On Facebook, someone raised a discussion on the impact of technology on sticky prices. The reasoning is that new technology that increases the amount of information being considered by price-setting agents, and/or delivers the relevant information at a faster rate, will help reduce the amount of time it takes for prices to adjust. If I understand the argument correctly, it mostly boils down to reducing the frictions attached to price arbitrage. If what we mean by sticky prices are non-equilibrium prices, or even the amount of trial-and-error necessary for prices to approach their equilibrium values, then this argument makes sense. But, I’m not convinced that this is the price stickiness that matters. At least, this is how I approach the price friction problem when it comes to, what we can broadly refer to, price level adjustments.

I can’t really offer a formal model. What this means is that my argument might be somewhat confusing, because it’s not exactly crystal clear to me, and I haven’t had the time to formalize it and think it through (see “Intuition and Math“). My main intention is, actually, to help me think through the problem and, if anybody is interested, discussing it. If you want to skip the introductory paragraphs, that make up a good chunk of this post — to introduce the reader to the problem —, skip the next four paragraphs (to the paragraph beginning with, “My intuition is…”).

To clarify what I mean by price friction within the context of price level adjustments, think about the issue in terms of changes in the demand for money. If the aggregate demand for money rises, the price level will fall. This is so, because if there is an increase in the demand for money its value will rise — we demand more, because the benefits accrued from holding it increase. This implies the value of money relative to other goods, all else being equal, will increase — everything else, in terms of money, will be worth less. In a frictionless world, when the demand for money rises all other prices will adjust to reflect the new relative valuations, and peoples’ real cash balances (the real value of their money) will increase (again, because other goods, in terms of money, have become cheaper) — this is what some economists call the “Pigou effect.”

However, if prices are sticky, we have to consider what happens if prices don’t adjust. This is essentially the consideration that drives monetary (dis)equilibrium theory (see “Theory of Monetary Gluts“). If prices don’t adjust when increasing their cash balances a shortage of money results, which can also be referred to as a general glut. To see why this is, assume the quantity of money is fixed. If the demand for money rises, people will hold on to their dollars instead of spending them. The amount of money being substituted for goods falls, and some subset of non-monetary goods will be essentially priced out of the market. Consequently, most economists — at least, those who believe sticky prices are empirically relevant — advocate increasing the quantity supplied of money, maintaining the price level.

The next question is, why would prices be sticky? Like I said, I’ve only taken a superficial look at the literature. But, the explanations I have read have never been too persuasive. For example, Leland Yeager, in “The Significance of Monetary Equilibrium,” contextualizes it almost as a game, where no firm wants to lower their prices first. But, the firm, in these cases, really only has three choices: (1) it can produce an excess amount of widgets; (2) it can reduce the amount of widgets it produces; or (3) it can reduce the price of its widgets. Inaction essentially implies that the firm will take a loss, so it doesn’t make sense to me that a firm hold out, and suffer excessive losses, out of the expectation of foregone benefits. The case, to me, seems the exact opposite: waiting carries a higher opportunity cost.

In “A Sticky-Price Manifesto,” Greg Mankiw and Larry Ball discuss some theories of price stickiness. One theory is the menu cost theory. Menu costs are the costs associated with price changes. The name comes from the costs of printing new menus to advertise the new, lower prices. Specifically, then, if the costs of the price adjustment are higher than the losses associated with maintaining the existing set of prices, firms will opt for the latter choice. They also propose a theory that is essentially the same as Yeager’s. But they frame it as an externality, in that a firm can hold-out from reducing its prices in the hope that other firms will reduce theirs instead — even explained this way, the real demand for the hold-out firm’s product will not shift outward once real cash balances adjust, rather firms with the cheaper product will sell more than the hold-out.

My intuition is that none of these explanations are really satisfactory. Rather than seeing it as a “frictions” problem, or a problem that should be assuaged over time, what if price rigidity is of a much more permanent nature? This would be similar in conclusion to Keynes’ own theory of “wage rigidity” — where the real wage can’t fall, because a decline in real wages will cause a decline in prices, maintaining real wages —, since the prediction is a permanent unemployment equilibrium. Rather than focus on wages, however, I assume that the fall in demand will impact firms asymmetrically, such that one firm will be much more impacted than others.

Suppose an industry with n firms is impacted by a fall in demand, caused by a rise in the demand for money. To make the model clearer, let’s take it to the extreme and assume that only one firm suffers the demand shortfall, such that n–1 firms can continue to sell the same quantity of output at the same price. Further, suppose that the distribution of inputs to firms is symmetric, implying that the higher the value of n is, the less the one firm can influence the price of inputs (i.e. if all firms reduce their demand for inputs, the price of inputs will fall). The result is that the one firm has to reduce its output, and the inputs that otherwise would have been purchased are now idle.

If this only happens to one industry, out of many, it might not seem significant. But, what if this is characteristic of many, or most, industries? The assumptions seem reasonable. In most sectors there are firms of different sizes, and changes in demand will impact firms differently. If the affected firm can’t influence the price of inputs, they’ll be forced to reduce output. This is what the theory of monetary (dis)equilibrium predicts. For output to be restored, the price level has to fall, or the quantity supplied of money has to increase.

The problem is not sector specific, even if only some out of many are affected by the demand shortage. Unless the prices of idle inputs falls to zero — at the extreme —, output will fall. We may be inclined to argue that if the demand for a firm’s output falls, it must be that that output is no longer valued (even though other firms can charge the original price and earn a profit). Since there is a shortage of money, however, there is no way that demand can be transferred. It’s not as if widget x has been substituted for widget y. The only reason widget x isn’t being purchased is because it has been priced out of the market. This continues to be true for whatever alternative kind of widgets could be produced with that idle part of the capital stock.

In my framework, the problem of price rigidity is a coordination failure. It assumes that money is non-neutral, and therefore changes in the demand for money will impact firms asymmetrically. At the extreme, a firm with no power to impact input prices (the inputs it demands) will have to cut output, because the alternative choice — a price reduction — isn’t possible (if the price of the input stays fixed and the price of the output falls, the profit margin will fall, and in this case we assume it turns negative). As a result, there is a permanent unemployment equilibrium. This theory loses relevance the more symmetric the demand shortfall is and/or the greater the market power of a particular firm. But, it’s distinct from information problems, where the problem is inadequate arbitrage (something that could be solved with better technology). That is, it’s not so much about “frictions” as much as it is about a failure of the pricing process (that has a potential private solution in the form of a flexible private banking system).