Oct 4

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.

Oct 4

Lope Gallego

Paul Samuelson

Paul A. Samuelson Paul Anthony Samuelson, 1915-2009, was an American economist and Professor at the Massachusetts Institute of Technology. He was the first American to win the Nobel Prize in Economic Sciences, in 1970; he was granted this prize for his contribution in raising the level of scientific analysis in economic theory.

Samuelson is sometimes referred to as the “father of modern economics”. His “Economics: An Introduction Analysis”, 1948, in which he explains the Keynesian economic principles, has been the most widely-spread economic textbook ever since, being translated to over 40 languages.

He is the author of the theory of revealed preference, that states the demand curve is not only utility-based. Regarding macroeconomics, he has insisted in the relation between the acceleration principle and the multiplier principle, and along his contributions to trade theory, he extended the Hecksher-Ohlin model by means of the factor price equalization theorem, by which it is said that free trade not only leads product prices to equalize, but also production factors prices.

Samuelson is considered to be the maximum formulator of the mixed economycharacteristics, one of the founders of Neo-Keynesianismand a key figure of neoclassical economics.

Oct 3

Lope Gallego

Maurice Allais

Maurice Félix Charles Allais, 1911-2010, was a French economist, physicist and Professor of Economics at the École Nationale Supérieure des Mines de Paris (Mines ParisTech). His pioneer contributions to the theory of markets and to the efficient utilization of resources, had him win the Noble Prize in Economic Sciences in 1988. He defined himself as a “Liberal Socialist”

Allais took Léon Walras’ and Vilfredo Pareto’s previous works regarding equilibrium and market efficiency, and developed them with a more rigorous mathematical formulation back up. He is also known for the Allais paradox, which is a breach in the decision theory, as it fails the expected utility theory. He was able to apply his theory of behaviour under uncertainty in the general equilibrium model, by demonstrating that a competitive allocation of risks leads to an optimal allocation of resources. Allais also made contributions in the area of monetary policy and studied the influence of non-rational behaviour in economic decisions, serving as an inspiration for Kahneman´s work.

Allais’ papers, always written in French, that stand out among his major works are: “Á la recherche d’une discipline économique” (In Search of an Economic Discipline), 1943, and “Économie et intérêt” (Economy and Interest), 1947.

Oct 2

Lope Gallego

Bertil Ohlin

Bertil G. Ohlin Bertil Gotthard Ohlin, 1899-1979, was a Swedish economist, politician and Professor of Economics at the University of Copenhagen and at the Stockholm School of Economics. Along with the British economist James Meade, he received the Nobel Prize in Economic Sciences in 1977, for their significant addition to the development of the theory of international trade and international capital movements.

Ohlin’s main contribution to the economic theory is found in his book “Interregional and International Trade”, 1933, in which he modernizes the theory of international trade and builds on a previous theorem belonging to Eli Heckscher, that has, ever since, been known as the Heckscher-Ohlin model. This model derives from David Ricardo‘s theory of comparative advantage (known as Ricardian trade theory). Its core idea is that each country will specialize in producing those products for which it has better factor endowment. This model predicts and explains the patterns and flows of international trade. However, this model would result to be proven incorrect by the Leontief paradox, nevertheless stimulating new contributions to explain it.

In the macroeconomics field, Ohlin less well known theories are also of great interest. He studied ways of stimulating and cutting demand throughout business cycles depending on the needs of the economy. His studies were a prelude to J. M. Keynes’ works.

Ohlin became the leader of the Liberal People´s Party from 1944 to 1967, being the main opposition party at that time, against the Social Democrat Government. During 1944 and 1945 he was appointed as Minister of Commerce for the wartime government.

Sep 30

Lope Gallego

Menu cost

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.

Sep 29

Lope Gallego

Wassily Leontief

Wassily Leontief, 1906-1999, was a Russian economist, naturalized an American citizen. He was Professor at the University of Kiel, Harvard University and New York University consecutively. He was awarded the Noble Prize in Economic Sciences in the year 1973, “for his developments of the input-output method and for its applications to important economic problems”.

Leontief is considered as being the father of the input-output technique, from which the production system is described as a network of deliveries among the numerous production sectors. This work relates to François Quesnay‘s earlier Tableau économique, which was a simpler way (but also less reliable) to understand economic flows. Leontief introduced this concept in his “The Structure of the American Economy, 1919-1929: An Empirical Application of Equilibrium Analysis”, 1941. He used his mathematical talent to analyse demand and supply elasticities with empirical work. The object of this analysis is to try and answer the question of how much does the production of each sector has to be increased, in order to meet the desires of consumers, investors and exporters, in case of an increase in demand. This system has been used in many areas, but it has been a major contribution when dealing with forecasts and planning at both the short and long term. Its utility has been proven at the public and private sectors and at the different economic theories.

In 1954, Leontief empirically tested the Heckscher-Ohlin model, using data from the year 1947 and the input-output table. The results of his research were surprising as they challenged the Heckscher-Ohlin theory. This discovery is known as the Leontief paradox which shows that a high capital-per worker country will have a lower capital-labour ratio in exports than in imports. Leontief´s finding motivated a search for a new theory of trade that could account for his results

Sep 28

Lope Gallego

Tjalling Koopmans

Tjalling C. Koopmans Tjalling Charles Koopmans, 1910-1985, was an American, Dutch born, economist and Professor at the University of Chicago, from 1946 to1955, and at Yale University, since 1955. Koopmans is mostly known for his theoretical developments in the field of econometrics, especially for works regarding optimal resources allocation. In 1975 he and Leonid Kantorovich were the joint winners of the Nobel Prize in Economic Sciences.

