 p -- that is, transportation is a very large component of the end price, then a 10% rise in transport costs means that wages drop from 0.5 p a (L^(1-a)) to 0.45 p a (L^(1-a)), which is a 10% drop. If transport costs rose by 30%, then this would drop to 0.35 p a (L^(1-a)), which is a 30% drop in wages. So to consider the impact of poor highway infrastructure, we just have to compare costs for the good infrastructure vs. the costs for the poor infrastructure, alongside the proportion of transport costs in the final market price. It seems that one simple conclusion is that manufacturing wages would be hurt a lot, while information technology wages would not be hurt so much. A more complete model would have included other inputs into production which themselves would need transporting, and therefore would have higher costs with poor infrastructure. I decided against including this in the model, because it would have required some more complicated mathematics in optimizing the amount purchased, and would have given a second order impact on wages through reducing the optimal quantity of purchased input. Economists have written much about transaction costs. I am afraid that I am relatively new to the literature, and therefore will not be using the term probably as it has become more rigorously defined by practitioners. Instead, I use the term to include things like transportation costs, administrative costs (e.g., costs of filling out and processing, as might be experienced in the medical field with insurance claims), legal costs, information gathering costs, etc. We can see that the simple model just presented helps us consider not just the impact of transportation costs on wages, but the impact of all transaction costs. In a recent article in Time magazine called "Bitter Pill: Why Medical Bills are Killing Us“, Steven Brill points to high administrative costs of the American medical system, and how that is making us all worse off. While some transaction costs can be controlled by companies or by social customs, most of them need government intervention, either through public investment or through establishing laws that serve to improve efficiency of transactions, thus reducing costs.

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