Description

This video helps understand how the Paasche index and the equivalent variation work. We start by analyzing the Paasche index analytically, then use a graphical representation to explain what the equivalent variation is.

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Price indices are used to monitor changes in prices levels over time. This is useful when separating real income from nominal income, as inflation is a drain on purchasing power. The two most basic indices are the Laspeyres index (named after Etienne Laspeyres) and the Paasche index (named after Hermann Paasche).

They work by dividing expense on a specific basket in the current period by how much the same basket would cost in the base period. The main difference is the quantities used.

A Paasche index of 1 means that the consumer could have afforded the same bundle of goods in the base period as they can now. This can be translated to the concept of equivalent variation: how much income would we have to take away from an individual, at the base price level, to have the same impact on their utility as the inflation between the base period and period 1? The Paasche index underestimates the equivalent variation.

Learn more by reading the dictionary entry.

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• Laspeyres index
• Income and substitution effects
• Marshallian and Hicksian demand curves

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• Slutsky’s equation
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Description

This video explains how to build the Marshallian and Hicksian demand curves. We analyse Hicks’ decomposition of the income and substitution effect, from which we derive both demand curves.

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Marshallian and Hicksian demands stem from two ways of looking at the same problem – how to obtain the utility we crave with the budget we have. Consumption duality expresses this problem as two sides of the same coin: keeping our budget fixed and maximising utility (primal demand, which leads us to Marshallian demand curves) or setting a target level of utility and minimising the cost associated with it (dual demand, which gives us Hicksian demand curves).

Leads us to the main difference between the two types of demand: Marshallian demand curves simply show the relationship between the price of a good and the quantity demanded of it. Hicksian demand curves show the relationship between the price of a good and the quantity demanded of it assuming that the prices of other goods and our level of utility remain constant.

Marshallian and Hicksian demand curves meet where the quantity demanded is equal for both sides of the consumer choice problem (maximising utility or minimising cost).

Marshallian demand makes more sense when we look at goods or services that make up a large part of our expenses. Here, the income effect is very large. However, for smaller purchases, we are willing to spend more or less any amount as long as we derive the utility we expect to.

Learn more by reading the dictionary entry.

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• Income and substitution effects
• Laspeyres index
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Description

This video explains what the income and substitution effects are, and how to analyse them in order to understand why we buy more goods when their price goes down.

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Generally, if the price of something goes down, we buy more of it. This is down to two effects:

• Income effect: because it’s less expensive, we have more purchasing power because it is a smaller drain on our personal finances.
• Substitution effect: because it offers more utility per unit of money, other alternatives become less attractive.

What Eugen Slutsky managed to do was find an equation that decomposes this effect based on Hicksian and Marshallian demand curves.

It is not always possible to tell what the total effect will be – if we are talking about inferior complementary goods, for example, the substitution and the income effects pull in opposite directions. In this case, the total effect will depend on which effect is stronger.

Learn more by reading the dictionary entry.

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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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• Utility maximisation
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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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