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.

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.

Business cycle, as Joseph Schumpeter saw it, is the economic activity fluctuation that occurs over time, and that comes from the succession of expansionary and contracting seasons. It is analysed comparing real GDP to potential GDP (Y*). There are a few common characteristics, which help differentiate cycles, such as its phases, the way it oscillates, the periodicity and a few stylized facts:

1. Phases:

Four phases can be distinguished, following Richard Lipsey’s classification:

-Trough or depression (A), characterized by a high rate of unemployment and low consumption levels in relation to its real capacity;

-Expansion or recovery (B) of previous employment, income and consumption levels, that usually comes together with a rising in prices;

-Peak (C), distinguished by factors full use, high investment and shortage of labour, particularly for high-skilled jobs;

-Recession (D), demands fall causing unemployment and decreasing production levels.

2. Oscillations:

3. Periodicity:

Economic cycles have been classified depending in their periodicity. The most common are:

-Very short cycles, with duration of 30-40 months; also known as Kitchin cycles, whose studies saw in stock rotation the origin of these cycles;

-Short cycles, with duration of 7-11 years; also known as Juglar cycles, which origin is based on subsequent inventions;

-Long cycles with duration of 15-25 years; commonly known as Kuznets cycles, whose analysis placed the origin of cycles in demographic factors such as birth rates or migrations;

-Very long or Kondratiev cycle with duration of 50-60 years. This cycles originate with breakthroughs in capital goods, such as the steam engine or the Internet.

4. Stylized facts:

Both over time and between countries (a few of numerous reviewed by Robert Lucas in his article “Understanding Business Cycles”, 1977):

-There is positive correlation between variables, which helps smooth fluctuations;

-Co-movement between some variables:

·output fluctuates in the same direction in different sectors (although different amplitudes may apply);

·investment and consumption are clearly pro-cyclical: investment leads and is more volatile, consumption lags and is rather stable;

·income: real wages and profits are pro-cyclical;

·employment and labour force are also pro-cyclical.

-Expansions are usually longer than recessions.

Many papers and works have been written on business cycles and different points of view have taken form. Keynesian economics tries to deal with the economic fluctuation to minimize their impact. Business cycles are seen as a proof of market failure, and justify government intervention in order to assure the correct level of economic activity. Until the optimum level of employment has not been reached, the economy will not be readjusted. Depending on the cycle phase, expansionary or contractionary economic policies may be used.

New Classical Macroeconomics supporters have also dealt with economic cycles, and as a result the Real business cycle theory arises as an alternative view to Keynesian´s. Kydland and Prescott, and in general the Chicago School, are mostly related with the development of this theory. For them, cycles are explained by technological shocks. The fluctuations in the economy are seen to be produced by shifts in the supply curve, as a result of changes in productivity levels. These shocks can be caused by different factors: technology innovation, unusual weather conditions, changes in raw material prices, new policies and regulatory measures, etc. What is basic for these shocks to occur is an alteration in the effectiveness of either capital or labour factors, and therefore changing productivity. As a result in changes in the production quantity, the supply curve shifts, implying a new equilibrium point in the supply and demand model.  Thus they believe that economy will reach its new equilibrium point, through the forces of demand and supply in itself, without the need for a government intervention. In fact from their view, government intervention will only worsen the situation.

In 1958, A. W. Phillips wrote a paper on Economica (London School of Economics), entitled “The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957”. Analysing data concerning money wages and unemployment rates in the UK, Phillips managed to draw a curve representing the inverse relation between these variables. It must be said that Irving Fisher had already pointed out a relationship between price levels and unemployment in his paper “A Statistical Relation between Unemployment and Price Changes”, 1926 (cleverly renamed later as “I Discovered the Phillips Curve”). The Phillips curve has evolved following other empirical studies, and is widely known nowadays, even though it has also been criticized.

In his article, Phillips drew a curve showing the inverse relation between the rate of change of money wage rates, as a percentage change per year () and the unemployment rate (U).

