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What’s the difference between market efficiency (as in efficient market hypothesis) and allocative efficiency? Do they mean the same? or are they connected?

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These words are somewhat context dependent, but let's have a go at an answer.


Definitions

Market efficiency: Prices reflect all available information.
In the EMH this is usually used in the context of financial markets and asset prices. A brief explanation: event X affects the price of asset Y. When event X becomes public, the price (in theory) immediately adjusts to reflect its effect; hearing about 5 minutes later you are no longer have an incentive to quickly buy or sell asset Y.

Allocative efficiency: Resources used in production, as well as final goods and services are allocated in an efficient way; altering the allocation could not result in a Pareto-improvement.


Relation

Allocative efficiency can in theory exist without prices and markets, e.g., in a command economy, while market efficiency cannot, thus the two concepts are not identical.

According to the First Welfare Theorem a competitive market where all actors are rational and everyone has perfect information leads to allocative efficiency. It is not believed that these conditions are fulfilled in real world markets; however there are people who believe that some markets are close to fulfilling them.

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