Asking About Prices: A New Approach to Understanding Price Stickiness

Chapter 13: Costs of Adjusting Prices

Chapter 13 Costs of Adjusting Prices The Theory of Adjustment Costs: Two Variants Among the simpler reasons why prices might be sticky is the idea that it is costly for firms to change their prices. Clearly, a profitmaximizing firm facing such adjustment costs will change its prices less often than an otherwise identical firm without such costs. Adjustment costs for prices are typically modeled in one of two ways. In the first variant, adjustment costs are convex and, where explicit solutions are needed, quadratic. The best-known example is by the economist Julio Rotemberg (1982). In his model, firms minimize the expected discounted present value of: Here p1 is the price that equates marginal revenue with marginal production costs, and is thus the price the firm would select in the absence of adjustment costs. The second term in 13.1 is the cost a firm incurs when changing its price. Rotemberg shows that the time path of prices takes the form: where tpt+j is the (rational) expectation, formulated at time t, of what p* will be at time t + j. In this expression, r denotes the firm's Costs ofAdjusting Prices 227 discount rate and a is the stable root of the following quadratic equation, which arises frequently in rational expectations models: 13.3 Z2 - [(1 ; r) + (2 + r)] z + (l + r) = O. The implication of equation 13.2 is that actual prices adjust sluggishly -specifically, with a geometric distributed lag-toward their long-run level. Rotemberg combines this microeconomic model of gradual price adjustment with a simple macroeconomic model in which the money supply drives aggregate demand, draws some implications, and tests the hypothesis of instantaneous price adjustment. While he rejects that hypothesis, there are problems with some of the other estimated parameters of his model. The quadratic cost assumption appears to have been borrowed uncritically from the literature on the costs of adjusting physical inputs.! But the analogy between physical adjustments and price adjustments is strained. Adjustment costs for physical inputs (for example, capital stock) are alleged to arise from such things as installation costs and disruptions in the production process. It seems reasonable to suppose that such costs are an increasing function of the size of the input change. The assumption that adjustment costs rise at an increasing rate is more dubious, but at least it is not totally implausible. However, changing a price does not disrupt activities on the factory floor. And it is hard to see why the cost of "installing" a price increase should be quadratic in the size of the price hike. Is it really four times as costly to change a price by twice as much? An alternative way to model adjustment costs is as a lump sum that must be paid any time the firm changes its price, namely: 13.4 Adjustment costs = f (a constant) =0 if ~p #: 0 if ~p = o. Thus, changing a price by a dollar costs the same as changing it by a nickel. Such adjustment costs have come to be called "menu costs" because the expense of printing new menus is the clearest example. The presence of menu costs can give rise to an optimal pricing strategy known as an (S,s) rule.2 Say a firm faces positive 228 Asking About Prices (though uncertain) aggregate inflation. If the firm keeps its own price constant, its real price will tend to fall over time at a stochastic rate. A firm pursuing an (S,s) rule waits until its real price reaches some lower threshold s, whereupon it instantaneously adjusts its nominal price so that its real price returns to the upper bound S.3 Until the work of economist Gregory Mankiw (1985), menu costs were thought to be too small to rationalize any substantial degree of price rigidity. But Mankiw pointed out that, because profit functions are flat near their optimum, even small menu costs can lead to large deviations between actual and (first-best) equilibrium prices.4 In Mankiw's model, a monopoly firm has constant marginal production costs in real terms and faces a downward-sloping demand curve. The standard solution equates real marginal cost to real marginal revenue, leading to an equilibrium real price p*. Nominal variables are proportional to real variables; think of the constant of proportionality as being nominal GDP, Y. The wrinkle in Mankiw's model is its assumption of nominal price rigidity: The firm must...