Two important things must be noted: the point where the curve crosses the abscissa, and the fact that the ordinate seems to work as an asymptote. The importance of the point of crossing must be highlighted (around 5,5%), since it is the rate of unemployment that an economy will have for a zero increase in the money wages. This point will be named, in further developments of the Phillips curve, Natural Rate of Unemployment and Non-Accelerating Inflation Rate of Unemployment (NAIRU). Regarding the asymptote, as the author pointed out, there was no data of higher rates of change in money wage, nor lower unemployment rates. It can be concluded that unemployment cannot be lowered beyond a certain level.

Two years later, Richard G. Lipsey would publish a paper in the same journal deepening the mathematics regarding the curve, as well as expanding Phillips’ research by doing further econometrical tests.

Also in 1960, Paul A. Samuelson and Robert M. Solow, in their “Analytical Aspects of Anti-Inflation Policy”, studied a similar relation, in this case using data from the United States. Although they used inflation (Π) instead of the rate of change in money wages, they came up with similar results. Even though the curve might seem different because of the scale used, the unemployment rate at price stability is the same as at money wage stability (around 5,5%), and there seem to be no way to lower unemployment beyond a certain level (around 1%).

It was in this paper that the Phillips curve was considered a “menu of choice” for the first time. This meant that, concerning policy making, governments would be able to choose between a low rate of unemployment with high inflation, and a higher rate of unemployment with lower inflation. However, as the authors pointed out, this menu had to be used only in the short-run, since certain policies or economic events might change the shape of the curve in the longer run.

In the mid 50s, and until the late 60s, the adaptive expectations hypothesis became popular, especially because of the works by Phillip Cagan and Milton Friedman. This hypothesis would endure almost unquestioned until the late 60s and early 70s, when economist Robert Lucas (among others) brought forward a rational expectations hypothesis, from earlier works by J. F. Muth.

The term natural rate of unemployment was introduced by Milton Friedman in 1968, in his article “The Role of Monetary Policy”, following his presidential address delivered at the annual meeting of the American Economic Association, in 1967. It is based in Knut Wicksell’ concept of “natural” rate, which defines how there will be no permanent changes in the considered variable below or above its natural level.

The natural rate of unemployment defines the level at which unemployment will remain, no matter how great the effects of monetary policy. The only way to permanently keep unemployment under its natural rate is to resort to higher and higher inflation rates, which in turn would be highly hazardous for the economy. This can be easily understood using an expectations-augmented Phillips curve.

Even though the natural rate of unemployment is usually merged in the economic literature with the term NAIRU, there are a few differences between both terms. These differences are summarized in the following grid:

The term NAIRU (non-accelerating inflation rate of unemployment) is a term first used by James Tobin in 1980, in his article “Stabilization Policy Ten Years After”. It refers to the level of unemployment at which the economy settles if monetary policy is held stable. In these terms, it can be associated to Friedman’s natural rate of unemployment.

The NAIRU is based on empirical evidence regarding inflation and unemployment. Indeed, in most countries, inflation rises when unemployment is low because of the higher demand this implies; correspondingly, inflation falls when unemployment is high. This relation explains how unemployment may be above or below the NAIRU level not only because of the effects of monetary policy, but also because other factors such as production costs or trade unions negotiation processes. The Layard-Nickell NAIRU model explains it quite simply.

Even though the term NAIRU is usually merged in the economic literature with the term natural rate of unemployment, there are a few differences between the two. These differences are summarized in the following grid:

Adaptive expectation models are ways of predicting an agent’s behaviour based on their past experiences and past expectations for that same event. They are first used by Irving Fisher in his book “The Purchasing Power of Money”, 1911, and further developed in the 1940s and 1950s, especially by Phillip Cagan in his article “The Monetary Dynamics of Hyper-Inflation”, 1956 and, most famously, by Milton Friedman in 1957, in his book “A Theory of the Consumption Function”.

