Description

This video shows how useful a good understanding of consumption duality can be. Starting with utility maximisation and cost minimisation, this video explores everything you need to understand about consumer theory. We also explain formulas such as Roy’s identity or the Hotelling/Shephard lemma.

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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 our utility function. 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 our cost function. The first order conditions give us Hicksian demand curves.

Learn more by reading the dictionary entry.

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Description

This video explains how cost minimisation works, both from the analytical and graphical points of view. We start analysing cost minimisation as the optimisation problem it is, followed by a graphical analysis of the optimum point of consumption.

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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.

Learn more by reading the dictionary entry.

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Description

This video explains how utility maximisation works, both from the analytical and graphical points of view. We start analysing utility maximisation as the optimisation problem it is, followed by a graphical analysis of the optimum point of consumption.

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Utility maximisation must be seen as an optimisation problem regarding the utility function and the budget constraint. An individual is 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.

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.

Learn more by reading the dictionary entry.

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Description

This video explains the very basics of the budget constraint, which is of great importance when dealing with consumption duality. We start by analysing its components, then explain how to draw the budget line and lastly we focus on different factors that can change its shape.

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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 provides the second half of the maximisation problem. We need to balance the utility we derive from consumption with the budget we have. This simply shows that our consumption is capped and that the more we spend on one good, the less we can on the other.

Learn more by reading the dictionary entry.

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Description

This video explains how to build an Edgeworth box, and how to analyse it. We start from two sets of indifference curves, then build the Edgeworth box and, finally, introduce the contract curve.

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In 1881, Francis Y. Edgeworth came up with a way of representing, using the same axis, indifference curves and the corresponding contract curve. He developed this model in his book “Mathematical Psychics: an Essay on the Application of Mathematics to the Moral Sciences”. However, the representation given, using as an example the work being done by Friday and wages being paid by Robinson Crusoe, is not the one we commonly know nowadays.

It was Vilfredo Pareto, in his book “Manual of Political Economy”, 1906, who developed Edgeworth’s ideas into a more understandable and simpler diagram, which today we call the Edgeworth box.

This diagram is widely used in welfare economics, game theory, or general equilibrium theory, to name a few subjects. It is easy to draw and can be easily explained.

Learn more by reading the dictionary entry.

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Description

This video explains how to calculate and use the marginal rate of substitution (MRS). We start by learning how to calculate it, then move on to use it in order to properly draw indifference curves and, finally, we analyse the MRS for different kinds of indifference curves.

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The marginal rate of substitution (MRS) can be defined as how many units of good x have to be given up in order to gain an extra unit of good y, while keeping the same level of utility. Therefore, it involves the trade-offs of goods, in order to change the allocation of bundles of goods while maintaining the same level of satisfaction. The MRS is linked with indifference curves, since the slope of this curve is the MRS.

The marginal rate of substitution should not be confused with the marginal rate of technical substitution or the marginal rate of transformation.

Learn more by reading the dictionary entry.

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Description

This video explains how indifference curves work and how to build them. We start analysing indifference curves as a way of representing utility, then we explain what the marginal rate of substitution is and, lastly, what different kinds of indifference curves there are.

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Indifference curves are lines in a coordinate system for which each of its points express a particular combination of a number of goods or bundles of goods that the consumer is indifferent to consume. This is, the consumer will have no preference between two bundles located in the same indifference curve, since they all provide the same degree of utility. The indifference curves, as we move away from the origin of coordinates, imply higher consumption and, therefore, increasing levels of utility.

Francis Y. Edgeworth, developed the mathematics concerning the drawing of indifference curves in his book “Mathematical Psychics: an Essay on the Application of Mathematics to the Moral Sciences”, 1881, from earlier works by William Stanley Jevons. However, Vilfredo Pareto was the first economist to draw indifference maps as we know them nowadays, in his book “Manual of Political Economy”, published in 1906.

Learn more by reading the dictionary entry.

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Description

This video explains the very basics of consumer’s preferences, and how to successfully build and understand a utility function. We start with basic rationality axioms, then we draw a utility function, and lastly we introduce the concept of indifference curves.

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Utility is the ‘satisfaction’ we get from using, owning, or doing something. It is what allows us to choose between options.

A preference function therefore assigns values to the ranking of a set of choices. This is useful as it allows us to see consumer behaviour as a maximisation problem: faced with a set of options and a budget constraint, we will choose what satisfies us most.

Utility functions follow the same code of conduct, the same axioms, as preferences, because they are simply numerical representations of them. That is, they are transitive, complete, continuous, and convex, for the same reasons.

The most important thing to point out is perhaps the fact that utility functions do not assign a numerical value to our preferences. They simply indicate order and magnitude of preference, that is, what we like more and by how much.

Learn more by reading the dictionary entry.

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