Quantity

FIGIJRE 6.3 A representative firms incentive to change its price in response to a fall in aggregate output (from D. Romer, 1993a)

If the firm changes its price, it produces at the point where marginal cost and marginal revenue are equal (Point C). The area of the shaded triangle in the diagram shows the additional profits to be gained from reducing price and increasing quantity produced. For the firm to be willing to hold its price fixed, the area of the triangle must be small.

The diagram reveals a crucial point: the firms incentive to reduce its price may be small even if it is harmed greatly by the fall in demand. The firm would prefer to face the original, higher demand curve, but of course it can only choose a point on the new demand curve. This is an example of the aggregate demand externality described in Section 6.6: the representative firm is harmed by the failure of other firms to cut their prices in the face of the fall in the money supply, just as it is harmed in Section 6.6 by a decision by all firms to raise their prices. As a result, the firm may find that the gain from reducing its price is small even if the shift in its demand curve is large. Thus there is no contradiction between the view that recessions have large costs and the hypothesis that they are caused by falls in aggregate demand and small barriers to price adjustment.

It is not possible, however, to proceed further using a purely diagrammatic analysis. To answer the question of whether the firms incentive to change its price is likely to be more or less than the menu cost for plausible cases, we must turn to a specific model and find the incentive for price adjustment for reasonable parameter values.

(6.84)

JVf / p. \ I-) / /f N(1+")/"

where the second line uses the fact that Y = M fP.We know from our earher analysis of this model that the profit-maximizing real price in the absence of the menu cost is 77/(77 -1) times marginal cost, or [77/(77 - lM/P)" (see [6.44[). It follows that the equilibrium when prices are flexible occurs when [77/(77 - DKM/P)/" = 1, or M/P = [(77 - l)/77]- (see [6.46]).

We want to find the condition for unchanged nominal prices to be a Nash equilibrium in the face of a departure of M from its expected value. That is, we want to find the condition under which, if aU other firms do not adjust their prices, a representative firm will not want to pay the menu cost and adjust its own price. This condition is wadj - wfixed < Z, where wadi is the representative firms profits if it adjusts its price to the new profit-maximizing level and other firms do not, ttfixed is its profits if no prices change, and Z is the menu cost. Thus we need to find these two profit levels.

Before proceeding, it is useful to have an idea of what value of the menu cost is plausible. The flexible-price equilibrium is symmetric, with each firms real revenue equal to aggregate output, Y. A menu cost that exceeds 1% of this quantity seems highly implausible: for most firms, the cost of a policy of much more frequent price adjustment (for example by simple indexation schemes) are almost surely much less than 1% of revenue. A menu cost of a few hundredths of a percent of revenue, on the other hand, does not seem unreasonable.

We can now turn to the profit calculations. Initially all firms are charging the same price, and by assumption, other firms do not change their prices. Thus if firm z does not adjust its price, we have Pt = P. Substituting this into (6.84) yields

™d = J-(p) ¹.85)

If the firm does adjust its price, it sets it to the profit-maximizing value, [77/(77 - / \ Substituting this into (6.84) yields

A Quantitative Example

As a baseUne case, we use the model of imperfect competition of Section 6.6. RecaU that in that model, firm zs real profit income equals the quantity sold, Y{Pi IP)~i, times price minus cost, / ) - (W/P) (see [6.37]). In addition, labor-market equilibrium requires that the real wage equals ", where v=l/(y-l) is the elasticity of labor supply (see [6.43]). Thus,

r,-l

\p) \p) U-i/

(6.86)

It is straightforward to check that ttadj and tthxed are equal when M/P equals its flexible-price equilibrium value, and that otherwise ttadj is greater

than ttfixed-

To find the firms incentive to change its price, we need values for 17 and p. Since labor supply appears relatively inelastic, consider = 0.1. Suppose also that 17 = 5, which implies that price is 1.25 times marginal cost. These parameter values imply that the flexible-price level of output is Y* = [(17 - II/t)]" 0.978. Now consider a firms incentive to adjust its price in response to a 3% fall in M with other prices unchanged. Substituting p = 0.1, t) = 5, and = 0.97 * into(6.85) and(6.86)yields 77-ADj-77FixED = 0.253.

Since y* is about 1, this calculation implies that the representative firms incentive to pay the menu cost in response to a 3% change in output is about a quarter of revenue. No plausible cost of price adjustment can prevent firms from changing their prices in the face of this incentive. Thus, in this setting firms adjust their prices in the face of all but the smallest shocks, and money is virtually neutral.

The source of the difficulty lies in the labor market. The labor market clears, and labor supply is relatively inelastic. Thus, as in Case 2 of Section 5.4, the real wage falls considerably when aggregate output falls. Producers costs are therefore very low, and thus they have a strong incentive to cut their prices and raise output. But this means that unchanged nominal prices cannot be an equilibrium.

6.12 The Need for Real Rigidity

General Considerations

Consider again a firm that is deciding whether to change its price in the face of a fall in aggregate demand with other prices held fixed. Figure 6.4 shows

Although ttadj - tthxed is sensitive to the values of v and r], there are no remotely reasonable values that imply that the mcentive for price adjustment is small. Consider, for example, = 3 (implying a markup of 5()%) and i- = 1 / 3. Even with these extreme values, the incentive to pay the menu cost is 0.8% of the flexible-price level of revenue for a 3% fall in output, and 2.4% for a 5% fall. Even though these incentives are much smaller than those in the baseline calculation, they still swamp any plausible cost of changing prices.

-It is not possible to avoid the problem by assuming that the cost of adjustment applies to wages rather than prices. In this case, the incentive to cut prices would indeed be low. But the incentive to cut wages would be high: firms (which could greatly reduce their labor costs) and workers (who could greatly increase their hours of work) would bid wages down.