Asking About Prices: A New Approach to Understanding Price Stickiness

Chapter 11: Cost-Based Pricing: Lags from the Chain of Production

Chapter 11 Cost-Based Pricing: Lags from the Chain of Production From little acorns, great oak trees grow. -ANONYMOUS The Theoretical Idea That prices depend on costs hardly qualifies as a new idea. Nor does it, by itself, constitute a theory of price rigidity. It simply says that prices are sticky if costs-presumably marginal costs-are. Since costs primarily depend on other prices (including wages), this statement borders on the tautological: some prices are sticky because others are. Indeed, it has been well known for decades that Keynesian (nominal) rigidity can be rooted in wage stickiness, with prices responding rapidly to wages. However, this book is devoted to theories of price stickiness, not wage stickiness. What takes the theory that prices are based on costs beyond the realm of tautology is the fact that goods pass through several stages of production on the way to their final users. For example, raw wood is milled into lumber, sold to a contractor, and becomes part of a house; iron ore is smelted into steel, which is used to make parts for an automobile; and so on. In his well-known survey of price stickiness, the economist Robert Gordon (1981) took the ancient idea that prices react to costs with a lag and gave it a modern twist. Gordon called attention to "the role of the input-output table in translating prompt price adjustment at the individual level to gradual price adjustment at the aggregate level."l The idea is that, if there are many links in the chain of production, short lags between cost changes and price changes at the level of the individual firm could cumulate into long 198 Asking About Prices lags between, say, money shocks and the eventual reaction of the aggregate price level. The idea is reminiscent of John Taylor's (1980) model of staggered wage contracts, and, shortly after Gordon's paper was published , the economist Olivier Blanchard (1983) provided the requisite formalism and equations. Blanchard's model is not actually based on an input-output table, but rather on a simpler linear chain of production. There are n stages of production, indexed 1, ... n, with stage 0 denoting raw materials and stage n representing final goods. The single input at each stage is the output from the previous stage, and production functions are assumed to be proportional and instantaneous. Hence for each stage i: 11.1 Yit = Yi-l,t + Ci, where y is log output and c; is an unimportant scale term. Prices are fixed for two periods in Blanchard's model. In particular , half of all prices are adjusted in even-numbered periods and half in odd, so the equilibrium pricing relationship for the price of the stage i good is:2 11.2 Pit = O.S Pi-1.t-l + O.S Et [Pi-l,t+l], where p is log price and the expectations operator denotes rational expectations.3 The primary input, which might be thought of as labor, is not produced but is instead supplied as an increasing function of its relative price: 11.3 YOt = b (POt - Pnt ) + et (b;:::: 0), where et is a disturbance term. Finally, the nominal demand for final goods is equal to the money supply: 11.4 Ynt = mt - Pnt· It is clear from the structure of the model that the macroeconomic lag in the adjustment of final-goods prices to the money supply depends on the microeconomic lag at each firm-which is one "period" in Blanchard's model-and the number of stages of pro- Cost-Based Pricing 199 duction, n. Specifically, since each lag in the chain of price adjustment takes either zero or two periods, and there are n/2 of each, full adjustment to a money shock takes n periods. But the time pattern of adjustment is complex and depends on the parameters band n. The chain-of-production idea surely makes intuitive sense. And no one doubts, first, that prices are based on costs (at least to some extent) and, second, that some time elapses between cost changes and price changes. How could it be otherwise? But it is less obvious that Gordon's cumulation hypothesis takes us very far in explaining aggregate price level stickiness-for at least three reasons. First, like so many other theories, this one seems designed to explain the prices of goods, particularly manufactured goods. But production of goods accounts for...