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.

Menu costs are costs that result from price changes. An easy way to understand menu costs is by means of a typical example: restaurants. When a restaurant manager wants to change prices, the cost of changing the menus (in order to show the new prices) must be taken into consideration. Therefore, the manager will need to assess whether the increase in prices will cover for the cost of printing new menus.

As Gregory Makiw demonstrates in his article “Small Menu Costs and Large Business Cycles: A Macroeconomic Model of Monopoly”, 1985, this menu costs may lead to a non-socially optimal situation. Indeed, Mankiw’s menu costs model shows how higher menu costs may lead to a situation where prices remain unchanged, thus provoking so called price stickiness.

Contrary to what economists from the New Classical Macroeconomics think, which is that business cycles are originated by shifts in supply (which originate mainly from technological shocks), New Keynesian economists believe that business cycles are originated by price stickiness.  This price stickiness might be explained by menu costs, since the slow adjustment of the economy may explain business cycles.

There is a great debate over the following question: are these menu costs really large enough to cause business cycles? An article from Daniel Levy et al., “The Magnitude of Menu Costs: Direct Evidence from Large U.S. Supermarket Chains”, 1997, demonstrates, using empirical evidence, that these menu costs are indeed large enough to cause business cycles. The authors use store-level data from five multistore supermarket chains to directly measure menu costs. They find that the menu costs per store at those chains average more than 35% of net profit margins, which may be forming a barrier to price changes. When applying these findings to theoretical models of menu costs, the authors conclude that these menu costs are large enough to be capable of having macroeconomic significance. Furthermore, they believe that these menu costs may cause considerable nominal rigidity in other industries or markets, thus amplifying the effects on business cycles. These menu costs, they say, vary largely due to local and regional legislation, which may require, for instance, a separate price tag on each item, thus increasing menu costs.

As in consumer’s theory (where consumption duality is analysed), the firm´s input decision has a dual nature. Finding the optimum levels of inputs, can not only be seen as a question of choosing the lowest isocost line tangent to the production isoquant (as seen when minimising cost), but also as a question of choosing the highest production isoquant tangent to a given isocost line (maximising production). In other words, having a cost function that sets a budget constraint, solving for the inputs allocation that gives the highest output.

The way to solve either problem is very similar: we look for the Lagrangian function and obtain first order conditions, then solve the system.

Video – Production duality:

Cost minimisation tries to answer the fundamental question of how to select inputs in order to produce a given output at a minimum cost.

A firm’s isocost line shows the cost of hiring factor inputs. This line gives us all possible combinations of inputs (here labour and capital) that can be purchased at a given cost.

Assuming that a certain amount of output wants to be achieved, we have several possible combinations to achieve it, but only one that minimises costs. The isocost line tangent to the isoquant, which represents the amount of output targeted, will reveal the input combination that results in the lowest cost, for that given output.

We can also use the method of Lagrangian systems to analytically solve a constrained minimisation problem. The first derivatives determine a system of equations that can be resolved by submitting our sought output to the restriction presented by the minimisation of costs:

Video – Cost minimisation:

Production maximisation must be seen as an optimisation problem regarding the production function, represented by isoquants, and a constraint regarding production costs, represented by an isocost line.

Producers are therefore faced with the following problem: faced with a set of possible production levels and a fixed budget, how to choose the level which maximises their production?

If we know the production function of a certain producer, and we know their budget, we have the two restrictions necessary to maximise their production. This can be done graphically, with the point where isocost and isoquant meet defining an optimum, as shown in the adjacent figure.

It can be also done mathematically, through a Lagrangian, where the first derivatives determine a system of equations that can be resolved by submitting our production function to the restriction presented by the budget:

Video – Production maximisation:

Revealed preference theory is attributable to Paul Samuelson in his article “Consumption Theory in Terms of Revealed Preference”, 1948. Consumer theory depends on the existence of preferences which materialise into utility functions. These utility functions are maximised by consumers subject to a budget restraint. The issue is that it is difficult to accept that individuals really have a definite mathematical formula in mind when choosing between different options. What revealed preference theory does is work backwards to assume that we can deduce these utility functions from consumer behaviour. Analysing these choices leads us backwards to a set of preferences that influences the choices they make. It therefore allows economists to study consumer behaviour empirically.

There are two main axioms to the theory, both based on completeness and transitivity:

WARP (Weak Axiom of Revealed Preference): If A is revealed preferred to B (A RP B), then it must be so in every case. That is, if a consumer ever chooses B, then we must assume that A was previously chosen and that the budget constraint had enough ‘left over’ to allow a consumer to choose B as well.

SARP (Strong Axiom of Revealed Preference): This adds transitivity. If there are only two goods, then it is clear that WARP already defines a consumer’s choice: A over B. However, the SARP adds the idea of indirectly revealing preferences: if A is chosen over B and B over C, SARP and transitivity dictate that A is also preferred to C, so A is indirectly revealed to be preferable to C (A R* C). This drastically reduces the amount of empirical evidence necessary to define consumer preferences.

In the case shown in the figure below, we know that C is indirectly preferred to B (C R* B) because it allows us to reach a higher utility curve. Because C and B define a space (R*), and we know that C, B and A are contained within R*(R*{(C,B)}), then we can say that C RP A RP B, that is, by knowing from observation that C is indirectly preferred to B, we can tell that C is revealed as preferable to A (C RP A) and that A is revealed as preferable to B (A RP B).

If we think of A, B and C as infinitely complex bundles of goods, we can map out all a consumer’s choices. In theory, we can track this backwards to actually build utility functions if we have access to unlimited data. Without actually having to do this, we can aggregate consumer data to reveal general truths about a certain population’s preferences.

Video – Revealed preference:

Goods are something that provides its holder some kind of satisfaction, and therefore has a utility. There are different kinds of goods, and different classifications can be arranged and identified. We can differentiate between consumption goods (durable or perishable) and capital goods. Classification depending in responsiveness to incomes changes (normal goods and inferior goods) and to price changes (ordinary goods and Giffen goods) can also be made.

-Normal goods are those whose demand increases due to a rise in income levels, having therefore a positive correlation, which implies that the elasticity of this kind of goods is always higher than 0.  Normal goods are divided in two categories, Superior goods and Necessary goods.

·Superior goods, also known as luxury goods, are those goods that displace the demand of inferior goods after a rise in consumers’ income. They are a kind of normal goods as their demand increases when income does as well, however, the difference is that they occupy the share of inferior goods. The elasticity of this kind of goods is, for this, always higher than 1.

·Necessary goods are those whose demand increases when income does, however the increase in demand is less than proportional to the rise in income. Elasticity of this goods is always between 0 and 1.

-Inferior goods are those whose demand moves in opposite direction to the income variation of consumers. This occurs because consumers’ preferences change to other goods that are more highly regarded.

-Ordinary goods are those goods whose demands move in opposite direction to the price variation. This means an increase in the price of the good will mean a decrease of its demand and the other way around.

-Giffen goods are those goods whose demand moves in the same direction as the price variation, this meaning, raising the price of the good will increase its demand, and the other way around. The explanation to this kind of goods comes from the “Snob Effect”, the more expensive a good is, the less people can afford it, and therefore becoming more precious and highly valued.