Big Ideas in Macroeconomics: A Nontechnical View by Kartik B. Athreya

Author:Kartik B. Athreya
Language: eng
Format: mobi, pdf
Published: 0101-01-01T00:00:00+00:00

5.3 The Radner Version of the ADM Economy

Arrow (1953) noted early on (in a paper not published in English until 1964) that “securities” or financial assets could, in principle, allow for the outcome of an ADM model to be replicated with far fewer markets than the archetypal Arrow-Debreu contingent commodities. These securities were special, as they were ones that paid off in only one contingency, and paid nothing in any other one, and for obvious reasons are called “Arrow securities.”

Radner followed this line of reasoning and imagined a market structure where instead of all trade happening at once as in the ADM setting, a small set of markets open prior to the resolution of any uncertainty. These markets allow for contingent trade in just one of the goods. Think of a world with just four physical goods—corn, wheat, alfalfa, and soybeans—in springtime, when planting is about to commence. In this economy, all eating takes places later, at harvest time. But think of the weather at harvest time as uncertain, taking one of three possible forms: sunny, cloudy, or rainy, each of which matters for the size of the harvest. After the harvest, imagine that the world ends.

In this physical setting, a Radner trading system or a Radner economy will allow only weather-contingent trade in springtime (before uncertainty is resolved) in only one of the physical goods—say corn. That is, participants in a Radner economy can take part in three forward markets in which they buy or sell promises to deliver or receive three goods— corn in rainy weather, corn in cloudy weather, and corn in sunny weather—before they know the harvest. But there would be no markets in any other goods (in our case, this just means no trade in wheat, alfalfa, or soybeans). The Radner economy then lets uncertainty over the weather resolve itself, but as soon as it does, it allows for a set of markets for immediate consumption in all goods. In our case, four markets would open: one for corn, one for wheat, one for alfalfa, and one for soybeans (and the weather would be whatever it turned out to be). These latter markets are typically called “spot” markets, because they are ones in which market participants buy and sell items for immediate consumption.

Notice that the Radner trading arrangement features fewer markets than the ADM model under uncertainty requires: instead of twelve markets (three forward markets each in corn, wheat, alfalfa, and soybeans), our current market arrangement features seven markets (three forward markets for corn in rainy, cloudy, or sunny weather, and four spot markets once the weather resolved itself). Crucially, as the number of goods and states grows, so does the difference in the number of required markets, and it grows dramatically. For instance, if there were 100 different types of crops and 20 kinds of weather, the Arrow-Debreu trading system would feature 2,000 markets, while the Radner would require just 120 markets.

More generally, under Radner trading, if there are L goods and S states,

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