Economics 314 Coursebook, 2009 Jeffrey Parker 12 AGGREGATE SUPPLY WITH STICKY PRICES Chapter 12 Contents A. Topics and Tools............................................................................. 1 B. Understanding Romer's Chapter 6, Part C .............................................2 Romer’s “building blocks” ............................................................................................. 2 Macroeconomic equilibrium with predetermined prices .................................................... 7 Macroeconomic equilibrium with “fixed” prices .............................................................. 8 Evaluation of the Fischer and Taylor models ................................................................ 10 The Caplin-Spulber model .......................................................................................... 11 Mankiw and Reis: sticky information vs. sticky prices .................................................... 12 C. Suggestions for Further Reading ....................................................... 14 Original papers on wage-contracting models .................................................................. 14 Papers on optimal indexing ......................................................................................... 14 Seminal papers on sticky prices .................................................................................... 14 Other theoretical approaches to price adjustment ............................................................ 14 D. Works Cited in Text ........................................................................ 15 A. Topics and Tools Part C of Romer’s Chapter 6 examines four specific models based on the ideas of nominal and real rigidity. The first model (Section 6.9) is one of “predetermined price” contracts that is based on the kind of contracts introduced in a wage context by Fischer (1977). The “fixed-price” model of Section 6.10 uses a slightly different assumption about the nature of price setting to yield quite different macroeconomic dynamics. This model follows the contract structure used by Taylor (1979). Both the Fischer and Taylor models specify that prices are set for fixed periods of time, as happens with periodic wage negotiation or annual catalogs, so-called “time-dependent pricing.” An alternative assumption, explored in Section 6.11, is “state-dependent pricing” in which prices are changed at possibly irregular intervals, de-12 – 2 pending on how far the established price is from the firm’s desired price. Section 6.13 develops the Mankiw-Reis model, in which the firm’s price changing interval is de-termined randomly. Mankiw and Reis (2002) hypothesize that such a model could result from the random arrival of information to any given firm about the underlying inflation rate in the economy. B. Understanding Romer's Chapter 6, Part C Part B of Romer’s chapter examined the incentives of each individual firm in de-ciding whether to change its price or keep it fixed. In Part C, we embed these firms into a macroeconomic model and consider the macroeconomic implications of price stickiness. Romer’s “building blocks” Romer begins in Section 6.8 by developing a dynamic version of the imperfect competition model of Section 6.4. This model is based on utility maximization by households and profit maximization by firms, so its microfoundations are quite com-pletely developed. Most of the elements of this model are familiar, but some take slightly new forms. For example, the utility function (6.59) is a discrete-time lifetime utility function similar to ones we used in the Diamond growth model and the real-business-cycle model. Utility is an “additively separable” sum of utility from consumption and dis-utility from labor. The additivity of the utility function simplifies the analysis by mak-ing the marginal utility of consumption independent of labor and vice versa. The condition V′ > 0 means that more work leads to more disutility (working is disliked), and V″ > 0 implies that the more you work, the greater is the marginal disutility of work. These conditions are the flip-side of an assumption that leisure has positive but diminishing marginal utility. The discount factor in equation (6.59) is written simply as β ∈ (0,1). In earlier chapters we wrote the discount factor as 1/(1 + ρ), where ρ is the marginal rate of time preference. You can think of β as equal to 1/(1 + ρ) if you wish; it is just a more compact notation. Equation (6.61) is the first-order condition relating to the trade-off between con-sumption at time t and labor at time t. It says that the marginal disutility of working (the left-hand side) must equal the marginal utility of the goods that can be bought with an additional unit of work (the right-hand side). The new Keynesian IS curve in equation (6.65) follows directly from the con-sumption Euler equation in log form. As with traditional IS curves, it slopes down-12 – 3 ward in (Y, r) space. This relationship between Y and r depends on future Y, which is quite different than the traditional IS curve, which depended on fiscal policy.1 The theory of the firm in the discussion on pages 312 through 314 is a little tricky. We usually simply assume that each firm maximizes the present value of its stream of profits. Here, the firm is assumed to maximize the utility of its stream of profits to the shareholders. With a competitive credit market, these assumptions are equivalent. To see this, consider Romer’s equation (2.47) in the discussion of the Di-amond model on page 78. This equation applies to the equilibrium between con-sumption in periods 1 and 2. Solving it for 1 + rt + 1 yields () () ()()()1,2, 1 1,11, 2, 12, 11111 .tttttttUCCCrCCUCθ−θ++θ−θ++′+ = +ρ = +ρ = +ρ′ (1) The right-hand equality in equation (1) follows directly from the definition of the util-ity function. In the Diamond model, individuals live for only two periods, so the only relevant comparison is between t and t + 1. The owners of firms in the new Keynesian model are longer-lived, so we must also consider consumption tradeoffs between more distant points in time. If we were to generalize equation (1) to reflect the tradeoff between consumption at time zero and time t, the corresponding equation would be ()()()()01111 .tttsstUCrrUC=′+≡ + = +ρ′∏ (2) Taking the reciprocals of both