Models are usually based around the following formula: 

E_t x_t+1 is our expectation (E) in year  for a variable x in the year t+1. It is based on our expectation from the year before (t-1) for variable x in our current year, and a weighted proportion of our past expectations. Remember that our expectations from last year were, in turn, based on those of the year before, so all our expectations from the first time we ever dared assume anything are contained within the equation.

λ will depend on how much we were off last year versus this year: if our predictions are proving to be volatile, we will be more likely to adjust them. It will also depend on how much groundbreaking new information we have received, rendering previous expectations useless. Basically, it depends on how much we feel we might have been off last year when we predicted things for next year.

The easiest way to know how adaptive expectations work, is to understand the expectations-augmented Phillips curve. Using also this same curve, it is also easy to understand how rational expectations work.

The expectations-augmented Phillips curve introduces adaptive expectations into the Phillips curve. These adaptive expectations, which date from Irving Fisher’s book “The Purchasing Power of Money”, 1911, were introduced into the Phillips curve by monetarists, specially Milton Friedman. Therefore, we could say that the expectations-augmented Phillips curve was first used to explain the monetarists’ view of the Phillips curve.

Adaptive expectations models led to an important shift in the perception of a government’s ability to act. Under Keynes’ money illusion, changes in nominal variables (prices, wages, etc…) were accepted by agents as real despite overall purchasing power remaining stable.

However, monetarism embraced the adaptive expectations theory to mean that people would stumble once or twice on the same stone, but not a third. In this way, if the government decided on an expansionist monetary policy, inflation would rise and unemployment would fall, based on the Phillips curve. However, a second or third time around, agents would be quick to associate higher inflation with rising salaries in a vicious circle, and adjust their behaviour accordingly based on past experiences. They would anticipate that inflation would drain their purchasing power accordingly, and monetary policy would have little effect. If we see this graphically:

Initially, unemployment and inflation are at point A. The government decides to embark on an expansionist monetary policy, which floods the markets with inexpensive credit, incentivising consumption. Expectations shift to point B along the Phillips curve: unemployment is reduced through economic stimulus with a trade off in the form of inflation. However, after a short period, agents will begin to associate expansionist policies with inflation, which means a drain on their resources, and they will push for higher wages. This will stop the consumption stimulus and also deincentivise hiring. Eventually, agents will shift their expectations curves to point C. A second time around, D will be achieved, leading more or less rapidly to point E. This is why, in the long term, inflation has little effect on unemployment and vice versa. Expansionist monetary policy will lead directly to inflation, with no permanent effect on unemployment.

In summary, monetarists sustained that the Phillips curve will hold up in the short term, but not in the long term. In the long term, the Phillips curve is completely vertical and determines the natural rate of unemployment, as Friedman puts it in his article “The role of Monetary Policy”, 1968.

Rational expectation models are those where an agent’s future predictions affect the value they assign to a variable in their current time period. In this sort of self-fulfilling prophecy, expectations become truths, and errors in forecasting future variables become random. This makes those forecasts valid, because present expectations about the future become dependent variables of future values. This model was developed and put forwards by John Muthin two articles: “Optimal Properties of Exponentially Weighted Forecasts”,1960, and “Rational Expectations and the Theory of Price Movements”, 1961 and later summarised by Peter Whittle in 1963, before becoming influential in Robert Lucas’ work in the 1970s. Particularly, Lucas developed the use of rational expectations in his article “Expectations and the Neutrality of Money”, 1972, in which he used Edmund Phelps’ island parable, though applying rational expectations, instead of adaptive expectations.

Mathematically, rational expectations can be represented as: 

Which simply means that the value of x today will be the value that we expected it to be plus a random error.

Essential to this hypothesis is the fact that individuals have perfect information and markets are perfect and tend towards equilibrium. This places us firmly back in the realm of neoclassical economics, whose main ideas where retaken by New Classical Macroeconomics.