Explore keplr-apps.net for a collection of tools that enhance your blockchain experience, including wallet management and decentralized application support. Get Metamask for secure crypto storage, seamless trading, and easy access to blockchain apps.

Jul 23

Consumption duality

There are two ways to solve a consumer’s choice problem. That is, we can either fix a budget and obtain the maximum utility from it (primal demand) or set a level of utility we want to achieve and minimise cost (dual demand).

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, utility maximisation, our Langrangian is as follows:

Subj. to:

So that:

That is, our Lagrangian is our utility function, which depends on x₁, x₂ minus the restriction- our budget. The first order conditions (which we obtain from the first derivatives) give us Marshallian demand curves.

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

Subj. to:

So that:
That is, our Lagrangian is our cost function, which depends on x₁, x₂ minus our utility function, which must equal a constant. The first order conditions give us Hicksian demand curves.

Video – Consumption duality:

Jul 22

Lope Gallego

Cost minimisation

Cost minimisation is a way of solving the optimisation problem regarding the utility function and the budget constraint, even though the most common way of doing this is by means of utility maximisation.

If we think about it, we don’t normally have a fixed budget for most purchases. We have a certain utility we expect to derive from them and we hope to spend as little as possible on them (but we don’t have a maximum budget).

In this case, it is utility that is fixed as a restriction, and cost that we can play around with. It’s like solving the consumer’s choice problem in a mirror image way to utility maximisation, and is associated with Hicksian demand curves.

The way we resolve this minimisation problem is very similar to utility maximisation, and is also done with a Lagrangian system, since there is a duality in consumption. In this case, we want to minimise our budget for a given utility:

Video – Cost minimisation:

Jul 22

Lope Gallego

Utility maximisation

Utility maximisation must be seen as an optimisation problem regarding the utility function and the budget constraint. These two sides of the problem, define Marshallian demand curves.

An individual is therefore faced with the following problem: faced with a set of choices, or baskets of goods, and a fixed budget, how to choose the basket which maximises their utility?

If we know an individual’s utility function, and we know their budget, we have the two restrictions necessary to maximise their utility. This can be done graphically, with the point where budget and utility function 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 utility function to the restriction presented by the budget:

Video – Utility maximisation:

Jul 22

Lope Gallego

Budget constraint

Consumer behaviour is a maximisation problem. It means making the most of our limited resources to maximise our utility. As consumers are insatiable, and utility functions grow with quantity, the only thing that limits our consumption is our own budget (assuming, of course, we are dealing with normal goods, not negative or harmful goods which consumption we want to limit).

A budget constraint (green line in the adjacent figure) provides the second half of the maximisation problem. We need to balance the utility we derive from consumption with the budget we have.

Supposing we have a choice of two goods, 1 and 2, then our restriction is as follows:

which simply means that our budget must be at least as much as the price of the two goods times their respective price.

This simply shows that our consumption is capped and that the more we spend on one good, the less we can on the other.

Video – Budget constraint:

Jul 22

Lope Gallego

George Akerlof

George Akerlof George Arthur Akerlof, born in 1940, is an American economist and professor at University of California, Berkeley. He was awarded the Nobel Prize in Economic Sciences in 2001 along with Michael Spence and Joseph E. Stiglitz.

He is best known for his contributions to asymmetric information theories: study of transactions in which one of the parties has better information than the other one. Adverse selection and moral hazard can result from the worst cases of asymmetric information in transactions between economic agents.

Akerlof’s key article on this subject is “The Market for Lemons: Quality Uncertainty and the Market Mechanism”, 1970, in which he develops a classical example of second hand car market in which the seller is the only one that truly has complete information about the quality of the car, to simply explain the risk of asymmetric information.

Jul 22

Lope Gallego

James Tobin

James Tobin, an American economist (1918-2002), and follower of Neo-Keynesian economics, thought that government intervention was necessary in order to stabilize the economy and to avoid recessions. He received the Nobel Prize in Economic Sciences in 1981 for his analysis of financial markets and their relation with decisions involving spending, employment, production and prices. In fact, Tobin discovered the relation between the market value, and the replacement value of an asset. This ratio is called Tobin´s Q, and it links the financial market to the markets of goods and services.

