Sep 28

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:

Sep 24

Lope Gallego

Gérard Debreu

Gerard Debreu Gérard Debreu, 1921-2004, was a French economist, mathematician and Professor of Economics at the University of California, Berkley. He was the winner of the Nobel Prize in Economic Sciences in 1983, for including new analytical methods into economic theory and for his contributions to the general equilibrium theory.

Along with Kenneth Arrow he published the way-out paper, “Existence of an Equilibrium for a Competitive Economy”, 1954, in which, using mathematical analysis, he demonstrated the existence of a general equilibrium.

Debreu is also the author of the book “Theory of Value: An Axiomatic Analysis of Economic Equilibrium”, 1959, where, using modern mathematics, he exposes a synthesis model of the market economy, based on the variables of price and the expressive equations from the different markets, and that relate in an efficient and coordinated way.

Sep 23

Lope Gallego

Gary Becker

Gary S. Becker Gary Stanley Becker, born in 1930, is an American economist and Professor at the University of Chicago where he teaches economics and sociology. He won the Nobel Prize in Economic Sciences in 1992 for his contributions to microeconomic analysis, which have extended the field to a wide range of human behaviour and interaction, including non-market behaviour.

Starting from his economic approach, Becker recognizes individuals as rational beings and utility maximization seekers, and each decision an individual takes will have been carried out using a cost-benefit analysis. He researched on this assumption in four analysis areas: human capital, criminality, sex and race discrimination and family behaviour.

Becker´s most noteworthy work is “Human Capital: A Theoretical and Empirical Analysis, with Special Reference to Education”, 1964. In this book he proposes the idea that a well prepared workforce is an important asset for any country, since the training of workers increases the productive capacity of the workforce. Furthermore, he also claims for the minimum salary elimination in order to encourage firms to hire a larger number of employees.

Sep 21

Lope Gallego

Cost minimisation (production)

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:

Sep 19

Lope Gallego

Production maximisation

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:

Sep 18

Lope Gallego

Harry Markowitz

Harry Markowitz, born in 1927, is an American Economist and Professor of Finance at the University of California, San Diego. He is one of the many disciples that the renowned Chicago School has given. Due to his contributions to financial economics he was rewarded with the Nobel Prize in Economic Sciences in 1990 along with William Sharpe and Merton Miller.

Markowitz has conducted researches on portfolio selection and diversification, and asset management in order to maximize its return. His most important work “Portfolio Selection: Efficient Diversification of Investments”, published in 1959, proves that the volatility, and therefore risk, of a diversified portfolio is lower than a portfolio dealing with a unique share.

The Harry Markowitz model, based on expected returns and standard deviation, first introduced in 1952, shows how to reduce risk when managing portfolios. Markowitz placed the foundations from which W. Sharpe would construct his capital assets pricing model (CAPM).

Markowitz’s work on portfolio theory has proven the use of financial microanalysis when dealing with economic analysis.

Sep 16

Lope Gallego

Rational expectations

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.