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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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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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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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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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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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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Description

This video explains how to build and analyse the production possibility frontier. We start by explaining the very basics about the production possibility frontier. Then, we show the relation between the marginal rate of transformation and the production possibility frontier. Finally, we explain how to use the Edgeworth box to derive the production possibility frontier.

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The production possibility frontier represents the quantity of output that can be obtained for a certain quantity of inputs using a given technology. Depending on the technology, the production possibility frontier will have different shapes.

The production possibility frontier can be derived from the contract curve on an Edgeworth box. The isoquants determine how much a certain input has to increase in order to compensate the decrease in the other input, maintaining the quantity of output produced unaltered. The slope of these curves is given by the marginal rate of technical substitution of each output.

The points where the isoquants of different outputs combination intersect, which are Pareto-optimal, allow us to draw the contract curve, from which the production possibility frontier can be derived. Since the technology is given, only one production possibility frontier can be derived from the contract curve (as opposed to the case of the utility possibility frontier).

Learn more by reading the dictionary entry.

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Description

This video shows what isocost lines are, and how important they are when analysing production. We start learning about the budgetary restriction they represent, and explain what happens when the cost of inputs change.

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Isocost lines show combinations of productive inputs that cost the same amount. They are the same concept as budget restrictions when looking at consumer behaviour.

In this case, r is the cost of capital and w is the cost of labour. Generally, we think of r as the interest rate the financial markets offer, as capital requires investment. Even if the capital can be paid for using a company’s own resources, r is still equivalent to the opportunity cost of having the money tied up in investments rather than in liquid assets which offer a return (r) by lending it to the markets. The cost of labour (w) is the salary paid to employees per unit of time.

Isocosts are usually represented graphically together with isoquant lines (which are combinations of productive inputs which produce a fixed quantity of outputs). The two have a tangency point, which determines the optimal production (where production is maximised or cost minimised).

Learn more by reading the dictionary entry.

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Description

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

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The marginal rate of technical substitution can be defined as, keeping constant the total output, how much input 1 have to decrease if input 2 increases by one extra unit. In other words, it shows the relation between inputs, and the trade-offs amongst them, without changing the level of total output. It is also worth mentioning that the marginal rate of technical substitution is equal to the slope of isoquants.

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

Learn more by reading the dictionary entry.

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Description

This video explains how to determine the economic region of production, using isoquants and isoclines. It also analyses marginal productivity of inputs, and how this may change the production process.

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The economic region of production shows the combinations of factors at a certain cost that make economic sense. Areas outside the economic region of production mean that at least one of the inputs has negative marginal productivity. This region is marked by what are called ridge lines, which are simply the boundaries beyond which one of the two factors is being overused. Therefore, outside the economic region of production, there is clear inefficiency, and the company would be better off using less of one of the two factors, bringing costs down whilst maintaining equal production output.

Learn more by reading the dictionary entry.

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