Tobin proposed the creation of a tax on international currency markets transactions -the so called “Tobin Tax”- in order to reduce speculation. He saw this tool as a means to promote freedom of trade; however it has also been encouraged by anti-globalization groups in order to reduce free trade.

Amongst other subjects, he also worked in the measuring of social welfare. Tobin believed GDP was not a good measure for accounting welfare, so he developed the concept of Measure of Economic Welfare as a more realistic measure. In his measurement, what does not create general satisfaction, such as armament, bureaucracy expenditure growth or new urban highways systems, must be left aside.

Jul 22

Lope Gallego

John Nash

John Forbes Nash (1928-2015) was an American mathematician that was Professor at Princeton University. In 1994 he received the Nobel Prize in Economic Sciences along with John Harsanyi and Reinhard Selten, for their works regarding game theory.

During the 50s (in papers originated after his PhD dissertation “Non-Cooperative Games”, 1950) he developed the so-called Nash Equilibrium that occurs when no player would change its strategy knowing the preferences and strategies of the other players. No player has anything to gain by changing only their own strategy unilaterally. This is, you would make your own best decision taking into account the other players’ decision.

His ideas and theories are not only used in economics and mathematics, but also in other very different fields such as politics and military theory.

Jul 22

Lope Gallego

Robert Mundell

Robert Mundell (born in 1932) is a Canadian economist and professor at Columbia University. He won the Noble Prize in Economic Sciences in 1999 for his theory in optimum currency areas, which focuses on a series of characteristics required so that monetary unions can be optimal, and therefore sustainable and economically efficient in the long run, as stated in his paper “A Theory of Optimum Currency Areas”, 1961. He raised special interest amongst European economists due to his support for the creation of a European Monetary Union and of the Euro.

He is a strong defender, and one of the developers, of supply-side economics that argues that economic growth will be most effective if it’s originated by supply-side policies.

Mundell and Marcus Fleming, from papers written separately by the two authors, designed the Mundell-Fleming model, -also called IS-LM-BoP model-, through which they expand the traditional IS-LM model into a context of an open economy. This model explains why there cannot be an economy with an independent monetary policy if it maintains a fixed exchange rate, and there is free movement of capital and payments; this situation is known as the “impossible trinity”. Mundell’s paper “Capital mobility and stabilization policy under fixed and flexible exchange rates”, 1963, analyses the case of perfect mobility of capital.

Given his contributions and thoughts about monetary policy, it can be said that Mundell belongs to the Chicago School and is a fervent supporter of an open economy, in the trend of globalization.

Jul 22

Lope Gallego

Robert Solow

Robert Merton Solow, born in 1924, is an American economist, pupil of Wassily Leontief, and Professor at the Massachusetts Technological Institute (MIT). We can identify Solow as a supporter of the Neo-Keynesian ideas and a great user of mathematics for supporting economic theories.

Most of his works and theories are based in the theory of economic growth, topic that he has studied and analysed thoroughly. In 1987 he was awarded with the Nobel Prize in Economic Sciences, for his works on economic growth. Solow believes that technological progress is a critical factor in economic growth.

In the Solow–Swan growth model, he determines long term economic growth using productivity, capital accumulation, population growth and technological progress, as main variables. Solow sustains in his paper “A Contribution to the Theory of Economic Growth”, 1956, that savings play a key role in economic growth, both as a positive factor, since it allows further investment, but also as a negative issue, since it can diminish the welfare of economic agents by diminishing consumption.

Jul 22

Lope Gallego

Paul Krugman

Paul Robin Krugman is an American economist born in 1953, who is identified with the New Keynesian Economics theories. He is an experimented lecturer and is actually working as Professor at Princeton University teaching both Economics and International Affairs.

He has published articles and papers in different newspapers and journals, and collaborates in the New York Times on a regular basis. It is thanks to Krugman’s communication abilities and his numerous publications, that he has become an international reference.

Krugman is best known for his research on international trade. He was awarded the Nobel Prize in Economics Sciences in 2008 for his work regarding the interpretation of patterns of international trade. He has broadened the general understanding of economic phenomena such as trade and the location of economic activities. In his paper “Increasing Returns, Monopolistic Competition, and International Trade”, 1978, Krugman sustains that trends and arrangements of international trade, and also the geographic congregation of wealth, can be explained by economies of scale and by consumer’s preferences for goods and services.