Inspired by Free Radical's post, I think I have figured out a simpler and clearer way to say what I want to say about Walras' Law.
Ask yourself the following question:
Q. Assume an economy where there are (say) 7 markets. Suppose 6 of those markets are in equilibrium (with quantity demanded equal to quantity supplied). Is it necessarily true that the 7th market must also be in equilibrium (with quantity demanded equal to quantity supplied)?
This is an open book exam, and you may Google if you wish.
This is a question for both macroeconomists and microeconomists. (And for non-economists too.)
My answer is "no".
Let there be 8 goods: money; and 7 others (apples, bananas, carrots, dates, eggs, figs, and grapes). There is: a market in which apples are bought and sold for money (the "apple market"); a market in which bananas are bought and sold for money (the "banana market");....and a market in which grapes are bought and sold for money (the "grape market"). Which makes 7 markets in all. And let each of those 7 foods have a price in terms of money. And let 6 of those 7 prices be perfectly flexible, and adjust to equalise quantity demanded and quantity supplied in a perfectly competitive market. But let the price of grapes be fixed by law.
[Update: in response to Arnold Kling. I mean the price of grapes is fixed by law in the same way that the price (rent) of rent controlled apartments is fixed by law. By making it illegal to buy or sell grapes at any price above or below $1 per kg. And not by the central bank buying and selling grapes at a fixed price to create a "grape standard" monetary system.]
It is perfectly possible to have an excess supply of grapes (if the price of grapes is fixed too high), even if all 6 other markets have quantity demanded equal to quantity supplied.
The "grape market" is a market where grapes are exchanged for money. If there is an excess supply of grapes, it means people want to sell more grapes than people want to buy. So some people will be unable to sell as many grapes as they want to sell. And that means that those same people are unable to "buy" as much money with grapes as they want to buy. If the price of grapes is fixed by law at $1 per kg, and there is an excess supply of 100kgs of grapes, and so an excess supply of $100 worth of grapes, then there is also a $100 excess demand for money in the market for grapes.
In any one of those 7 markets, at any price (whether fixed by law or not) the value of the excess supply (demand) of apples (or whatever) must equal the excess demand (supply) for money in that same market. Simply because people plan on paying (and getting paid) for the stuff they buy (and sell).
And that same thing holds true in a barter economy, where there is no money. If there is a market where apples and bananas can be swapped (the "apple-banana market") the value of the excess supply (demand) for apples in that market must equal the value of the excess demand (supply) of bananas in that market.
And that same thing holds true in a market where arbitrary combinations of 3 or more goods can be swapped for arbitrary combinations of those same 3 or more goods. ("Can I swap a basket of 10 apples and 5 bananas for the same value of carrots?"). The values of the excess demands must sum to zero in that particular market.
And the same thing holds true in an economy where there is only one market where arbitrary combinations of all goods can be swapped for arbitrary of all goods. The values of the excess demands must sum to zero in that one market.
And only in that last case, an economy with only one market where all goods are traded for all goods, is it true that the values of the excess demands of all goods must sum to zero for the whole economy.
Walras' Law is true and useful for the economy as a whole only if there is only one market in the whole economy, where all goods are traded for all goods. But that is not a monetary economy. And it is not a real world economy.
In a monetary exchange economy, where every other good is bought and sold for only one good, that we call "money", there are as many different excess demands (supplies) for money as there are markets. There can be an excess demand for money in the apple market, and an excess supply of money in the banana market.
Is that what you thought? Is that what you were taught? Is that what you have read about Walras' Law?
And does that make it simpler and clearer?