Nov 5

C.4 Long run cost analysis

Description

In the long run, no cost is fixed. This video explains how to analyse cost curves in the long run. We’ll see how they form derived from multiple short run cost curves.

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We can determine our production level and adjust plant sizes, investment in capital and labour accordingly. This gives us unlimited options. Depending on the scale we choose to implement, each level of production will be associated to new, short run cost curves. When we exhaust the infrastructure these provide us, we can upgrade to a new production level and so forth. The actual long run cost curve is made up of all of these individual scenarios, built up year after year.

Marginal costs only really make sense in the long run for each individual level of production. At optimal levels of production for each level, they intersect the long run average cost curve where this meets the short run average cost curve. This is what determines our optimal level of production.

The other important lesson to take away from this is the fact that, when we reach the optimal point where efficiency is at its best, average and marginal costs are the same, as happened in the short run.

Learn more by reading the dictionary entry.

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Nov 5

Lope Gallego

B.12 Returns to scale (production in the long run)

Description

This video introduces the concept of returns to scale, which is needed in order to understand how production processes behave in the long run. Also, it shows what the elasticity of returns of scale is, and how to use it.

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When dealing with long run production, the main change from short run production is that we can vary the levels of fixed inputs we use (capital, K), as well as variable inputs (labour, L). Our levels of production will be determined by our returns to scale.

Production in the long run will determine the average size of a business in the sector. Positive returns to scale, the most common scenario, will naturally attract a concentration of very large businesses, as is often the case in industrial, capital intensive sectors. Getting it right is crucial for another reason: in the long term, market equilibrium will determine that the total production of a certain good will be such to eliminate economic profits.

Learn more by reading the dictionary entry.

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Nov 5

Lope Gallego

B.11 Production in the short run

Description

This video explains the basics of production analysis, focusing on the short run. We first learn how to draw the Average and Marginal productivity, and the explain what the output elasticity is.

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The short run is considered the period of time where fixed costs are still fixed, which basically means that, if you have a factory, you have to make do with it because you can neither sell it, nor make it bigger, nor rent half of it: you are stuck with it for the time being. Capital is also considered fixed, meaning that, in the short run, all you can play around with are your variable costs, being labour the most commonly used variable cost.

In the video, three phases are shown. In phase I, average and marginal productivity increase with each added unit. Phase I ends in the extensive margin (or technical optimum), being this the line that splits phases I and II. Phase II is where we should ideally be: average productivity drops with each added unit, but marginal productivity is still positive. The line that separates phases II and III is called the intensive margin (or technical maximum), from which there will be too much variable input for each level of fixed input. When marginal productivity becomes negative, we enter phase III, and we should consider reducing labour.

Learn more by reading the dictionary entry.

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Nov 5

Lope Gallego

B.10 Production duality

Description

This video shows how useful a good understanding of production duality can be. Starting with production maximisation and cost minimisation, this video explores everything you need to understand about production duality.

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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 our production function. When dealing with dual demand, that is, cost minimisation, our Lagrangian is our cost function.

Learn more by reading the dictionary entry.

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Nov 5

Lope Gallego

B.9 Cost minimisation

Description

This video explains how cost minimisation works when dealing with production, 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 production.

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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 (usually simplified by using 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.

Learn more by reading the dictionary entry.

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Nov 5

Lope Gallego

B.8 Production maximisation

Description

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

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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.

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.

Learn more by reading the dictionary entry.

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Nov 5

Lope Gallego

B.7 Marginal rate of transformation

Description

This video explains what the marginal rate of transformation is, and shows its relationship with the production possibility frontier. We also analyse how the marginal rate of transformation determines the opportunity cost in production.

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The marginal rate of transformation can be defined as how many units of good x have to stop being produced in order to produce an extra unit of good y, while keeping constant the use of production factors and the technology being used. It involves the relation between the production of different outputs, while maintaining constant the same level of production factors.

The marginal rate of transformation is related to the production possibility frontier. The slope of the curves shows how a reallocation of the production can end with a different bundle of production, using the same quantity of inputs.

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

Learn more by reading the dictionary entry.

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Jul 22

Lope Gallego

A.14 Revealed preference

Description

This video explains how revealed preference theory works. We’ll learn how to use both the Weak and Strong Axioms of Revealed Preference, in order to derive a utility function from consumer behaviour.

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Revealed preference theory is attributable to Paul Samuelson, who developed the concept in his article “Consumption Theory in Terms of Revealed Preference”, in 1948. Consumer theory depends on the existence of preferences, which materialise into utility functions. These utility functions are maximised by consumers subject to a budget restraint. The issue is that it is difficult to accept that individuals really have a definite mathematical formula in mind when choosing between different options. What revealed preference theory does is work backwards to assume that we can deduce these utility functions from consumer behaviour. Analysing these choices leads us backwards to a set of preferences that influences the choices they make. It therefore allows economists to study consumer behaviour empirically.

There are two main axioms to the theory, both based on completeness and transitivity: the Weak Axiom of Revealed Preference and the Strong Axiom of Revealed Preference, which adds transitivity.

If we compare bundles of goods, we can map out all a consumer’s choices. In theory, we can track this backwards to actually build utility functions if we have access to unlimited data. Without actually having to do this, we can aggregate consumer data to reveal general truths about a certain population’s preferences.

Learn more by reading the dictionary entry.

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Jul 22

Lope Gallego

Perfect competition II

Firms in a perfectly competitive market may encounter some problems that can decrease their competitiveness and may even force them out of the market. The way they deal with problems such as taxes or other factors that increase their costs will determine whether they can stay in the market. In this Learning Path we’ll learn about these problems, how firms’ cost structures change, and how an equilibrium is reached in the market.

In order to understand all this, we’ll learn about:

Comparative analysis:

Comparative statics, used to analyse changes in equilibriums;

Economic surplus, which determines how well a firm is doing;

Cost variations may force a firm out of the market;

Taxes, imposed to consumers, producers or both.

Market clearing:

Supply and demand, how to determine them and how they behave;

Market clearing, which determines how the equilibrium is reached;

Cobweb models, a strange way to get to the equilibrium.

Jan 30

Lope Gallego

Perfect competition I

Even though perfect competition is hard to come by, it’s a good starting point to understand market structures. It’s been used to analyse markets for centuries. From Adam Smith and his invisible hand, to economists such as Edward Chamberlin and Joan Robinson, who analysed different market structures, perfect competition has been used to compare different competitive situations, and to understand how marketplaces work. A deep understanding of how competitive markets work and are formed is the cornerstone to understand why it’s so hard to reach them.

In this first Learning Path on perfect competition, we’ll start by analysing firms’ cost structure, before analysing their interaction in the market. We’ll learn about:

Perfect competition, a basic definition.

The firm:

Period analysis, in order to understand how time affects cost functions;

Short run cost analysis, how fixed factors determine cost structures;

Long run cost analysis, which considers variable factors.

The industry and the market:

Supply and demand, the basics of how markets work;

Short run supply curve, or how firms react to changes in market supply or demand;

Long run supply curve, which considers also potential entry of new firms.