Competitive Equilibrium

Micro

In the very basic economic course, in most of the times, we just need to make sure that:

$$\text{Supply}=\text{Demand}$$

And then we are done. But in a more advanced way, we often face a situation that there are multiple markets, and multiple goods, making the problem non-linear. For example, there are $L$ goods, and $N$ consumers, each consumer may have a nonlinear utility function (for example, a cobb-douglas utility function). In this case, before solving the equilibrium, we need to first prove that there exists an equilibrium. Thus we need to introduce Kakutani’s Fixed Point Theorem.

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Before jumping into the upper-hemi continuous, we have to know what is correspondence,

Todo

• What is Walras Law?
• How to understand Endowment?
• Kakutani’s Fixed Point Theorem

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Lecture Notes

• The hard thing is to prove the existence of competitive equilibrium. The main tool is Kakutani’s Fixed Point Theorem.
• And there’s a new concept which is called Endowment $e$.
• A Hedonic Price is to reflect the price of a good which can’t be measured directly, it’s not explicit. E.g. You WTP of not to live from a noisy street.
• $\theta$ is kind of type variable, ${\theta }_l$ means that the unit utility you get from consuming one more unit of good $l$.
• When we talk about “gross”, refer to the Marshallian Demand, when we say “net”, think about the Hicksian Demand.