In his “Analysis of Production as an Efficient Combination of Activities”, 1951, Koopmans develops what is known as activity analysis, a theory that uses new ways of understanding the relations between inputs and outputs of a production process, in order to explain the correlation between efficiency in production, and the existence of a system to calculate prices. His research helped explain the links between the normative allocation theory, and the general equilibrium theory. The rigour and clarity of Koopmans works became the example to follow of mathematical economics.

His meaningful Cass-Koopmans model, which was based on Frank P. Ramsey´s previous works, is an economic growth model similar to Solow´s model, but differing in having an endogenous savings rate. This model´s aim is to establish the optimum course for investment and consumption, paying special attention to preferences and utility over time.

Sep 27

Lope Gallego

Cahuc’s adjustment costs model

The static theory of labour demand does not specify how, or how long adjustments between production factors take. It is therefore necessary to consider the notion of adjustment costs, such as costs incurred by a company to change the number of factors.

We will follow the lines followed in the model of adjustment costs seen in “Le marché du travail”, 2001, by Pierre Cahuc. These adjustments involve production costs that do not correspond to the activity itself. There are two kinds of adjustment costs:

-Internal adjustment costs: those caused by the loss of efficiency due to reorganization within the company (for example, training for use of new machinery, training of new employees to existing machinery, etc.).

-External adjustment costs: those who can be differentiated from production variations (for example, hiring experts to implement the changes, layoff payments, etc.).

As Cahuc explains, previous studies on the labour markets in the United States and France allow us to compare the situation of two types of markets:

-Recruitment costs are higher than firing costs in the U.S.;

-Firing costs are higher than recruitment costs in France;

-Recruitment costs in the U.S. are higher than in France;

-Firing costs are higher in France than in the U.S.

Furthermore, these studies conclude that these costs increase with the level of wage and/or training.

Employment protection by the public sector is less rigorous in the U.S., Canada or the U.K. than in France, Germany and southern Europe. Furthermore, these studies conclude that much of the higher cost of firing in Europe is due to administrative or regulatory costs (due to the legislation of each country).

LINEAR FORMULATION:

In most jobs, costs are represented by a symmetric convex function (usually quadratic). However, this does not explain asymmetrical adjustments and discontinuous employment. Thus, we see the linear formulation, which is commonly used nowadays.

This representation will show us how companies sometimes hire or fire employees, or remain as they are.

c_h and c_f represent hiring costs (h) and firing costs (f). Adjustment of employment will therefore be asymmetricif c_h≠ c_f.

EMPLOYMENT ADJUSTMENT:

It is possible to differentiate the effects of c_h and c_f when adopting a linear function. Furthermore, the linearity will see how the adjustment in the levels of labour can be immediate.

We define the adjustment cost function as:

The producer’s problem is choosing the level of labour that maximises its profits:

(r=is the rate at which future profits are actualised to present value)

The employment level is given by the equation:

which translates into the following conditions:

The producer will hire labour as long as its productivity is higher than the adjustment costs of hiring.

Producer will start firing employees as soon as productivity falls to the point where firing employees becomes profitable.

In all other cases, the producer maintains its level of staff. As we assume w, r, c_h and c_f constant, we can define employment levels L_h and L_fas:

The company adjusts its level of workers L_h (respectively L_f) if this is higher (respectively lower) than the initial level of employment L₀. If not, it means that L₀ is maintained between L_h and L_f, its optimal level:

GRAPHICAL ANALYSIS:

The curves in the lower half of the adjacent figure represent the relationship between initial employment and final employment levels. The conclusions we can derive from this model are:

-↑c_f: An increase in firing costs (U.S. spending levels to levels of FR.) Prevents staff adjustment downwards, and no incentive to hire;

-↑c_h: Increased recruitment costs (FR. spending levels to U.S. levels) prevents new hires;

-↓c_h: A lower recruitment cost always has positive effects on employment because it increases the optimal level of employment L_h;

Therefore, this model explains:

· higher unemployment in France (for little flexibility when firing);

· when wages are equal in both economies, U.S. production levels will be higher;

· in recessions, the situation is worse in France because it’s hard to fire employees;

· in times of expansion, the situation is worse in the U.S. because it’s hard to hire.

The main conclusion that can be derived from this model is that proper management of the costs of hiring and firing ensures greater stability in the demand for labour.

Sep 26

Lope Gallego

Dale Mortensen

Dale T. Mortensen
Dale Thomas Mortensen, born in 1939, is an American economist and Professor of Economics at the Northwestern University. In 2010, Mortesen was awarded the Nobel Prize in Economic Sciences along with Christopher Pissarides and Peter Diamond for their analysis of labour markets with job search friction. Mortesen has contributed to the formulation of a theoretical framework for job search markets, expanding the theory and applying it to labour markets.

In 1970 Mortensen published his article, “Job Search, the Duration of Unemployment, and the Phillips Curve”. In this article he presents his search modelapplied to labour economics. His model tries to justify the unemployment phenomena even when demand for labour is not fulfilled, thus implying the existence of job vacancies. For Mortensen, workers will spend time searching for a job; however this searching process will be variable and heterogeneous for each worker. His models go against what was previously stipulated by neoclassical models. Mortensen also analyses how regulations and economic policies affects unemployment, job vacancies and wages and concludes that high unemployment benefits are ineffective, as they will make job searches longer.

Sep 25

Lope Gallego

Production duality

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.

When dealing with primal demand, that is, output maximisation, our Langrangian is as follows:

Subj. to:

So that:

That is, our Lagrangian is our production function, which depends on K, L, minus the restriction- our budget.123456

When dealing with dual demand, that is, cost minimisation, our Lagrangian system is as follows:

Subj. to:

So that:

Our Lagrangian is our cost function (depends on K, L), minus our production function, which must equal a constant.

Video – Production duality: