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Jan 23

B.2 Isoquants

Description

With this video, you’ll be able to understand what isoquants are, and how they can help analyse production. You’ll learn the main characteristics of different types of isoquants, as well as what the marginal rate of technical substitution is.

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An isoquant shows the different combinations of K and L that produce a certain amount of a good or service. Graphically, the shape of an isoquant will depend on the type of good or service we are looking at. The shape of isoquants is also in close relation with the terms marginal rate of technical substitution and returns to scale.

It is also worth discussing isoclines, which are lines that ‘join up’ the different production regions. Having defined and decided the optimal levels of K and L we need to produce the different quantities, the line that passes through these optimal levels is an isocline. In other words, it is the line that joins points where the marginal rate of technical substitution of each isoquant is constant:

Learn more by reading the dictionary entry.

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Jan 23

Lope Gallego

B.1 Production function

Description

This video explains how the production function can be built in order to analyse it. We start by explaining the main characteristics of production functions, then show its relationship with returns to scale and, finally, introduce the concept of isoquants.

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A production function shows how much can be produced with a certain set of resources. Generally, when looking at production, we assume there are two factors involved in production: capital (K) and labour (L), as this allows us graphical representations of isoquants. However, any analysis made with 2 factors can mathematically be extended to n factors. Therefore, a production function can be expressed as q = f(K,L), which simply means that q (quantity) is a function of the amount of capital and labour invested.

It is well worth introducing here another concept: marginal productivity, which is how much more quantity we could produce by adding one unit more of a factor. As is logical, this will depend on how we are employing the factors we already have. The marginal product is the partial derivative of the production function with respect to the factor we are examining.

Marginal productivity decreases with each additional unit. At a certain point, the more workers we have, for example, the more each additional worker will be redundant if we do not invest in other necessary factors. This is the same as saying that the second derivative is negative. At that point, production is as efficient as possible.

Learn more by reading the dictionary entry.

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Jan 22

Lope Gallego

A.13 Characteristics demand

Description

This video helps understand how characteristics demand works. We start with a simple example, using just two brands. Then, we’ll see what happens when we allow for convex demand curves. Finally, we’ll see how a new brand might change the analysis.

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Characteristics demand theory states that consumers derive utility not from the actual contents of the basket but from the characteristics of the goods in it. This theory was developed by Kelvin Lancaster in 1966 in his paper “A New Approach to Consumer Theory”.

This approach allows us to predict how preferences will change when we change the options or baskets presented to consumers by studying how these vary according to the change in the characteristics that make them up. With conventional theory, the introduction of a new option meant that we could not reliably predict how this would slot into the consumer’s preference map. However, by relying on a study of the characteristics rather than the goods or service involved, we can predict how changes will affect a consumer’s behaviour without needing to start once again empirically.

Characteristic demand theory also helps justify the existence of brands. Luxury brands are able to charge a surprice for their products by differentiating themselves from competitors that sell similar goods.

Learn more by reading the dictionary entry.

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Jan 22

Lope Gallego

A.12 Paasche index

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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Jan 22

Lope Gallego

A.11 Laspeyres index

Description

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

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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.

What this translates to is that a Laspeyres index of 1 means that, as the nominator is the same as the denominator, an individual can afford the same basket of goods in the current period as he did in the base period. As the quantities are the same, this just leaves price as a variable, which must remain unchanged. This translates to the concept of compensated variation: by how much do we need to increase an individual’s income in order to offset inflation?

The Laspeyres index overestimates this compensated variation: it assumes that inflation has a greater effect than it does.

Learn more by reading the dictionary entry.

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Jan 22

Lope Gallego

A.10 Marshallian and Hicksian demand curves

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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Jan 22

Lope Gallego

A.9 Income and substitution effects

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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Jan 22

Lope Gallego

A.8 Consumption duality

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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Jan 22

Lope Gallego

A.7 Cost minimisation

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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Jan 22

Lope Gallego

A.6 Utility maximisation

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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