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DeLong Smackdown Watch: Say's Law, Walras' Law, and Monetary Policy

I think this is directed at me...

Nick Rowe:

Worthwhile Canadian Initiative: Say's Law, Walras' Law, and monetary policy: People (and firms and governments) face budget constraints. If people formulate their demands and supplies of goods reflecting that budget constraint, then we get Walras Law. The individual's planned purchases of goods must be financed by planned sales of goods, including money. So the value of each individual's excess supplies of goods must equal his excess demand for money. Aggregate across all individuals (plus firms and governments) and we get Walras' Law: the value of the excess supplies of goods must equal the excess demand for money....

[That] would only be right if we are talking about notional excess demands and supplies. A notional demand or supply of apples is the amount of apples that people would want to buy or sell if they ignored any constraints on the quantity of other goods they were able to buy and sell.... Walras' Law is true if it is interpreted to be speaking about notional excess supplies and demands. But if we are out of equilibrium, there will be excess demands in some markets, and/or excess supplies in other markets, and people will not be able to buy or sell as much as they want to, because they won't always be able to find willing buyers or sellers. They will be quantity constrained. The insight of Clower and Patinkin was to recognise that quantity constraints in one market will spillover into demands and supplies in other markets. If I want to buy apples, but can't because there's an excess demand for apples, I might decide to buy pears instead. If I want to sell labour, but can't because there's an excess supply of labour, I might decide to buy less carrots. In disequilibrium, people (and firms and governments) face quantity constraints as well as budget constraints. If people formulate their demands and supplies of goods to maximise utility subject to their budget constraint and subject to quantity constraints, we get constrained (or effective) demand and supply functions, not notional demand and supply functions.

I go to the supermarket with $10 in my pocket planning to buy $10 worth of apples and no pears. Those are notional demands. Excess demand for apples $10, and excess supply of money $10. Walras' Law applies. But when I get to the store there are no apples, so I re-maximise my utility function, including that quantity constraint, and decide to buy $10 of pears. Excess demand for apples $10 (because I still want the apples). Excess demand for pears $10 (because I can't buy apples). Total excess demand for goods (apples plus pears) $20. But what's the excess supply of money corresponding to that excess demand for goods? $20? But I only have $10 in my pocket....

In a Walrasian economy, with one big market, and a unified decision, Walras' Law is true. The sum of the excess supplies for goods will equal the excess demand for money (though it is hard to see what "money" could mean in such an economy"). But in a monetary exchange economy, with N markets, there are N decisions, and N different definitions of the excess demand for money, each corresponding to one of those N decisions.... But that total excess demand for money across all markets won't correspond to any economically meaningful concept. It does not represent the extra amount of money that people want to hold.

Now, what's all this got to do with monetary policy in the current recession (if anyone's still reading)?

If the problem is a deficiency of aggregate demand, then firms have an excess supply of output.... Households have an excess supply of labour. They want to sell more labour but cannot.... So the output market shows an excess supply of output matched by an excess demand for money (by firms). But firms don't want to hold that money; they want to spend it on labour.... What's happening in the bond market?... suppose the bond market is in equilibrium, either because interest rates adjust quickly, or because people are indifferent between holding additional bonds and additional money. Then there is no excess demand for money in the bond market.

If you accept my description in the above two paragraphs, then the current recession is a monetary phenomenon... fiscal policy, if successful, must be a continuation of monetary policy by other means. It is an attempt to reduce the demand(s) for money. It works, if it does work, either by reducing the private demand(s) for money (increasing velocity), or because the government has a lower demand for money than the private sector, so switching demand from the private to government sector increases the average velocity of circulation.

There is an excess demand for money in the output market. And another excess demand for money in the labour market. But this does not mean that firms and households want to hold more money; if they got it they would want to spend it (or most of it). So the central bank would not need to create anywhere near as much money as those excess demands for money would indicate.... Just because one market is satiated with money does not mean that the economy as a whole is satiated with money. In a monetary exchange economy, there are as many different excess demands for money as there are goods (excluding money). If central banks "run out of ammunition" in one market, they can just switch to one of the other N-1 markets. And the market for very short term and very safe and very liquid bonds is a very peculiar market for central banks to be operating in anyway, just because they are so close to money. If we used apples for money, it would be like the central bank operating in the market for pears. At the right relative price, apples and pears might become perfect substitutes, and open market operations might become irrelevant...