General Equilibrium

When we have studied equilibria so far, it has always been so-called partial equilibria. (A partial equilibrium is one where we assume that “everything else is unchanged.”) However, we have also seen that a change in one variable can lead to changes in many other variables, so the restriction that everything else is unchanged may not be very realistic. For example, a price change can affect the price of close substitutes and complementary goods. We will now study how interactions between two individuals in a very simple economy lead to a general equilibrium, i.e. a simultaneous equilibrium in all markets.

A Robinson Crusoe Economy

Consider an economy with only two agents on a desert island: Robinson and Friday. Those two are then the only consumers and the only producers. Let us assume that they also produce only two goods: Coconuts and fish. The question is then how much coconuts and fish to produce, and how to allocate them among themselves.

Efficiency

We have already mentioned efficiency several times in this book. Efficiency is about how much waste there is in an economy; less waste means more efficient. There are several related ways to define efficiency. An often-used measure of efficiency regarding allocations is Pareto efficiency. The definition of Pareto efficiency is:

• Pareto improvement. A change in allocation such that

1. No one is worse off; and
2. At least one, possibly several, is better off.

• Pareto efficient or Pareto optimal. An allocation such that

1. No Pareto improvements are possible.

The Edgeworth Box

consumer theory. We described, for instance, indifference curves and the budget line. If we consider an exchange economy in which the quantities of the goods are fixed, we have a zero-sum game. This means that one individual can only get quantities that the other ones do not get; there is, for instance, no growth in the economy. The name “zero-sum game” comes from the fact that, the sum of what some people gain and what others lose is always zero.

Suppose that Robinson and Friday have different preferences over coconuts and fish, and that these look like in Figure 18.1. Since the quantities of the two goods are fixed, we can combine these two indifference maps into one by taking one of them, for instance Fridays, turning it upside-down and putting it over Robinson’s. We then get a picture such as the one in Figure 18.2. (The additional information in the figure will be explained below.) Such a diagram is called an Edgeworth-box.

Note that the scales in the Edgeworth box are in opposite direction for the two agents. Upwards along the Y-axis, Robinson gets more fish while Friday gets less. To the right along the X-axis, Robinson gets more coconuts and Friday gets less. Also, be aware of which preference curves belong to which individual: The full lines belong to Robinson while the broken lines belong to Friday.

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