Production possibilities frontier

In this situation we can see that even though we have assumed that both the consumer and producer act only in their own interests, the resulting equilibrium is Pareto efficient. We can now go on and generalise this somewhat. We can plot the varying combinations of output an economy can produce by devoting resources to different types of activity using a production possibilities set. The outermost line is called the production possibilities frontier.

The production possibilities frontier for an economy can be formed by adding all the individual frontiers together. For an economy, the frontier will typically be the rounded shape shown in figure 6. In an economy that is capable of producing the production set depicted in figure, which will be the production and consumption levels? Will these levels be Pareto efficient? There are a number of things needed to determine these levels: 1) Assume the amount produced is (x1,x2), this is what is available for consumption.

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Therefore we can plot an Edgeworth box dimensions (x1,x2). 2) If we assume a firm producing (x1,x2), and two consumers paid wages by the firm (a little like earlier) then because we are in a closed economy all production is consumed by the two consumers. We can do the analysis carried out earlier within this Edgeworth box to give us an equilibrium consumption. 3) The marginal rate of transformation is the rate at which one good can be “transformed” into another – i. e. how much production of good 1 would have to be given up to make some more good.

The marginal rate of transformation must equal the marginal rate of substitution. If the two were not equal (Say the consumer would give up 2 good 1 for 1 good 2, and the firm could make 2 good 2 whilst only giving up 1 good 1), it would be beneficial for firms to increase production of good 2. They would do this until MRT = MRS. This is shown by the isoprofit line in figure.

The furthest line out attainable by the firm is when the isoprofit line is tangent to the frontier 4) From (3), production must occur where MRT = MRS, i. e.the slope of the frontier is the MRT this only happens at the equilibrium production point. We can thus see that the necessary conditions for Pareto efficiency are met: it is not possible to make anyone in this economy better off without making someone worse off. All are maximising their goals given that the others are maximising their own. The MRS of each consumer and the MRT of the firm are all equal. We can say that in a competitive economy, if each agent maximises his own goals, Pareto efficiency will result. How does this result relate to the question?

The first statement “An Economy in which people selfishly pursue their own objectives could never achieve the objectives of a fair society” is damaged by the analysis done. We have shown that if there are two consumers and one firm, given certain other conditions we will end up with a Pareto optimal situation. However, the statement talks of “the objectives of a fair society” – where fairness contains the ideas of both efficiency, and of equity. An equitable society is a society in which consumer A does not prefer consumer B’s bundle, and B does not prefer A’s.

In our society, a endowment where A had everything and B had nothing could still be pareto efficient, but not by any means fair. In addition, the first statement’s “People who selfishly pursue their own objectives” may be a monopolist and a number of consumers, in which case we already know that Pareto inefficiency may occur (The monopolist equates MC with MR to decide where to produce, the people want to buy more output at lower prices, but it will not because extra production will depress the price for all units) – the society will not be fair.

It may also be true that the production functions we draw in the Edgeworth box are flawed – in the case of externalities for example, with the situation of missing markets. This is shown in figure 7. Here we have an imaginary Edgeworth box with axes for smoke and money. Person A likes to smoke, Person B dislikes smoke, and likes clean air. Both like money – the idea here is that in the pareto optimal situation, if smoking is made legal, money helps compensate B for A’s smoke (x1). If smoking is illegal, A can pay B some amount to be allowed to smoke (x).

Both these points are Pareto efficient – we have introduced a market for smoke! However, in reality there exists no such market – either A suffers due to a smoking ban (? ) or B suffers due to the liberal laws (? 1). Both these points are Pareto inefficient. There also exist many other goods where a fair allocation may not be achieved if left to people who just pursue their own objectives. Public goods are such an example. Everyone may agree that it is good to some basic defence service for a country.

However it is not possible to set up a market for such public goods, as they are non-excludable – i.e. if it is provided then everyone gets the benefit, whether they have paid or not. From an individual’s point of view, even if you support the idea of defence, the utility maximising decision is to say that you don’t want it – you will get the benefits if it is provided anyway. This is known as the free rider problem. Every consumer will understate their preferences, and as such the good will not be provided – the Pareto optimal position will probably not be achieved (Does one feel safe in a country with no way whatsoever of protecting itself?!).

Overall, the statement “An Economy in which people selfishly pursue their own objectives could never achieve the objectives of a fair society” is not strictly true – if people pursue their own aims in a framework manipulated by the government then a fair society can result. If people pursue their own aims we can get Pareto efficiency (Given the right conditions) and Pareto efficiency is one element of fairness. The “invisible hand” theory of Adam Smith is a way of summarising this result.

If everybody behaves selfishly, a socially desirable outcome will result – an allocation where no-one can be made better off without making someone else worse off. To analyse the second statement “Competitive markets are efficient, so we should not attempt to change them” we can apply similar methods as before. It is true that competitive markets (Given convex preferences etc. ) are efficient, but this does not necessarily mean that we should not change them. The First Welfare Theorem tells us this – every equilibrium is efficient.

However, efficiency is only one desirable outcome – how about fairness. It is also important to consider market failure – missing markets, information breakdowns. The assertion of the second statement is true – competitive markets are efficient. However, a market that is just efficient may leave some consumers with nothing – it may not necessarily be fair. As such the conclusion drawn is wrong. Some competitive markets may require transfers of endowments in order to maximise social welfare, and some markets may not be suitable for competition (Externalities for example)


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