New Keynesian Economics: Mankiw’s menu cost model

New Keynesian Economics argue that menu costs are the reason for price stickiness. Price stickiness, the suboptimal adjustment of prices in response to demand shocks, can result in business cycles. Gregory Mankiw proved in 1985 in his article “Small Menu Costs and Large Business Cycles: A Macroeconomic Model of Monopoly” that sticky prices can be both privately efficient and socially inefficient. In fact, as Mankiw points out, even small menu costs can cause large welfare losses.

Mankiw uses a static model of a monopoly firm’s pricing decision, which starts by setting its price in advance and changes it ex post, but incurring in a small menu cost. The monopoly faces a constant cost function and an inverse demand function:

C = kqN

where

C: total nominal cost of production

q: quantity produced

k: constant

P = f(q)N

where

P: nominal price

N is a nominal scale variable, which denotes the exogenous level of aggregate demand. It can be regarded, for instance, as the overall price level. C and P increase proportionally to the level of nominal demand N.

Now, let c = C/N and p = P/N, which will turn the firm’s problem independent of aggregate demand:

c = kq

p = f(q)

In the figure below, we see the producer surplus (profits earned by the firm), equal to the rectangle between k and p_m. On the other hand, the excess value over the price paid represents consumer surplus, the triangle above profits. Total surplus, which represents welfare, is the sum of consumer and producer surplus.

The firm needs to set its price one period ahead based on expectations about future aggregate demand, being this price p_mN^e. If expectations are correct ex post, the observed price p₀ is p_m. If not, the observed price is p_m(N^e/N).

First scenario

The first case Mankiw examines is when aggregate demand N is lower than expected, and therefore p₀ is higher than p_m, as shown in the figure below. The producer surplus is lowered by B-A (since profits as seen before were equal to rectangle B plus the rectangle to its left), which is positive because p_m is by definition the profit-maximising price. Social welfare (or total surplus) is reduced by B+C, and therefore the reduction in welfare due to the contraction in aggregate demand is larger than the loss in the surplus of the firm.

Now, let’s suppose that the firm is capable of changing its price ex post, at a menu cost of z. The firm can then reduce its price from p₀ to p_m and obtain additional profits of B-A, which the firm will do if B-A > z. However, from the point of view of a social planner, the firm should lower its prize if and only if B+C > z. Let’s see Mankiw’s propositions on different outcomes:

-Proposition 1. Following a contraction in demand, if the firm cuts its price, then doing so is socially optimal (if it cuts it, is because B-A > z and therefore B+C > z+A+C > z).

-Proposition 2. Following a contraction in demand, if B+C > z > B-A, then the firm does not cut its price to p_m, even if it would be socially optimal (the inefficiency results because printing new menus result in an external benefit of C+A).

-Proposition 3. A contraction in aggregate demand reduces social welfare unambiguously, as shown by the sum of producer and consumer surplus. If the producer reduces its price, then the contraction only has the menu cost z. If the firm does not cut its price, then the contraction has the cost of B+C (probably much larger than z).

Second scenario

The second case Mankiw analyses is an expansion in aggregate demand (N > N^e), and therefore p₀ <p_m. Firstly, let’s see what happens when p₀ > k (N/N^e < p_m/k), as shown in our third figure. In this case, producer surplus is reduced by D-F, which is positive (p_m maximises the firm’s profits) and social welfare increases by E+F. The firm will reset its price if the increase in profits beats the menu cost. In other words, the firm will change its price if D-F > z.

-Proposition 4. If there is an expansion in demand and if the firm resets its price, social welfare decreases by the menu cost. If it doesn’t, total surplus increases by E+F.

Third scenario

Now, let’s see what happens if N/N^e > p_m/k, and therefore p₀ < k. Then, social welfare decreases by a positive or negative amount of I-J, which makes for an uncertain welfare effect. The firm’s profits, which are now negative, have been reduced by G+H+I. If G+H+I > z, then the firm will reset its price to p_m. Doing so would be socially optimal if I-J > z.

-Proposition 5. If the firm resets its price following the expansion in demand mentioned, social welfare (total surplus) will decrease by the menu cost z. If it doesn’t, total surplus does not decrease by more than the menu cost (if the firm doesn’t reset its price is because G+H+I < z, which implies that I-J < z-J-G-H < z and therefore the social welfare reduction I-J < z).

-Proposition 6 (as a summary of previous propositions). An expansion in aggregate demand may either increase welfare or reduce it, but never more than the menu cost. On the other hand, a contraction in aggregate demand will reduce welfare, possibly in an amount much larger than the menu cost.

Conclusion

To sum up, Mankiw demonstrates that private incentives ensures a high price adjustment when aggregate demand expands, but a small adjustment following a contraction in aggregate demand. From a social planner’s point of view, prices may be stuck too high, but never too low, which translates into downward price stickiness, although not into an upward rigidity. Mankiw also points out that a more complete model (general equilibrium) will probably show higher degrees of price stickiness, since interfirm purchases will exacerbate price rigidity. Therefore, the main conclusion of this paper (that small menu costs can translate into large inefficiency effects) would certainly remain in a general equilibrium model.

Regarding economic policies required to alleviate these problems, Mankiw explains how an active monetary policy is required. More particularly, he mentions policies that aim at the pricing mechanism, such as tax-based incomes policy and other supply-side policies.